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Towards Practical Mean Bounds for Small Samples | null | Historically, to bound the mean for small sample sizes, practitioners have had to choose between using methods with unrealistic assumptions about the unknown distribution (e.g., Gaussianity) and methods like Hoeffding’s inequality that use weaker assumptions but produce much looser (wider) intervals. In 1969, \citet{Anderson1969} proposed a mean confidence interval strictly better than or equal to Hoeffding’s whose only assumption is that the distribution’s support is contained in an interval $[a,b]$. For the first time since then, we present a new family of bounds that compares favorably to Anderson’s. We prove that each bound in the family has {\em guaranteed coverage}, i.e., it holds with probability at least $1-\alpha$ for all distributions on an interval $[a,b]$. Furthermore, one of the bounds is tighter than or equal to Anderson’s for all samples. In simulations, we show that for many distributions, the gain over Anderson’s bound is substantial. | My Phan, Philip Thomas, Erik Learned-Miller | null | null | 2,021 | icml |
Dense for the Price of Sparse: Improved Performance of Sparsely Initialized Networks via a Subspace Offset | null | That neural networks may be pruned to high sparsities and retain high accuracy is well established. Recent research efforts focus on pruning immediately after initialization so as to allow the computational savings afforded by sparsity to extend to the training process. In this work, we introduce a new ‘DCT plus Sparse’ layer architecture, which maintains information propagation and trainability even with as little as 0.01% trainable parameters remaining. We show that standard training of networks built with these layers, and pruned at initialization, achieves state-of-the-art accuracy for extreme sparsities on a variety of benchmark network architectures and datasets. Moreover, these results are achieved using only simple heuristics to determine the locations of the trainable parameters in the network, and thus without having to initially store or compute with the full, unpruned network, as is required by competing prune-at-initialization algorithms. Switching from standard sparse layers to DCT plus Sparse layers does not increase the storage footprint of a network and incurs only a small additional computational overhead. | Ilan Price, Jared Tanner | null | null | 2,021 | icml |
BANG: Bridging Autoregressive and Non-autoregressive Generation with Large Scale Pretraining | null | In this paper, we propose BANG, a new pretraining model to Bridge the gap between Autoregressive (AR) and Non-autoregressive (NAR) Generation. AR and NAR generation can be uniformly regarded as to what extent previous tokens can be attended, and BANG bridges AR and NAR generation through designing a novel model structure for large-scale pre-training. A pretrained BANG model can simultaneously support AR, NAR, and semi-NAR generation to meet different requirements. Experiments on question generation (SQuAD 1.1), summarization (XSum), and dialogue generation (PersonaChat) show that BANG improves NAR and semi-NAR performance significantly as well as attaining comparable performance with strong AR pretrained models. Compared with the semi-NAR strong baselines, BANG achieves absolute improvements of 14.01 and 5.24 in the overall scores of SQuAD 1.1 and XSum, respectively. In addition, BANG achieves absolute improvements of 10.73, 6.39, and 5.90 in the overall scores of SQuAD, XSUM, and PersonaChat compared with the NAR strong baselines, respectively. Our code will be made publicly available. | Weizhen Qi, Yeyun Gong, Jian Jiao, Yu Yan, Weizhu Chen, Dayiheng Liu, Kewen Tang, Houqiang Li, Jiusheng Chen, Ruofei Zhang, Ming Zhou, Nan Duan | null | null | 2,021 | icml |
Global Prosody Style Transfer Without Text Transcriptions | null | Prosody plays an important role in characterizing the style of a speaker or an emotion, but most non-parallel voice or emotion style transfer algorithms do not convert any prosody information. Two major components of prosody are pitch and rhythm. Disentangling the prosody information, particularly the rhythm component, from the speech is challenging because it involves breaking the synchrony between the input speech and the disentangled speech representation. As a result, most existing prosody style transfer algorithms would need to rely on some form of text transcriptions to identify the content information, which confines their application to high-resource languages only. Recently, SpeechSplit has made sizeable progress towards unsupervised prosody style transfer, but it is unable to extract high-level global prosody style in an unsupervised manner. In this paper, we propose AutoPST, which can disentangle global prosody style from speech without relying on any text transcriptions. AutoPST is an Autoencoder-based Prosody Style Transfer framework with a thorough rhythm removal module guided by the self-expressive representation learning. Experiments on different style transfer tasks show that AutoPST can effectively convert prosody that correctly reflects the styles of the target domains. | Kaizhi Qian, Yang Zhang, Shiyu Chang, Jinjun Xiong, Chuang Gan, David Cox, Mark Hasegawa-Johnson | null | null | 2,021 | icml |
Provably Efficient Fictitious Play Policy Optimization for Zero-Sum Markov Games with Structured Transitions | null | While single-agent policy optimization in a fixed environment has attracted a lot of research attention recently in the reinforcement learning community, much less is known theoretically when there are multiple agents playing in a potentially competitive environment. We take steps forward by proposing and analyzing new fictitious play policy optimization algorithms for two-player zero-sum Markov games with structured but unknown transitions. We consider two classes of transition structures: factored independent transition and single-controller transition. For both scenarios, we prove tight $\widetilde{\mathcal{O}}(\sqrt{T})$ regret bounds after $T$ steps in a two-agent competitive game scenario. The regret of each player is measured against a potentially adversarial opponent who can choose a single best policy in hindsight after observing the full policy sequence. Our algorithms feature a combination of Upper Confidence Bound (UCB)-type optimism and fictitious play under the scope of simultaneous policy optimization in a non-stationary environment. When both players adopt the proposed algorithms, their overall optimality gap is $\widetilde{\mathcal{O}}(\sqrt{T})$. | Shuang Qiu, Xiaohan Wei, Jieping Ye, Zhaoran Wang, Zhuoran Yang | null | null | 2,021 | icml |
Budgeted Heterogeneous Treatment Effect Estimation | null | Heterogeneous treatment effect (HTE) estimation is receiving increasing interest due to its important applications in fields such as healthcare, economics, and education. Current HTE estimation methods generally assume the existence of abundant observational data, though the acquisition of such data can be costly. In some real scenarios, it is easy to access the pre-treatment covariates and treatment assignments, but expensive to obtain the factual outcomes. To make HTE estimation more practical, in this paper, we examine the problem of estimating HTEs with a budget constraint on observational data, aiming to obtain accurate HTE estimates with limited costs. By deriving an informative generalization bound and connecting to active learning, we propose an effective and efficient method which is validated both theoretically and empirically. | Tian Qin, Tian-Zuo Wang, Zhi-Hua Zhou | null | null | 2,021 | icml |
On Reward-Free RL with Kernel and Neural Function Approximations: Single-Agent MDP and Markov Game | null | To achieve sample efficiency in reinforcement learning (RL), it necessitates to efficiently explore the underlying environment. Under the offline setting, addressing the exploration challenge lies in collecting an offline dataset with sufficient coverage. Motivated by such a challenge, we study the reward-free RL problem, where an agent aims to thoroughly explore the environment without any pre-specified reward function. Then, given any extrinsic reward, the agent computes the optimal policy via offline RL with data collected in the exploration stage. Moreover, we tackle this problem under the context of function approximation, leveraging powerful function approximators. Specifically, we propose to explore via an optimistic variant of the value-iteration algorithm incorporating kernel and neural function approximations, where we adopt the associated exploration bonus as the exploration reward. Moreover, we design exploration and planning algorithms for both single-agent MDPs and zero-sum Markov games and prove that our methods can achieve $\widetilde{\mathcal{O}}(1 /\varepsilon^2)$ sample complexity for generating a $\varepsilon$-suboptimal policy or $\varepsilon$-approximate Nash equilibrium when given an arbitrary extrinsic reward. To the best of our knowledge, we establish the first provably efficient reward-free RL algorithm with kernel and neural function approximators. | Shuang Qiu, Jieping Ye, Zhaoran Wang, Zhuoran Yang | null | null | 2,021 | icml |
Optimization Planning for 3D ConvNets | null | It is not trivial to optimally learn a 3D Convolutional Neural Networks (3D ConvNets) due to high complexity and various options of the training scheme. The most common hand-tuning process starts from learning 3D ConvNets using short video clips and then is followed by learning long-term temporal dependency using lengthy clips, while gradually decaying the learning rate from high to low as training progresses. The fact that such process comes along with several heuristic settings motivates the study to seek an optimal "path" to automate the entire training. In this paper, we decompose the path into a series of training "states" and specify the hyper-parameters, e.g., learning rate and the length of input clips, in each state. The estimation of the knee point on the performance-epoch curve triggers the transition from one state to another. We perform dynamic programming over all the candidate states to plan the optimal permutation of states, i.e., optimization path. Furthermore, we devise a new 3D ConvNets with a unique design of dual-head classifier to improve spatial and temporal discrimination. Extensive experiments on seven public video recognition benchmarks demonstrate the advantages of our proposal. With the optimization planning, our 3D ConvNets achieves superior results when comparing to the state-of-the-art recognition methods. More remarkably, we obtain the top-1 accuracy of 80.5% and 82.7% on Kinetics-400 and Kinetics-600 datasets, respectively. | Zhaofan Qiu, Ting Yao, Chong-Wah Ngo, Tao Mei | null | null | 2,021 | icml |
Hierarchical Clustering of Data Streams: Scalable Algorithms and Approximation Guarantees | null | We investigate the problem of hierarchically clustering data streams containing metric data in R^d. We introduce a desirable invariance property for such algorithms, describe a general family of hyperplane-based methods enjoying this property, and analyze two scalable instances of this general family against recently popularized similarity/dissimilarity-based metrics for hierarchical clustering. We prove a number of new results related to the approximation ratios of these algorithms, improving in various ways over the literature on this subject. Finally, since our algorithms are principled but also very practical, we carry out an experimental comparison on both synthetic and real-world datasets showing competitive results against known baselines. | Anand Rajagopalan, Fabio Vitale, Danny Vainstein, Gui Citovsky, Cecilia M Procopiuc, Claudio Gentile | null | null | 2,021 | icml |
End-to-End Learning of Coherent Probabilistic Forecasts for Hierarchical Time Series | null | This paper presents a novel approach for hierarchical time series forecasting that produces coherent, probabilistic forecasts without requiring any explicit post-processing reconciliation. Unlike the state-of-the-art, the proposed method simultaneously learns from all time series in the hierarchy and incorporates the reconciliation step into a single trainable model. This is achieved by applying the reparameterization trick and casting reconciliation as an optimization problem with a closed-form solution. These model features make end-to-end learning of hierarchical forecasts possible, while accomplishing the challenging task of generating forecasts that are both probabilistic and coherent. Importantly, our approach also accommodates general aggregation constraints including grouped and temporal hierarchies. An extensive empirical evaluation on real-world hierarchical datasets demonstrates the advantages of the proposed approach over the state-of-the-art. | Syama Sundar Rangapuram, Lucien D Werner, Konstantinos Benidis, Pedro Mercado, Jan Gasthaus, Tim Januschowski | null | null | 2,021 | icml |
MSA Transformer | null | Unsupervised protein language models trained across millions of diverse sequences learn structure and function of proteins. Protein language models studied to date have been trained to perform inference from individual sequences. The longstanding approach in computational biology has been to make inferences from a family of evolutionarily related sequences by fitting a model to each family independently. In this work we combine the two paradigms. We introduce a protein language model which takes as input a set of sequences in the form of a multiple sequence alignment. The model interleaves row and column attention across the input sequences and is trained with a variant of the masked language modeling objective across many protein families. The performance of the model surpasses current state-of-the-art unsupervised structure learning methods by a wide margin, with far greater parameter efficiency than prior state-of-the-art protein language models. | Roshan M Rao, Jason Liu, Robert Verkuil, Joshua Meier, John Canny, Pieter Abbeel, Tom Sercu, Alexander Rives | null | null | 2,021 | icml |
Generative Particle Variational Inference via Estimation of Functional Gradients | null | Recently, particle-based variational inference (ParVI) methods have gained interest because they can avoid arbitrary parametric assumptions that are common in variational inference. However, many ParVI approaches do not allow arbitrary sampling from the posterior, and the few that do allow such sampling suffer from suboptimality. This work proposes a new method for learning to approximately sample from the posterior distribution. We construct a neural sampler that is trained with the functional gradient of the KL-divergence between the empirical sampling distribution and the target distribution, assuming the gradient resides within a reproducing kernel Hilbert space. Our generative ParVI (GPVI) approach maintains the asymptotic performance of ParVI methods while offering the flexibility of a generative sampler. Through carefully constructed experiments, we show that GPVI outperforms previous generative ParVI methods such as amortized SVGD, and is competitive with ParVI as well as gold-standard approaches like Hamiltonian Monte Carlo for fitting both exactly known and intractable target distributions. | Neale Ratzlaff, Qinxun Bai, Li Fuxin, Wei Xu | null | null | 2,021 | icml |
Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting | null | In this work, we propose TimeGrad, an autoregressive model for multivariate probabilistic time series forecasting which samples from the data distribution at each time step by estimating its gradient. To this end, we use diffusion probabilistic models, a class of latent variable models closely connected to score matching and energy-based methods. Our model learns gradients by optimizing a variational bound on the data likelihood and at inference time converts white noise into a sample of the distribution of interest through a Markov chain using Langevin sampling. We demonstrate experimentally that the proposed autoregressive denoising diffusion model is the new state-of-the-art multivariate probabilistic forecasting method on real-world data sets with thousands of correlated dimensions. We hope that this method is a useful tool for practitioners and lays the foundation for future research in this area. | Kashif Rasul, Calvin Seward, Ingmar Schuster, Roland Vollgraf | null | null | 2,021 | icml |
Disentangling Sampling and Labeling Bias for Learning in Large-output Spaces | null | Negative sampling schemes enable efficient training given a large number of classes, by offering a means to approximate a computationally expensive loss function that takes all labels into account. In this paper, we present a new connection between these schemes and loss modification techniques for countering label imbalance. We show that different negative sampling schemes implicitly trade-off performance on dominant versus rare labels. Further, we provide a unified means to explicitly tackle both sampling bias, arising from working with a subset of all labels, and labeling bias, which is inherent to the data due to label imbalance. We empirically verify our findings on long-tail classification and retrieval benchmarks. | Ankit Singh Rawat, Aditya K Menon, Wittawat Jitkrittum, Sadeep Jayasumana, Felix Yu, Sashank Reddi, Sanjiv Kumar | null | null | 2,021 | icml |
Policy Caches with Successor Features | null | Transfer in reinforcement learning is based on the idea that it is possible to use what is learned in one task to improve the learning process in another task. For transfer between tasks which share transition dynamics but differ in reward function, successor features have been shown to be a useful representation which allows for efficient computation of action-value functions for previously-learned policies in new tasks. These functions induce policies in the new tasks, so an agent may not need to learn a new policy for each new task it encounters, especially if it is allowed some amount of suboptimality in those tasks. We present new bounds for the performance of optimal policies in a new task, as well as an approach to use these bounds to decide, when presented with a new task, whether to use cached policies or learn a new policy. | Mark Nemecek, Ronald Parr | null | null | 2,021 | icml |
No-regret Algorithms for Capturing Events in Poisson Point Processes | null | Inhomogeneous Poisson point processes are widely used models of event occurrences. We address \emph{adaptive sensing of Poisson Point processes}, namely, maximizing the number of captured events subject to sensing costs. We encode prior assumptions on the rate function by modeling it as a member of a known \emph{reproducing kernel Hilbert space} (RKHS). By partitioning the domain into separate small regions, and using heteroscedastic linear regression, we propose a tractable estimator of Poisson process rates for two feedback models: \emph{count-record}, where exact locations of events are observed, and \emph{histogram} feedback, where only counts of events are observed. We derive provably accurate anytime confidence estimates for our estimators for sequentially acquired Poisson count data. Using these, we formulate algorithms based on optimism that provably incur sublinear count-regret. We demonstrate the practicality of the method on problems from crime modeling, revenue maximization as well as environmental monitoring. | Mojmir Mutny, Andreas Krause | null | null | 2,021 | icml |
Causality-aware counterfactual confounding adjustment as an alternative to linear residualization in anticausal prediction tasks based on linear learners | null | Linear residualization is a common practice for confounding adjustment in machine learning applications. Recently, causality-aware predictive modeling has been proposed as an alternative causality-inspired approach for adjusting for confounders. In this paper, we compare the linear residualization approach against the causality-aware confounding adjustment in anticausal prediction tasks. Our comparisons include both the settings where the training and test sets come from the same distributions, as well as, when the training and test sets are shifted due to selection biases. In the absence of dataset shifts, we show that the causality-aware approach tends to (asymptotically) outperform the residualization adjustment in terms of predictive performance in linear learners. Importantly, our results still holds even when the true model generating the data is not linear. We illustrate our results in both regression and classification tasks. Furthermore, in the presence of dataset shifts in the joint distribution of the confounders and outcome variables, we show that the causality-aware approach is more stable than linear residualization. | Elias Chaibub Neto | null | null | 2,021 | icml |
Bayesian Algorithm Execution: Estimating Computable Properties of Black-box Functions Using Mutual Information | null | In many real world problems, we want to infer some property of an expensive black-box function f, given a budget of T function evaluations. One example is budget constrained global optimization of f, for which Bayesian optimization is a popular method. Other properties of interest include local optima, level sets, integrals, or graph-structured information induced by f. Often, we can find an algorithm A to compute the desired property, but it may require far more than T queries to execute. Given such an A, and a prior distribution over f, we refer to the problem of inferring the output of A using T evaluations as Bayesian Algorithm Execution (BAX). To tackle this problem, we present a procedure, InfoBAX, that sequentially chooses queries that maximize mutual information with respect to the algorithm’s output. Applying this to Dijkstra’s algorithm, for instance, we infer shortest paths in synthetic and real-world graphs with black-box edge costs. Using evolution strategies, we yield variants of Bayesian optimization that target local, rather than global, optima. On these problems, InfoBAX uses up to 500 times fewer queries to f than required by the original algorithm. Our method is closely connected to other Bayesian optimal experimental design procedures such as entropy search methods and optimal sensor placement using Gaussian processes. | Willie Neiswanger, Ke Alexander Wang, Stefano Ermon | null | null | 2,021 | icml |
Implicit-PDF: Non-Parametric Representation of Probability Distributions on the Rotation Manifold | null | In the deep learning era, the vast majority of methods to predict pose from a single image are trained to classify or regress to a single given ground truth pose per image. Such methods have two main shortcomings, i) they cannot represent uncertainty about the predictions, and ii) they cannot handle symmetric objects, where multiple (potentially infinite) poses may be correct. Only recently these shortcomings have been addressed, but current approaches as limited in that they cannot express the full rich space of distributions on the rotation manifold. To this end, we introduce a method to estimate arbitrary, non-parametric distributions on SO(3). Our key idea is to represent the distributions implicitly, with a neural network that estimates the probability density, given the input image and a candidate pose. At inference time, grid sampling or gradient ascent can be used to find the most likely pose, but it is also possible to evaluate the density at any pose, enabling reasoning about symmetries and uncertainty. This is the most general way of representing distributions on manifolds, and to demonstrate its expressive power we introduce a new dataset containing symmetric and nearly-symmetric objects. Our method also shows advantages on the popular object pose estimation benchmarks ModelNet10-SO(3) and T-LESS. Code, data, and visualizations may be found at implicit-pdf.github.io. | Kieran A Murphy, Carlos Esteves, Varun Jampani, Srikumar Ramalingam, Ameesh Makadia | null | null | 2,021 | icml |
Quantitative Understanding of VAE as a Non-linearly Scaled Isometric Embedding | null | Variational autoencoder (VAE) estimates the posterior parameters (mean and variance) of latent variables corresponding to each input data. While it is used for many tasks, the transparency of the model is still an underlying issue. This paper provides a quantitative understanding of VAE property through the differential geometric and information-theoretic interpretations of VAE. According to the Rate-distortion theory, the optimal transform coding is achieved by using an orthonormal transform with PCA basis where the transform space is isometric to the input. Considering the analogy of transform coding to VAE, we clarify theoretically and experimentally that VAE can be mapped to an implicit isometric embedding with a scale factor derived from the posterior parameter. As a result, we can estimate the data probabilities in the input space from the prior, loss metrics, and corresponding posterior parameters, and further, the quantitative importance of each latent variable can be evaluated like the eigenvalue of PCA. | Akira Nakagawa, Keizo Kato, Taiji Suzuki | null | null | 2,021 | icml |
Bias-Variance Reduced Local SGD for Less Heterogeneous Federated Learning | null | Recently, local SGD has got much attention and been extensively studied in the distributed learning community to overcome the communication bottleneck problem. However, the superiority of local SGD to minibatch SGD only holds in quite limited situations. In this paper, we study a new local algorithm called Bias-Variance Reduced Local SGD (BVR-L-SGD) for nonconvex distributed optimization. Algorithmically, our proposed bias and variance reduced local gradient estimator fully utilizes small second-order heterogeneity of local objectives and suggests randomly picking up one of the local models instead of taking the average of them when workers are synchronized. Theoretically, under small heterogeneity of local objectives, we show that BVR-L-SGD achieves better communication complexity than both the previous non-local and local methods under mild conditions, and particularly BVR-L-SGD is the first method that breaks the barrier of communication complexity $\Theta(1/\varepsilon)$ for general nonconvex smooth objectives when the heterogeneity is small and the local computation budget is large. Numerical results are given to verify the theoretical findings and give empirical evidence of the superiority of our method. | Tomoya Murata, Taiji Suzuki | null | null | 2,021 | icml |
Classifying high-dimensional Gaussian mixtures: Where kernel methods fail and neural networks succeed | null | A recent series of theoretical works showed that the dynamics of neural networks with a certain initialisation are well-captured by kernel methods. Concurrent empirical work demonstrated that kernel methods can come close to the performance of neural networks on some image classification tasks. These results raise the question of whether neural networks only learn successfully if kernels also learn successfully, despite being the more expressive function class. Here, we show that two-layer neural networks with *only a few neurons* achieve near-optimal performance on high-dimensional Gaussian mixture classification while lazy training approaches such as random features and kernel methods do not. Our analysis is based on the derivation of a set of ordinary differential equations that exactly track the dynamics of the network and thus allow to extract the asymptotic performance of the network as a function of regularisation or signal-to-noise ratio. We also show how over-parametrising the neural network leads to faster convergence, but does not improve its final performance. | Maria Refinetti, Sebastian Goldt, Florent Krzakala, Lenka Zdeborova | null | null | 2,021 | icml |
Integrated Defense for Resilient Graph Matching | null | A recent study has shown that graph matching models are vulnerable to adversarial manipulation of their input which is intended to cause a mismatching. Nevertheless, there is still a lack of a comprehensive solution for further enhancing the robustness of graph matching against adversarial attacks. In this paper, we identify and study two types of unique topology attacks in graph matching: inter-graph dispersion and intra-graph assembly attacks. We propose an integrated defense model, IDRGM, for resilient graph matching with two novel defense techniques to defend against the above two attacks simultaneously. A detection technique of inscribed simplexes in the hyperspheres consisting of multiple matched nodes is proposed to tackle inter-graph dispersion attacks, in which the distances among the matched nodes in multiple graphs are maximized to form regular simplexes. A node separation method based on phase-type distribution and maximum likelihood estimation is developed to estimate the distribution of perturbed graphs and separate the nodes within the same graphs over a wide space, for defending intra-graph assembly attacks, such that the interference from the similar neighbors of the perturbed nodes is significantly reduced. We evaluate the robustness of our IDRGM model on real datasets against state-of-the-art algorithms. | Jiaxiang Ren, Zijie Zhang, Jiayin Jin, Xin Zhao, Sixing Wu, Yang Zhou, Yelong Shen, Tianshi Che, Ruoming Jin, Dejing Dou | null | null | 2,021 | icml |
Simultaneous Similarity-based Self-Distillation for Deep Metric Learning | null | Deep Metric Learning (DML) provides a crucial tool for visual similarity and zero-shot retrieval applications by learning generalizing embedding spaces, although recent work in DML has shown strong performance saturation across training objectives. However, generalization capacity is known to scale with the embedding space dimensionality. Unfortunately, high dimensional embeddings also create higher retrieval cost for downstream applications. To remedy this, we propose S2SD - Simultaneous Similarity-based Self-distillation. S2SD extends DML with knowledge distillation from auxiliary, high-dimensional embedding and feature spaces to leverage complementary context during training while retaining test-time cost and with negligible changes to the training time. Experiments and ablations across different objectives and standard benchmarks show S2SD offering highly significant improvements of up to 7% in Recall@1, while also setting a new state-of-the-art. | Karsten Roth, Timo Milbich, Bjorn Ommer, Joseph Paul Cohen, Marzyeh Ghassemi | null | null | 2,021 | icml |
Sharf: Shape-conditioned Radiance Fields from a Single View | null | We present a method for estimating neural scenes representations of objects given only a single image. The core of our method is the estimation of a geometric scaffold for the object and its use as a guide for the reconstruction of the underlying radiance field. Our formulation is based on a generative process that first maps a latent code to a voxelized shape, and then renders it to an image, with the object appearance being controlled by a second latent code. During inference, we optimize both the latent codes and the networks to fit a test image of a new object. The explicit disentanglement of shape and appearance allows our model to be fine-tuned given a single image. We can then render new views in a geometrically consistent manner and they represent faithfully the input object. Additionally, our method is able to generalize to images outside of the training domain (more realistic renderings and even real photographs). Finally, the inferred geometric scaffold is itself an accurate estimate of the object’s 3D shape. We demonstrate in several experiments the effectiveness of our approach in both synthetic and real images. | Konstantinos Rematas, Ricardo Martin-Brualla, Vittorio Ferrari | null | null | 2,021 | icml |
Representation Matters: Assessing the Importance of Subgroup Allocations in Training Data | null | Collecting more diverse and representative training data is often touted as a remedy for the disparate performance of machine learning predictors across subpopulations. However, a precise framework for understanding how dataset properties like diversity affect learning outcomes is largely lacking. By casting data collection as part of the learning process, we demonstrate that diverse representation in training data is key not only to increasing subgroup performances, but also to achieving population-level objectives. Our analysis and experiments describe how dataset compositions influence performance and provide constructive results for using trends in existing data, alongside domain knowledge, to help guide intentional, objective-aware dataset design | Esther Rolf, Theodora T Worledge, Benjamin Recht, Michael Jordan | null | null | 2,021 | icml |
Interpreting and Disentangling Feature Components of Various Complexity from DNNs | null | This paper aims to define, visualize, and analyze the feature complexity that is learned by a DNN. We propose a generic definition for the feature complexity. Given the feature of a certain layer in the DNN, our method decomposes and visualizes feature components of different complexity orders from the feature. The feature decomposition enables us to evaluate the reliability, the effectiveness, and the significance of over-fitting of these feature components. Furthermore, such analysis helps to improve the performance of DNNs. As a generic method, the feature complexity also provides new insights into existing deep-learning techniques, such as network compression and knowledge distillation. | Jie Ren, Mingjie Li, Zexu Liu, Quanshi Zhang | null | null | 2,021 | icml |
LEGO: Latent Execution-Guided Reasoning for Multi-Hop Question Answering on Knowledge Graphs | null | Answering complex natural language questions on knowledge graphs (KGQA) is a challenging task. It requires reasoning with the input natural language questions as well as a massive, incomplete heterogeneous KG. Prior methods obtain an abstract structured query graph/tree from the input question and traverse the KG for answers following the query tree. However, they inherently cannot deal with missing links in the KG. Here we present LEGO, a Latent Execution-Guided reasOning framework to handle this challenge in KGQA. LEGO works in an iterative way, which alternates between (1) a Query Synthesizer, which synthesizes a reasoning action and grows the query tree step-by-step, and (2) a Latent Space Executor that executes the reasoning action in the latent embedding space to combat against the missing information in KG. To learn the synthesizer without step-wise supervision, we design a generic latent execution guided bottom-up search procedure to find good execution traces efficiently in the vast query space. Experimental results on several KGQA benchmarks demonstrate the effectiveness of our framework compared with previous state of the art. | Hongyu Ren, Hanjun Dai, Bo Dai, Xinyun Chen, Michihiro Yasunaga, Haitian Sun, Dale Schuurmans, Jure Leskovec, Denny Zhou | null | null | 2,021 | icml |
Training Data Subset Selection for Regression with Controlled Generalization Error | null | Data subset selection from a large number of training instances has been a successful approach toward efficient and cost-effective machine learning. However, models trained on a smaller subset may show poor generalization ability. In this paper, our goal is to design an algorithm for selecting a subset of the training data, so that the model can be trained quickly, without significantly sacrificing on accuracy. More specifically, we focus on data subset selection for $L_2$ regularized regression problems and provide a novel problem formulation which seeks to minimize the training loss with respect to both the trainable parameters and the subset of training data, subject to error bounds on the validation set. We tackle this problem using several technical innovations. First, we represent this problem with simplified constraints using the dual of the original training problem and show that the objective of this new representation is a monotone and $\alpha$-submodular function, for a wide variety of modeling choices. Such properties lead us to develop SELCON, an efficient majorization-minimization algorithm for data subset selection, that admits an approximation guarantee even when the training provides an imperfect estimate of the trained model. Finally, our experiments on several datasets show that SELCON trades off accuracy and efficiency more effectively than the current state-of-the-art. | Durga S, Rishabh Iyer, Ganesh Ramakrishnan, Abir De | null | null | 2,021 | icml |
Unsupervised Part Representation by Flow Capsules | null | Capsule networks aim to parse images into a hierarchy of objects, parts and relations. While promising, they remain limited by an inability to learn effective low level part descriptions. To address this issue we propose a way to learn primary capsule encoders that detect atomic parts from a single image. During training we exploit motion as a powerful perceptual cue for part definition, with an expressive decoder for part generation within a layered image model with occlusion. Experiments demonstrate robust part discovery in the presence of multiple objects, cluttered backgrounds, and occlusion. The learned part decoder is shown to infer the underlying shape masks, effectively filling in occluded regions of the detected shapes. We evaluate FlowCapsules on unsupervised part segmentation and unsupervised image classification. | Sara Sabour, Andrea Tagliasacchi, Soroosh Yazdani, Geoffrey Hinton, David J Fleet | null | null | 2,021 | icml |
Dueling Convex Optimization | null | We address the problem of convex optimization with preference (dueling) feedback. Like the traditional optimization objective, the goal is to find the optimal point with the least possible query complexity, however, without the luxury of even a zeroth order feedback. Instead, the learner can only observe a single noisy bit which is win-loss feedback for a pair of queried points based on their function values. % The problem is certainly of great practical relevance as in many real-world scenarios, such as recommender systems or learning from customer preferences, where the system feedback is often restricted to just one binary-bit preference information. % We consider the problem of online convex optimization (OCO) solely by actively querying $\{0,1\}$ noisy-comparison feedback of decision point pairs, with the objective of finding a near-optimal point (function minimizer) with the least possible number of queries. %a very general class of monotonic, non-decreasing transfer functions, and analyze the problem for any $d$-dimensional smooth convex function. % For the non-stationary OCO setup, where the underlying convex function may change over time, we prove an impossibility result towards achieving the above objective. We next focus only on the stationary OCO problem, and our main contribution lies in designing a normalized gradient descent based algorithm towards finding a $\epsilon$-best optimal point. Towards this, our algorithm is shown to yield a convergence rate of $\tilde O(\nicefrac{d\beta}{\epsilon \nu^2})$ ($\nu$ being the noise parameter) when the underlying function is $\beta$-smooth. Further we show an improved convergence rate of just $\tilde O(\nicefrac{d\beta}{\alpha \nu^2} \log \frac{1}{\epsilon})$ when the function is additionally also $\alpha$-strongly convex. | Aadirupa Saha, Tomer Koren, Yishay Mansour | null | null | 2,021 | icml |
Stochastic Sign Descent Methods: New Algorithms and Better Theory | null | Various gradient compression schemes have been proposed to mitigate the communication cost in distributed training of large scale machine learning models. Sign-based methods, such as signSGD (Bernstein et al., 2018), have recently been gaining popularity because of their simple compression rule and connection to adaptive gradient methods, like ADAM. In this paper, we analyze sign-based methods for non-convex optimization in three key settings: (i) standard single node, (ii) parallel with shared data and (iii) distributed with partitioned data. For single machine case, we generalize the previous analysis of signSGD relying on intuitive bounds on success probabilities and allowing even biased estimators. Furthermore, we extend the analysis to parallel setting within a parameter server framework, where exponentially fast noise reduction is guaranteed with respect to number of nodes, maintaining $1$-bit compression in both directions and using small mini-batch sizes. Next, we identify a fundamental issue with signSGD to converge in distributed environment. To resolve this issue, we propose a new sign-based method, {\em Stochastic Sign Descent with Momentum (SSDM)}, which converges under standard bounded variance assumption with the optimal asymptotic rate. We validate several aspects of our theoretical findings with numerical experiments. | Mher Safaryan, Peter Richtarik | null | null | 2,021 | icml |
On Signal-to-Noise Ratio Issues in Variational Inference for Deep Gaussian Processes | null | We show that the gradient estimates used in training Deep Gaussian Processes (DGPs) with importance-weighted variational inference are susceptible to signal-to-noise ratio (SNR) issues. Specifically, we show both theoretically and via an extensive empirical evaluation that the SNR of the gradient estimates for the latent variable’s variational parameters decreases as the number of importance samples increases. As a result, these gradient estimates degrade to pure noise if the number of importance samples is too large. To address this pathology, we show how doubly-reparameterized gradient estimators, originally proposed for training variational autoencoders, can be adapted to the DGP setting and that the resultant estimators completely remedy the SNR issue, thereby providing more reliable training. Finally, we demonstrate that our fix can lead to consistent improvements in the predictive performance of DGP models. | Tim G. J. Rudner, Oscar Key, Yarin Gal, Tom Rainforth | null | null | 2,021 | icml |
Optimal regret algorithm for Pseudo-1d Bandit Convex Optimization | null | We study online learning with bandit feedback (i.e. learner has access to only zeroth-order oracle) where cost/reward functions $\f_t$ admit a "pseudo-1d" structure, i.e. $\f_t(\w) = \loss_t(\pred_t(\w))$ where the output of $\pred_t$ is one-dimensional. At each round, the learner observes context $\x_t$, plays prediction $\pred_t(\w_t; \x_t)$ (e.g. $\pred_t(\cdot)=⟨\x_t, \cdot⟩$) for some $\w_t \in \mathbb{R}^d$ and observes loss $\loss_t(\pred_t(\w_t))$ where $\loss_t$ is a convex Lipschitz-continuous function. The goal is to minimize the standard regret metric. This pseudo-1d bandit convex optimization problem (\SBCO) arises frequently in domains such as online decision-making or parameter-tuning in large systems. For this problem, we first show a regret lower bound of $\min(\sqrt{dT}, T^{3/4})$ for any algorithm, where $T$ is the number of rounds. We propose a new algorithm \sbcalg that combines randomized online gradient descent with a kernelized exponential weights method to exploit the pseudo-1d structure effectively, guaranteeing the {\em optimal} regret bound mentioned above, up to additional logarithmic factors. In contrast, applying state-of-the-art online convex optimization methods leads to $\tilde{O}\left(\min\left(d^{9.5}\sqrt{T},\sqrt{d}T^{3/4}\right)\right)$ regret, that is significantly suboptimal in terms of $d$. | Aadirupa Saha, Nagarajan Natarajan, Praneeth Netrapalli, Prateek Jain | null | null | 2,021 | icml |
Just How Toxic is Data Poisoning? A Unified Benchmark for Backdoor and Data Poisoning Attacks | null | Data poisoning and backdoor attacks manipulate training data in order to cause models to fail during inference. A recent survey of industry practitioners found that data poisoning is the number one concern among threats ranging from model stealing to adversarial attacks. However, it remains unclear exactly how dangerous poisoning methods are and which ones are more effective considering that these methods, even ones with identical objectives, have not been tested in consistent or realistic settings. We observe that data poisoning and backdoor attacks are highly sensitive to variations in the testing setup. Moreover, we find that existing methods may not generalize to realistic settings. While these existing works serve as valuable prototypes for data poisoning, we apply rigorous tests to determine the extent to which we should fear them. In order to promote fair comparison in future work, we develop standardized benchmarks for data poisoning and backdoor attacks. | Avi Schwarzschild, Micah Goldblum, Arjun Gupta, John P Dickerson, Tom Goldstein | null | null | 2,021 | icml |
Recomposing the Reinforcement Learning Building Blocks with Hypernetworks | null | The Reinforcement Learning (RL) building blocks, i.e. $Q$-functions and policy networks, usually take elements from the cartesian product of two domains as input. In particular, the input of the $Q$-function is both the state and the action, and in multi-task problems (Meta-RL) the policy can take a state and a context. Standard architectures tend to ignore these variables’ underlying interpretations and simply concatenate their features into a single vector. In this work, we argue that this choice may lead to poor gradient estimation in actor-critic algorithms and high variance learning steps in Meta-RL algorithms. To consider the interaction between the input variables, we suggest using a Hypernetwork architecture where a primary network determines the weights of a conditional dynamic network. We show that this approach improves the gradient approximation and reduces the learning step variance, which both accelerates learning and improves the final performance. We demonstrate a consistent improvement across different locomotion tasks and different algorithms both in RL (TD3 and SAC) and in Meta-RL (MAML and PEARL). | Elad Sarafian, Shai Keynan, Sarit Kraus | null | null | 2,021 | icml |
Equivariant message passing for the prediction of tensorial properties and molecular spectra | null | Message passing neural networks have become a method of choice for learning on graphs, in particular the prediction of chemical properties and the acceleration of molecular dynamics studies. While they readily scale to large training data sets, previous approaches have proven to be less data efficient than kernel methods. We identify limitations of invariant representations as a major reason and extend the message passing formulation to rotationally equivariant representations. On this basis, we propose the polarizable atom interaction neural network (PaiNN) and improve on common molecule benchmarks over previous networks, while reducing model size and inference time. We leverage the equivariant atomwise representations obtained by PaiNN for the prediction of tensorial properties. Finally, we apply this to the simulation of molecular spectra, achieving speedups of 4-5 orders of magnitude compared to the electronic structure reference. | Kristof Schütt, Oliver Unke, Michael Gastegger | null | null | 2,021 | icml |
State Entropy Maximization with Random Encoders for Efficient Exploration | null | Recent exploration methods have proven to be a recipe for improving sample-efficiency in deep reinforcement learning (RL). However, efficient exploration in high-dimensional observation spaces still remains a challenge. This paper presents Random Encoders for Efficient Exploration (RE3), an exploration method that utilizes state entropy as an intrinsic reward. In order to estimate state entropy in environments with high-dimensional observations, we utilize a k-nearest neighbor entropy estimator in the low-dimensional representation space of a convolutional encoder. In particular, we find that the state entropy can be estimated in a stable and compute-efficient manner by utilizing a randomly initialized encoder, which is fixed throughout training. Our experiments show that RE3 significantly improves the sample-efficiency of both model-free and model-based RL methods on locomotion and navigation tasks from DeepMind Control Suite and MiniGrid benchmarks. We also show that RE3 allows learning diverse behaviors without extrinsic rewards, effectively improving sample-efficiency in downstream tasks. | Younggyo Seo, Lili Chen, Jinwoo Shin, Honglak Lee, Pieter Abbeel, Kimin Lee | null | null | 2,021 | icml |
Descending through a Crowded Valley - Benchmarking Deep Learning Optimizers | null | Choosing the optimizer is considered to be among the most crucial design decisions in deep learning, and it is not an easy one. The growing literature now lists hundreds of optimization methods. In the absence of clear theoretical guidance and conclusive empirical evidence, the decision is often made based on anecdotes. In this work, we aim to replace these anecdotes, if not with a conclusive ranking, then at least with evidence-backed heuristics. To do so, we perform an extensive, standardized benchmark of fifteen particularly popular deep learning optimizers while giving a concise overview of the wide range of possible choices. Analyzing more than 50,000 individual runs, we contribute the following three points: (i) Optimizer performance varies greatly across tasks. (ii) We observe that evaluating multiple optimizers with default parameters works approximately as well as tuning the hyperparameters of a single, fixed optimizer. (iii) While we cannot discern an optimization method clearly dominating across all tested tasks, we identify a significantly reduced subset of specific optimizers and parameter choices that generally lead to competitive results in our experiments: Adam remains a strong contender, with newer methods failing to significantly and consistently outperform it. Our open-sourced results are available as challenging and well-tuned baselines for more meaningful evaluations of novel optimization methods without requiring any further computational efforts. | Robin M Schmidt, Frank Schneider, Philipp Hennig | null | null | 2,021 | icml |
A Representation Learning Perspective on the Importance of Train-Validation Splitting in Meta-Learning | null | An effective approach in meta-learning is to utilize multiple “train tasks” to learn a good initialization for model parameters that can help solve unseen “test tasks” with very few samples by fine-tuning from this initialization. Although successful in practice, theoretical understanding of such methods is limited. This work studies an important aspect of these methods: splitting the data from each task into train (support) and validation (query) sets during meta-training. Inspired by recent work (Raghu et al., 2020), we view such meta-learning methods through the lens of representation learning and argue that the train-validation split encourages the learned representation to be {\em low-rank} without compromising on expressivity, as opposed to the non-splitting variant that encourages high-rank representations. Since sample efficiency benefits from low-rankness, the splitting strategy will require very few samples to solve unseen test tasks. We present theoretical results that formalize this idea for linear representation learning on a subspace meta-learning instance, and experimentally verify this practical benefit of splitting in simulations and on standard meta-learning benchmarks. | Nikunj Saunshi, Arushi Gupta, Wei Hu | null | null | 2,021 | icml |
Learning Intra-Batch Connections for Deep Metric Learning | null | The goal of metric learning is to learn a function that maps samples to a lower-dimensional space where similar samples lie closer than dissimilar ones. Particularly, deep metric learning utilizes neural networks to learn such a mapping. Most approaches rely on losses that only take the relations between pairs or triplets of samples into account, which either belong to the same class or two different classes. However, these methods do not explore the embedding space in its entirety. To this end, we propose an approach based on message passing networks that takes all the relations in a mini-batch into account. We refine embedding vectors by exchanging messages among all samples in a given batch allowing the training process to be aware of its overall structure. Since not all samples are equally important to predict a decision boundary, we use an attention mechanism during message passing to allow samples to weigh the importance of each neighbor accordingly. We achieve state-of-the-art results on clustering and image retrieval on the CUB-200-2011, Cars196, Stanford Online Products, and In-Shop Clothes datasets. To facilitate further research, we make available the code and the models at https://github.com/dvl-tum/intra_batch_connections. | Jenny Denise Seidenschwarz, Ismail Elezi, Laura Leal-Taixé | null | null | 2,021 | icml |
Online Submodular Resource Allocation with Applications to Rebalancing Shared Mobility Systems | null | Motivated by applications in shared mobility, we address the problem of allocating a group of agents to a set of resources to maximize a cumulative welfare objective. We model the welfare obtainable from each resource as a monotone DR-submodular function which is a-priori unknown and can only be learned by observing the welfare of selected allocations. Moreover, these functions can depend on time-varying contextual information. We propose a distributed scheme to maximize the cumulative welfare by designing a repeated game among the agents, who learn to act via regret minimization. We propose two design choices for the game rewards based on upper confidence bounds built around the unknown welfare functions. We analyze them theoretically, bounding the gap between the cumulative welfare of the game and the highest cumulative welfare obtainable in hindsight. Finally, we evaluate our approach in a realistic case study of rebalancing a shared mobility system (i.e., positioning vehicles in strategic areas). From observed trip data, our algorithm gradually learns the users’ demand pattern and improves the overall system operation. | Pier Giuseppe Sessa, Ilija Bogunovic, Andreas Krause, Maryam Kamgarpour | null | null | 2,021 | icml |
Top-k eXtreme Contextual Bandits with Arm Hierarchy | null | Motivated by modern applications, such as online advertisement and recommender systems, we study the top-$k$ extreme contextual bandits problem, where the total number of arms can be enormous, and the learner is allowed to select $k$ arms and observe all or some of the rewards for the chosen arms. We first propose an algorithm for the non-extreme realizable setting, utilizing the Inverse Gap Weighting strategy for selecting multiple arms. We show that our algorithm has a regret guarantee of $O(k\sqrt{(A-k+1)T \log (|F|T)})$, where $A$ is the total number of arms and $F$ is the class containing the regression function, while only requiring $\tilde{O}(A)$ computation per time step. In the extreme setting, where the total number of arms can be in the millions, we propose a practically-motivated arm hierarchy model that induces a certain structure in mean rewards to ensure statistical and computational efficiency. The hierarchical structure allows for an exponential reduction in the number of relevant arms for each context, thus resulting in a regret guarantee of $O(k\sqrt{(\log A-k+1)T \log (|F|T)})$. Finally, we implement our algorithm using a hierarchical linear function class and show superior performance with respect to well-known benchmarks on simulated bandit feedback experiments using extreme multi-label classification datasets. On a dataset with three million arms, our reduction scheme has an average inference time of only 7.9 milliseconds, which is a 100x improvement. | Rajat Sen, Alexander Rakhlin, Lexing Ying, Rahul Kidambi, Dean Foster, Daniel N Hill, Inderjit S. Dhillon | null | null | 2,021 | icml |
RRL: Resnet as representation for Reinforcement Learning | null | The ability to autonomously learn behaviors via direct interactions in uninstrumented environments can lead to generalist robots capable of enhancing productivity or providing care in unstructured settings like homes. Such uninstrumented settings warrant operations only using the robot’s proprioceptive sensor such as onboard cameras, joint encoders, etc which can be challenging for policy learning owing to the high dimensionality and partial observability issues. We propose RRL: Resnet as representation for Reinforcement Learning {–} a straightforward yet effective approach that can learn complex behaviors directly from proprioceptive inputs. RRL fuses features extracted from pre-trained Resnet into the standard reinforcement learning pipeline and delivers results comparable to learning directly from the state. In a simulated dexterous manipulation benchmark, where the state of the art methods fails to make significant progress, RRL delivers contact rich behaviors. The appeal of RRL lies in its simplicity in bringing together progress from the fields of Representation Learning, Imitation Learning, and Reinforcement Learning. Its effectiveness in learning behaviors directly from visual inputs with performance and sample efficiency matching learning directly from the state, even in complex high dimensional domains, is far from obvious. | Rutav M Shah, Vikash Kumar | null | null | 2,021 | icml |
GANMEX: One-vs-One Attributions using GAN-based Model Explainability | null | Attribution methods have been shown as promising approaches for identifying key features that led to learned model predictions. While most existing attribution methods rely on a baseline input for performing feature perturbations, limited research has been conducted to address the baseline selection issues. Poor choices of baselines limit the ability of one-vs-one explanations for multi-class classifiers, which means the attribution methods were not able to explain why an input belongs to its original class but not the other specified target class. Achieving one-vs-one explanation is crucial when certain classes are more similar than others, e.g. two bird types among multiple animals, by focusing on key differentiating features rather than shared features across classes. In this paper, we present GANMEX, a novel approach applying Generative Adversarial Networks (GAN) by incorporating the to-be-explained classifier as part of the adversarial networks. Our approach effectively selects the baseline as the closest realistic sample belong to the target class, which allows attribution methods to provide true one-vs-one explanations. We showed that GANMEX baselines improved the saliency maps and led to stronger performance on multiple evaluation metrics over the existing baselines. Existing attribution results are known for being insensitive to model randomization, and we demonstrated that GANMEX baselines led to better outcome under the cascading randomization of the model. | Sheng-Min Shih, Pin-Ju Tien, Zohar Karnin | null | null | 2,021 | icml |
Zoo-Tuning: Adaptive Transfer from A Zoo of Models | null | With the development of deep networks on various large-scale datasets, a large zoo of pretrained models are available. When transferring from a model zoo, applying classic single-model-based transfer learning methods to each source model suffers from high computational cost and cannot fully utilize the rich knowledge in the zoo. We propose \emph{Zoo-Tuning} to address these challenges, which learns to adaptively transfer the parameters of pretrained models to the target task. With the learnable channel alignment layer and adaptive aggregation layer, Zoo-Tuning \emph{adaptively aggregates channel aligned pretrained parameters to derive the target model}, which simultaneously promotes knowledge transfer and adapts source models to downstream tasks. The adaptive aggregation substantially reduces the computation cost at both training and inference. We further propose lite Zoo-Tuning with the temporal ensemble of batch average gating values to reduce the storage cost at the inference time. We evaluate our approach on a variety of tasks, including reinforcement learning, image classification, and facial landmark detection. Experiment results demonstrate that the proposed adaptive transfer learning approach can more effectively and efficiently transfer knowledge from a zoo of models. | Yang Shu, Zhi Kou, Zhangjie Cao, Jianmin Wang, Mingsheng Long | null | null | 2,021 | icml |
Collaborative Bayesian Optimization with Fair Regret | null | Bayesian optimization (BO) is a popular tool for optimizing complex and costly-to-evaluate black-box objective functions. To further reduce the number of function evaluations, any party performing BO may be interested to collaborate with others to optimize the same objective function concurrently. To do this, existing BO algorithms have considered optimizing a batch of input queries in parallel and provided theoretical bounds on their cumulative regret reflecting inefficiency. However, when the objective function values are correlated with real-world rewards (e.g., money), parties may be hesitant to collaborate if they risk incurring larger cumulative regret (i.e., smaller real-world reward) than others. This paper shows that fairness and efficiency are both necessary for the collaborative BO setting. Inspired by social welfare concepts from economics, we propose a new notion of regret capturing these properties and a collaborative BO algorithm whose convergence rate can be theoretically guaranteed by bounding the new regret, both of which share an adjustable parameter for trading off between fairness vs. efficiency. We empirically demonstrate the benefits (e.g., increased fairness) of our algorithm using synthetic and real-world datasets. | Rachael Hwee Ling Sim, Yehong Zhang, Bryan Kian Hsiang Low, Patrick Jaillet | null | null | 2,021 | icml |
Dynamic Planning and Learning under Recovering Rewards | null | Motivated by emerging applications such as live-streaming e-commerce, promotions and recommendations, we introduce a general class of multi-armed bandit problems that have the following two features: (i) the decision maker can pull and collect rewards from at most $K$ out of $N$ different arms in each time period; (ii) the expected reward of an arm immediately drops after it is pulled, and then non-parametrically recovers as the idle time increases. With the objective of maximizing expected cumulative rewards over $T$ time periods, we propose, construct and prove performance guarantees for a class of “Purely Periodic Policies”. For the offline problem when all model parameters are known, our proposed policy obtains an approximation ratio that is at the order of $1-\mathcal O(1/\sqrt{K})$, which is asymptotically optimal when $K$ grows to infinity. For the online problem when the model parameters are unknown and need to be learned, we design an Upper Confidence Bound (UCB) based policy that approximately has $\widetilde{\mathcal O}(N\sqrt{T})$ regret against the offline benchmark. Our framework and policy design may have the potential to be adapted into other offline planning and online learning applications with non-stationary and recovering rewards. | David Simchi-Levi, Zeyu Zheng, Feng Zhu | null | null | 2,021 | icml |
On the Power of Localized Perceptron for Label-Optimal Learning of Halfspaces with Adversarial Noise | null | We study {\em online} active learning of homogeneous halfspaces in $\mathbb{R}^d$ with adversarial noise where the overall probability of a noisy label is constrained to be at most $\nu$. Our main contribution is a Perceptron-like online active learning algorithm that runs in polynomial time, and under the conditions that the marginal distribution is isotropic log-concave and $\nu = \Omega(\epsilon)$, where $\epsilon \in (0, 1)$ is the target error rate, our algorithm PAC learns the underlying halfspace with near-optimal label complexity of $\tilde{O}\big(d \cdot \polylog(\frac{1}{\epsilon})\big)$ and sample complexity of $\tilde{O}\big(\frac{d}{\epsilon} \big)$. Prior to this work, existing online algorithms designed for tolerating the adversarial noise are subject to either label complexity polynomial in $\frac{1}{\epsilon}$, or suboptimal noise tolerance, or restrictive marginal distributions. With the additional prior knowledge that the underlying halfspace is $s$-sparse, we obtain attribute-efficient label complexity of $\tilde{O}\big( s \cdot \polylog(d, \frac{1}{\epsilon}) \big)$ and sample complexity of $\tilde{O}\big(\frac{s}{\epsilon} \cdot \polylog(d) \big)$. As an immediate corollary, we show that under the agnostic model where no assumption is made on the noise rate $\nu$, our active learner achieves an error rate of $O(OPT) + \epsilon$ with the same running time and label and sample complexity, where $OPT$ is the best possible error rate achievable by any homogeneous halfspace. | Jie Shen | null | null | 2,021 | icml |
Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariances | null | We study how permutation symmetries in overparameterized multi-layer neural networks generate ‘symmetry-induced’ critical points. Assuming a network with $ L $ layers of minimal widths $ r_1^*, \ldots, r_{L-1}^* $ reaches a zero-loss minimum at $ r_1^*! \cdots r_{L-1}^*! $ isolated points that are permutations of one another, we show that adding one extra neuron to each layer is sufficient to connect all these previously discrete minima into a single manifold. For a two-layer overparameterized network of width $ r^*+ h =: m $ we explicitly describe the manifold of global minima: it consists of $ T(r^*, m) $ affine subspaces of dimension at least $ h $ that are connected to one another. For a network of width $m$, we identify the number $G(r,m)$ of affine subspaces containing only symmetry-induced critical points that are related to the critical points of a smaller network of width $r
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BibTeX
@InProceedings{pmlr-v139-simsek21a,
title = {Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariances},
author = {Simsek, Berfin and Ged, Fran{\c{c}}ois and Jacot, Arthur and Spadaro, Francesco and Hongler, Clement and Gerstner, Wulfram and Brea, Johanni},
booktitle = {Proceedings of the 38th International Conference on Machine Learning},
pages = {9722--9732},
year = {2021},
editor = {Meila, Marina and Zhang, Tong},
volume = {139},
series = {Proceedings of Machine Learning Research},
month = {18--24 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v139/simsek21a/simsek21a.pdf},
url = {https://proceedings.mlr.press/v139/simsek21a.html},
abstract = {We study how permutation symmetries in overparameterized multi-layer neural networks generate ‘symmetry-induced’ critical points. Assuming a network with $ L $ layers of minimal widths $ r_1^*, \ldots, r_{L-1}^* $ reaches a zero-loss minimum at $ r_1^*! \cdots r_{L-1}^*! $ isolated points that are permutations of one another, we show that adding one extra neuron to each layer is sufficient to connect all these previously discrete minima into a single manifold. For a two-layer overparameterized network of width $ r^*+ h =: m $ we explicitly describe the manifold of global minima: it consists of $ T(r^*, m) $ affine subspaces of dimension at least $ h $ that are connected to one another. For a network of width $m$, we identify the number $G(r,m)$ of affine subspaces containing only symmetry-induced critical points that are related to the critical points of a smaller network of width $r
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%0 Conference Paper
%T Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariances
%A Berfin Simsek
%A François Ged
%A Arthur Jacot
%A Francesco Spadaro
%A Clement Hongler
%A Wulfram Gerstner
%A Johanni Brea
%B Proceedings of the 38th International Conference on Machine Learning
%C Proceedings of Machine Learning Research
%D 2021
%E Marina Meila
%E Tong Zhang
%F pmlr-v139-simsek21a
%I PMLR
%P 9722--9732
%U https://proceedings.mlr.press/v139/simsek21a.html
%V 139
%X We study how permutation symmetries in overparameterized multi-layer neural networks generate ‘symmetry-induced’ critical points. Assuming a network with $ L $ layers of minimal widths $ r_1^*, \ldots, r_{L-1}^* $ reaches a zero-loss minimum at $ r_1^*! \cdots r_{L-1}^*! $ isolated points that are permutations of one another, we show that adding one extra neuron to each layer is sufficient to connect all these previously discrete minima into a single manifold. For a two-layer overparameterized network of width $ r^*+ h =: m $ we explicitly describe the manifold of global minima: it consists of $ T(r^*, m) $ affine subspaces of dimension at least $ h $ that are connected to one another. For a network of width $m$, we identify the number $G(r,m)$ of affine subspaces containing only symmetry-induced critical points that are related to the critical points of a smaller network of width $r
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APA
Simsek, B., Ged, F., Jacot, A., Spadaro, F., Hongler, C., Gerstner, W. & Brea, J.. (2021). Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariances. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:9722-9732 Available from https://proceedings.mlr.press/v139/simsek21a.html.
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Supplementary PDF | Berfin Simsek, François Ged, Arthur Jacot, Francesco Spadaro, Clement Hongler, Wulfram Gerstner, Johanni Brea | null | null | 2,021 | icml |
Accelerating Feedforward Computation via Parallel Nonlinear Equation Solving | null | Feedforward computation, such as evaluating a neural network or sampling from an autoregressive model, is ubiquitous in machine learning. The sequential nature of feedforward computation, however, requires a strict order of execution and cannot be easily accelerated with parallel computing. To enable parallelization, we frame the task of feedforward computation as solving a system of nonlinear equations. We then propose to find the solution using a Jacobi or Gauss-Seidel fixed-point iteration method, as well as hybrid methods of both. Crucially, Jacobi updates operate independently on each equation and can be executed in parallel. Our method is guaranteed to give exactly the same values as the original feedforward computation with a reduced (or equal) number of parallelizable iterations, and hence reduced time given sufficient parallel computing power. Experimentally, we demonstrate the effectiveness of our approach in accelerating (i) backpropagation of RNNs, (ii) evaluation of DenseNets, and (iii) autoregressive sampling of MADE and PixelCNN++, with speedup factors between 2.1 and 26 under various settings. | Yang Song, Chenlin Meng, Renjie Liao, Stefano Ermon | null | null | 2,021 | icml |
Flow-based Attribution in Graphical Models: A Recursive Shapley Approach | null | We study the attribution problem in a graphical model, wherein the objective is to quantify how the effect of changes at the source nodes propagates through the graph. We develop a model-agnostic flow-based attribution method, called recursive Shapley value (RSV). RSV generalizes a number of existing node-based methods and uniquely satisfies a set of flow-based axioms. In addition to admitting a natural characterization for linear models and facilitating mediation analysis for non-linear models, RSV satisfies a mix of desirable properties discussed in the recent literature, including implementation invariance, sensitivity, monotonicity, and affine scale invariance. | Raghav Singal, George Michailidis, Hoiyi Ng | null | null | 2,021 | icml |
PC-MLP: Model-based Reinforcement Learning with Policy Cover Guided Exploration | null | Model-based Reinforcement Learning (RL) is a popular learning paradigm due to its potential sample efficiency compared to model-free RL. However, existing empirical model-based RL approaches lack the ability to explore. This work studies a computationally and statistically efficient model-based algorithm for both Kernelized Nonlinear Regulators (KNR) and linear Markov Decision Processes (MDPs). For both models, our algorithm guarantees polynomial sample complexity and only uses access to a planning oracle. Experimentally, we first demonstrate the flexibility and the efficacy of our algorithm on a set of exploration challenging control tasks where existing empirical model-based RL approaches completely fail. We then show that our approach retains excellent performance even in common dense reward control benchmarks that do not require heavy exploration. | Yuda Song, Wen Sun | null | null | 2,021 | icml |
Variance Reduction via Primal-Dual Accelerated Dual Averaging for Nonsmooth Convex Finite-Sums | null | Structured nonsmooth convex finite-sum optimization appears in many machine learning applications, including support vector machines and least absolute deviation. For the primal-dual formulation of this problem, we propose a novel algorithm called \emph{Variance Reduction via Primal-Dual Accelerated Dual Averaging (\vrpda)}. In the nonsmooth and general convex setting, \vrpda has the overall complexity $O(nd\log\min \{1/\epsilon, n\} + d/\epsilon )$ in terms of the primal-dual gap, where $n$ denotes the number of samples, $d$ the dimension of the primal variables, and $\epsilon$ the desired accuracy. In the nonsmooth and strongly convex setting, the overall complexity of \vrpda becomes $O(nd\log\min\{1/\epsilon, n\} + d/\sqrt{\epsilon})$ in terms of both the primal-dual gap and the distance between iterate and optimal solution. Both these results for \vrpda improve significantly on state-of-the-art complexity estimates—which are $O(nd\log \min\{1/\epsilon, n\} + \sqrt{n}d/\epsilon)$ for the nonsmooth and general convex setting and $O(nd\log \min\{1/\epsilon, n\} + \sqrt{n}d/\sqrt{\epsilon})$ for the nonsmooth and strongly convex setting—with a simpler and more straightforward algorithm and analysis. Moreover, both complexities are better than \emph{lower} bounds for general convex finite-sum optimization, because our approach makes use of additional, commonly occurring structure. Numerical experiments reveal competitive performance of \vrpda compared to state-of-the-art approaches. | Chaobing Song, Stephen J Wright, Jelena Diakonikolas | null | null | 2,021 | icml |
More Powerful and General Selective Inference for Stepwise Feature Selection using Homotopy Method | null | Conditional selective inference (SI) has been actively studied as a new statistical inference framework for data-driven hypotheses. The basic idea of conditional SI is to make inferences conditional on the selection event characterized by a set of linear and/or quadratic inequalities. Conditional SI has been mainly studied in the context of feature selection such as stepwise feature selection (SFS). The main limitation of the existing conditional SI methods is the loss of power due to over-conditioning, which is required for computational tractability. In this study, we develop a more powerful and general conditional SI method for SFS using the homotopy method which enables us to overcome this limitation. The homotopy-based SI is especially effective for more complicated feature selection algorithms. As an example, we develop a conditional SI method for forward-backward SFS with AIC-based stopping criteria and show that it is not adversely affected by the increased complexity of the algorithm. We conduct several experiments to demonstrate the effectiveness and efficiency of the proposed method. | Kazuya Sugiyama, Vo Nguyen Le Duy, Ichiro Takeuchi | null | null | 2,021 | icml |
Decomposed Mutual Information Estimation for Contrastive Representation Learning | null | Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation. | Alessandro Sordoni, Nouha Dziri, Hannes Schulz, Geoff Gordon, Philip Bachman, Remi Tachet Des Combes | null | null | 2,021 | icml |
Causal Curiosity: RL Agents Discovering Self-supervised Experiments for Causal Representation Learning | null | Humans show an innate ability to learn the regularities of the world through interaction. By performing experiments in our environment, we are able to discern the causal factors of variation and infer how they affect the dynamics of our world. Analogously, here we attempt to equip reinforcement learning agents with the ability to perform experiments that facilitate a categorization of the rolled-out trajectories, and to subsequently infer the causal factors of the environment in a hierarchical manner. We introduce a novel intrinsic reward, called causal curiosity, and show that it allows our agents to learn optimal sequences of actions, and to discover causal factors in the dynamics. The learned behavior allows the agent to infer a binary quantized representation for the ground-truth causal factors in every environment. Additionally, we find that these experimental behaviors are semantically meaningful (e.g., to differentiate between heavy and light blocks, our agents learn to lift them), and are learnt in a self-supervised manner with approximately 2.5 times less data than conventional supervised planners. We show that these behaviors can be re-purposed and fine-tuned (e.g., from lifting to pushing or other downstream tasks). Finally, we show that the knowledge of causal factor representations aids zero-shot learning for more complex tasks. | Sumedh A Sontakke, Arash Mehrjou, Laurent Itti, Bernhard Schölkopf | null | null | 2,021 | icml |
What Makes for End-to-End Object Detection? | null | Object detection has recently achieved a breakthrough for removing the last one non-differentiable component in the pipeline, Non-Maximum Suppression (NMS), and building up an end-to-end system. However, what makes for its one-to-one prediction has not been well understood. In this paper, we first point out that one-to-one positive sample assignment is the key factor, while, one-to-many assignment in previous detectors causes redundant predictions in inference. Second, we surprisingly find that even training with one-to-one assignment, previous detectors still produce redundant predictions. We identify that classification cost in matching cost is the main ingredient: (1) previous detectors only consider location cost, (2) by additionally introducing classification cost, previous detectors immediately produce one-to-one prediction during inference. We introduce the concept of score gap to explore the effect of matching cost. Classification cost enlarges the score gap by choosing positive samples as those of highest score in the training iteration and reducing noisy positive samples brought by only location cost. Finally, we demonstrate the advantages of end-to-end object detection on crowded scenes. | Peize Sun, Yi Jiang, Enze Xie, Wenqi Shao, Zehuan Yuan, Changhu Wang, Ping Luo | null | null | 2,021 | icml |
Oblivious Sketching-based Central Path Method for Linear Programming | null | In this work, we propose a sketching-based central path method for solving linear programmings, whose running time matches the state of the art results [Cohen, Lee, Song STOC 19; Lee, Song, Zhang COLT 19]. Our method opens up the iterations of the central path method and deploys an "iterate and sketch" approach towards the problem by introducing a new coordinate-wise embedding technique, which may be of independent interest. Compare to previous methods, the work [Cohen, Lee, Song STOC 19] enjoys feasibility while being non-oblivious, and [Lee, Song, Zhang COLT 19] is oblivious but infeasible, and relies on $\mathit{dense}$ sketching matrices such as subsampled randomized Hadamard/Fourier transform matrices. Our method enjoys the benefits of being both oblivious and feasible, and can use $\mathit{sparse}$ sketching matrix [Nelson, Nguyen FOCS 13] to speed up the online matrix-vector multiplication. Our framework for solving LP naturally generalizes to a broader class of convex optimization problems including empirical risk minimization. | Zhao Song, Zheng Yu | null | null | 2,021 | icml |
Scalable Variational Gaussian Processes via Harmonic Kernel Decomposition | null | We introduce a new scalable variational Gaussian process approximation which provides a high fidelity approximation while retaining general applicability. We propose the harmonic kernel decomposition (HKD), which uses Fourier series to decompose a kernel as a sum of orthogonal kernels. Our variational approximation exploits this orthogonality to enable a large number of inducing points at a low computational cost. We demonstrate that, on a range of regression and classification problems, our approach can exploit input space symmetries such as translations and reflections, and it significantly outperforms standard variational methods in scalability and accuracy. Notably, our approach achieves state-of-the-art results on CIFAR-10 among pure GP models. | Shengyang Sun, Jiaxin Shi, Andrew Gordon Gordon Wilson, Roger B Grosse | null | null | 2,021 | icml |
AutoSampling: Search for Effective Data Sampling Schedules | null | Data sampling acts as a pivotal role in training deep learning models. However, an effective sampling schedule is difficult to learn due to its inherent high-dimension as a hyper-parameter. In this paper, we propose an AutoSampling method to automatically learn sampling schedules for model training, which consists of the multi-exploitation step aiming for optimal local sampling schedules and the exploration step for the ideal sampling distribution. More specifically, we achieve sampling schedule search with shortened exploitation cycle to provide enough supervision. In addition, we periodically estimate the sampling distribution from the learned sampling schedules and perturb it to search in the distribution space. The combination of two searches allows us to learn a robust sampling schedule. We apply our AutoSampling method to a variety of image classification tasks illustrating the effectiveness of the proposed method. | Ming Sun, Haoxuan Dou, Baopu Li, Junjie Yan, Wanli Ouyang, Lei Cui | null | null | 2,021 | icml |
Reinforcement Learning for Cost-Aware Markov Decision Processes | null | Ratio maximization has applications in areas as diverse as finance, reward shaping for reinforcement learning (RL), and the development of safe artificial intelligence, yet there has been very little exploration of RL algorithms for ratio maximization. This paper addresses this deficiency by introducing two new, model-free RL algorithms for solving cost-aware Markov decision processes, where the goal is to maximize the ratio of long-run average reward to long-run average cost. The first algorithm is a two-timescale scheme based on relative value iteration (RVI) Q-learning and the second is an actor-critic scheme. The paper proves almost sure convergence of the former to the globally optimal solution in the tabular case and almost sure convergence of the latter under linear function approximation for the critic. Unlike previous methods, the two algorithms provably converge for general reward and cost functions under suitable conditions. The paper also provides empirical results demonstrating promising performance and lending strong support to the theoretical results. | Wesley Suttle, Kaiqing Zhang, Zhuoran Yang, Ji Liu, David Kraemer | null | null | 2,021 | icml |
DFAC Framework: Factorizing the Value Function via Quantile Mixture for Multi-Agent Distributional Q-Learning | null | In fully cooperative multi-agent reinforcement learning (MARL) settings, the environments are highly stochastic due to the partial observability of each agent and the continuously changing policies of the other agents. To address the above issues, we integrate distributional RL and value function factorization methods by proposing a Distributional Value Function Factorization (DFAC) framework to generalize expected value function factorization methods to their distributional variants. DFAC extends the individual utility functions from deterministic variables to random variables, and models the quantile function of the total return as a quantile mixture. To validate DFAC, we demonstrate DFAC’s ability to factorize a simple two-step matrix game with stochastic rewards and perform experiments on all Super Hard tasks of StarCraft Multi-Agent Challenge, showing that DFAC is able to outperform expected value function factorization baselines. | Wei-Fang Sun, Cheng-Kuang Lee, Chun-Yi Lee | null | null | 2,021 | icml |
Of Moments and Matching: A Game-Theoretic Framework for Closing the Imitation Gap | null | We provide a unifying view of a large family of previous imitation learning algorithms through the lens of moment matching. At its core, our classification scheme is based on whether the learner attempts to match (1) reward or (2) action-value moments of the expert’s behavior, with each option leading to differing algorithmic approaches. By considering adversarially chosen divergences between learner and expert behavior, we are able to derive bounds on policy performance that apply for all algorithms in each of these classes, the first to our knowledge. We also introduce the notion of moment recoverability, implicit in many previous analyses of imitation learning, which allows us to cleanly delineate how well each algorithmic family is able to mitigate compounding errors. We derive three novel algorithm templates (AdVIL, AdRIL, and DAeQuIL) with strong guarantees, simple implementation, and competitive empirical performance. | Gokul Swamy, Sanjiban Choudhury, J. Andrew Bagnell, Steven Wu | null | null | 2,021 | icml |
Parallel tempering on optimized paths | null | Parallel tempering (PT) is a class of Markov chain Monte Carlo algorithms that constructs a path of distributions annealing between a tractable reference and an intractable target, and then interchanges states along the path to improve mixing in the target. The performance of PT depends on how quickly a sample from the reference distribution makes its way to the target, which in turn depends on the particular path of annealing distributions. However, past work on PT has used only simple paths constructed from convex combinations of the reference and target log-densities. This paper begins by demonstrating that this path performs poorly in the setting where the reference and target are nearly mutually singular. To address this issue, we expand the framework of PT to general families of paths, formulate the choice of path as an optimization problem that admits tractable gradient estimates, and propose a flexible new family of spline interpolation paths for use in practice. Theoretical and empirical results both demonstrate that our proposed methodology breaks previously-established upper performance limits for traditional paths. | Saifuddin Syed, Vittorio Romaniello, Trevor Campbell, Alexandre Bouchard-Cote | null | null | 2,021 | icml |
A Language for Counterfactual Generative Models | null | We present Omega, a probabilistic programming language with support for counterfactual inference. Counterfactual inference means to observe some fact in the present, and infer what would have happened had some past intervention been taken, e.g. “given that medication was not effective at dose x, what is the probability that it would have been effective at dose 2x?.” We accomplish this by introducing a new operator to probabilistic programming akin to Pearl’s do, define its formal semantics, provide an implementation, and demonstrate its utility through examples in a variety of simulation models. | Zenna Tavares, James Koppel, Xin Zhang, Ria Das, Armando Solar-Lezama | null | null | 2,021 | icml |
EfficientNetV2: Smaller Models and Faster Training | null | This paper introduces EfficientNetV2, a new family of convolutional networks that have faster training speed and better parameter efficiency than previous models. To develop these models, we use a combination of training-aware neural architecture search and scaling, to jointly optimize training speed and parameter efficiency. The models were searched from the search space enriched with new ops such as Fused-MBConv. Our experiments show that EfficientNetV2 models train much faster than state-of-the-art models while being up to 6.8x smaller. Our training can be further sped up by progressively increasing the image size during training, but it often causes a drop in accuracy. To compensate for this accuracy drop, we propose an improved method of progressive learning, which adaptively adjusts regularization (e.g. data augmentation) along with image size. With progressive learning, our EfficientNetV2 significantly outperforms previous models on ImageNet and CIFAR/Cars/Flowers datasets. By pretraining on the same ImageNet21k, our EfficientNetV2 achieves 87.3% top-1 accuracy on ImageNet ILSVRC2012, outperforming the recent ViT by 2.0% accuracy while training 5x-11x faster using the same computing resources. | Mingxing Tan, Quoc Le | null | null | 2,021 | icml |
Sequential Domain Adaptation by Synthesizing Distributionally Robust Experts | null | Least squares estimators, when trained on few target domain samples, may predict poorly. Supervised domain adaptation aims to improve the predictive accuracy by exploiting additional labeled training samples from a source distribution that is close to the target distribution. Given available data, we investigate novel strategies to synthesize a family of least squares estimator experts that are robust with regard to moment conditions. When these moment conditions are specified using Kullback-Leibler or Wasserstein-type divergences, we can find the robust estimators efficiently using convex optimization. We use the Bernstein online aggregation algorithm on the proposed family of robust experts to generate predictions for the sequential stream of target test samples. Numerical experiments on real data show that the robust strategies systematically outperform non-robust interpolations of the empirical least squares estimators. | Bahar Taskesen, Man-Chung Yue, Jose Blanchet, Daniel Kuhn, Viet Anh Nguyen | null | null | 2,021 | icml |
SGA: A Robust Algorithm for Partial Recovery of Tree-Structured Graphical Models with Noisy Samples | null | We consider learning Ising tree models when the observations from the nodes are corrupted by independent but non-identically distributed noise with unknown statistics. Katiyar et al. (2020) showed that although the exact tree structure cannot be recovered, one can recover a partial tree structure; that is, a structure belonging to the equivalence class containing the true tree. This paper presents a systematic improvement of Katiyar et al. (2020). First, we present a novel impossibility result by deriving a bound on the necessary number of samples for partial recovery. Second, we derive a significantly improved sample complexity result in which the dependence on the minimum correlation $\rho_{\min}$ is $\rho_{\min}^{-8}$ instead of $\rho_{\min}^{-24}$. Finally, we propose Symmetrized Geometric Averaging (SGA), a more statistically robust algorithm for partial tree recovery. We provide error exponent analyses and extensive numerical results on a variety of trees to show that the sample complexity of SGA is significantly better than the algorithm of Katiyar et al. (2020). SGA can be readily extended to Gaussian models and is shown via numerical experiments to be similarly superior. | Anshoo Tandon, Aldric Han, Vincent Tan | null | null | 2,021 | icml |
Sinkhorn Label Allocation: Semi-Supervised Classification via Annealed Self-Training | null | Self-training is a standard approach to semi-supervised learning where the learner’s own predictions on unlabeled data are used as supervision during training. In this paper, we reinterpret this label assignment process as an optimal transportation problem between examples and classes, wherein the cost of assigning an example to a class is mediated by the current predictions of the classifier. This formulation facilitates a practical annealing strategy for label assignment and allows for the inclusion of prior knowledge on class proportions via flexible upper bound constraints. The solutions to these assignment problems can be efficiently approximated using Sinkhorn iteration, thus enabling their use in the inner loop of standard stochastic optimization algorithms. We demonstrate the effectiveness of our algorithm on the CIFAR-10, CIFAR-100, and SVHN datasets in comparison with FixMatch, a state-of-the-art self-training algorithm. | Kai Sheng Tai, Peter D Bailis, Gregory Valiant | null | null | 2,021 | icml |
1-bit Adam: Communication Efficient Large-Scale Training with Adam’s Convergence Speed | null | Scalable training of large models (like BERT and GPT-3) requires careful optimization rooted in model design, architecture, and system capabilities. From a system standpoint, communication has become a major bottleneck, especially on commodity systems with standard TCP interconnects that offer limited network bandwidth. Communication compression is an important technique to reduce training time on such systems. One of the most effective ways to compress communication is via error compensation compression, which offers robust convergence speed, even under 1-bit compression. However, state-of-the-art error compensation techniques only work with basic optimizers like SGD and momentum SGD, which are linearly dependent on the gradients. They do not work with non-linear gradient-based optimizers like Adam, which offer state-of-the-art convergence efficiency and accuracy for models like BERT. In this paper, we propose 1-bit Adam that reduces the communication volume by up to 5x, offers much better scalability, and provides the same convergence speed as uncompressed Adam. Our key finding is that Adam’s variance becomes stable (after a warmup phase) and can be used as a fixed precondition for the rest of the training (compression phase). We performed experiments on up to 256 GPUs and show that 1-bit Adam enables up to 3.3x higher throughput for BERT-Large pre-training and up to 2.9x higher throughput for SQuAD fine-tuning. In addition, we provide theoretical analysis for 1-bit Adam. | Hanlin Tang, Shaoduo Gan, Ammar Ahmad Awan, Samyam Rajbhandari, Conglong Li, Xiangru Lian, Ji Liu, Ce Zhang, Yuxiong He | null | null | 2,021 | icml |
DriftSurf: Stable-State / Reactive-State Learning under Concept Drift | null | When learning from streaming data, a change in the data distribution, also known as concept drift, can render a previously-learned model inaccurate and require training a new model. We present an adaptive learning algorithm that extends previous drift-detection-based methods by incorporating drift detection into a broader stable-state/reactive-state process. The advantage of our approach is that we can use aggressive drift detection in the stable state to achieve a high detection rate, but mitigate the false positive rate of standalone drift detection via a reactive state that reacts quickly to true drifts while eliminating most false positives. The algorithm is generic in its base learner and can be applied across a variety of supervised learning problems. Our theoretical analysis shows that the risk of the algorithm is (i) statistically better than standalone drift detection and (ii) competitive to an algorithm with oracle knowledge of when (abrupt) drifts occur. Experiments on synthetic and real datasets with concept drifts confirm our theoretical analysis. | Ashraf Tahmasbi, Ellango Jothimurugesan, Srikanta Tirthapura, Phillip B Gibbons | null | null | 2,021 | icml |
Synthesizer: Rethinking Self-Attention for Transformer Models | null | The dot product self-attention is known to be central and indispensable to state-of-the-art Transformer models. But is it really required? This paper investigates the true importance and contribution of the dot product-based self-attention mechanism on the performance of Transformer models. Via extensive experiments, we find that (1) random alignment matrices surprisingly perform quite competitively and (2) learning attention weights from token-token (query-key) interactions is useful but not that important after all. To this end, we propose \textsc{Synthesizer}, a model that learns synthetic attention weights without token-token interactions. In our experiments, we first show that simple Synthesizers achieve highly competitive performance when compared against vanilla Transformer models across a range of tasks, including machine translation, language modeling, text generation and GLUE/SuperGLUE benchmarks. When composed with dot product attention, we find that Synthesizers consistently outperform Transformers. Moreover, we conduct additional comparisons of Synthesizers against Dynamic Convolutions, showing that simple Random Synthesizer is not only $60%$ faster but also improves perplexity by a relative $3.5%$. Finally, we show that simple factorized Synthesizers can outperform Linformers on encoding only tasks. | Yi Tay, Dara Bahri, Donald Metzler, Da-Cheng Juan, Zhe Zhao, Che Zheng | null | null | 2,021 | icml |
T-SCI: A Two-Stage Conformal Inference Algorithm with Guaranteed Coverage for Cox-MLP | null | It is challenging to deal with censored data, where we only have access to the incomplete information of survival time instead of its exact value. Fortunately, under linear predictor assumption, people can obtain guaranteed coverage for the confidence interval of survival time using methods like Cox Regression. However, when relaxing the linear assumption with neural networks (e.g., Cox-MLP \citep{katzman2018deepsurv,kvamme2019time}), we lose the guaranteed coverage. To recover the guaranteed coverage without linear assumption, we propose two algorithms based on conformal inference. In the first algorithm \emph{WCCI}, we revisit weighted conformal inference and introduce a new non-conformity score based on partial likelihood. We then propose a two-stage algorithm \emph{T-SCI}, where we run WCCI in the first stage and apply quantile conformal inference to calibrate the results in the second stage. Theoretical analysis shows that T-SCI returns guaranteed coverage under milder assumptions than WCCI. We conduct extensive experiments on synthetic data and real data using different methods, which validate our analysis. | Jiaye Teng, Zeren Tan, Yang Yuan | null | null | 2,021 | icml |
Understanding Invariance via Feedforward Inversion of Discriminatively Trained Classifiers | null | A discriminatively trained neural net classifier can fit the training data perfectly if all information about its input other than class membership has been discarded prior to the output layer. Surprisingly, past research has discovered that some extraneous visual detail remains in the unnormalized logits. This finding is based on inversion techniques that map deep embeddings back to images. We explore this phenomenon further using a novel synthesis of methods, yielding a feedforward inversion model that produces remarkably high fidelity reconstructions, qualitatively superior to those of past efforts. When applied to an adversarially robust classifier model, the reconstructions contain sufficient local detail and global structure that they might be confused with the original image in a quick glance, and the object category can clearly be gleaned from the reconstruction. Our approach is based on BigGAN (Brock, 2019), with conditioning on logits instead of one-hot class labels. We use our reconstruction model as a tool for exploring the nature of representations, including: the influence of model architecture and training objectives (specifically robust losses), the forms of invariance that networks achieve, representational differences between correctly and incorrectly classified images, and the effects of manipulating logits and images. We believe that our method can inspire future investigations into the nature of information flow in a neural net and can provide diagnostics for improving discriminative models. We provide pre-trained models and visualizations at \url{https://sites.google.com/view/understanding-invariance/home}. | Piotr Teterwak, Chiyuan Zhang, Dilip Krishnan, Michael C Mozer | null | null | 2,021 | icml |
Understanding the Dynamics of Gradient Flow in Overparameterized Linear models | null | We provide a detailed analysis of the dynamics ofthe gradient flow in overparameterized two-layerlinear models. A particularly interesting featureof this model is that its nonlinear dynamics can beexactly solved as a consequence of a large num-ber of conservation laws that constrain the systemto follow particular trajectories. More precisely,the gradient flow preserves the difference of theGramian matrices of the input and output weights,and its convergence to equilibrium depends onboth the magnitude of that difference (which isfixed at initialization) and the spectrum of the data.In addition, and generalizing prior work, we proveour results without assuming small, balanced orspectral initialization for the weights. Moreover,we establish interesting mathematical connectionsbetween matrix factorization problems and differ-ential equations of the Riccati type. | Salma Tarmoun, Guilherme Franca, Benjamin D Haeffele, Rene Vidal | null | null | 2,021 | icml |
Resource Allocation in Multi-armed Bandit Exploration: Overcoming Sublinear Scaling with Adaptive Parallelism | null | We study exploration in stochastic multi-armed bandits when we have access to a divisible resource that can be allocated in varying amounts to arm pulls. We focus in particular on the allocation of distributed computing resources, where we may obtain results faster by allocating more resources per pull, but might have reduced throughput due to nonlinear scaling. For example, in simulation-based scientific studies, an expensive simulation can be sped up by running it on multiple cores. This speed-up however, is partly offset by the communication among cores, which results in lower throughput than if fewer cores were allocated to run more trials in parallel. In this paper, we explore these trade-offs in two settings. First, in a fixed confidence setting, we need to find the best arm with a given target success probability as quickly as possible. We propose an algorithm which trades off between information accumulation and throughput and show that the time taken can be upper bounded by the solution of a dynamic program whose inputs are the gaps between the sub-optimal and optimal arms. We also prove a matching hardness result. Second, we present an algorithm for a fixed deadline setting, where we are given a time deadline and need to maximize the probability of finding the best arm. We corroborate our theoretical insights with simulation experiments that show that the algorithms consistently match or outperform baseline algorithms on a variety of problem instances. | Brijen Thananjeyan, Kirthevasan Kandasamy, Ion Stoica, Michael Jordan, Ken Goldberg, Joseph Gonzalez | null | null | 2,021 | icml |
Diffusion Earth Mover’s Distance and Distribution Embeddings | null | We propose a new fast method of measuring distances between large numbers of related high dimensional datasets called the Diffusion Earth Mover’s Distance (EMD). We model the datasets as distributions supported on common data graph that is derived from the affinity matrix computed on the combined data. In such cases where the graph is a discretization of an underlying Riemannian closed manifold, we prove that Diffusion EMD is topologically equivalent to the standard EMD with a geodesic ground distance. Diffusion EMD can be computed in {Õ}(n) time and is more accurate than similarly fast algorithms such as tree-based EMDs. We also show Diffusion EMD is fully differentiable, making it amenable to future uses in gradient-descent frameworks such as deep neural networks. Finally, we demonstrate an application of Diffusion EMD to single cell data collected from 210 COVID-19 patient samples at Yale New Haven Hospital. Here, Diffusion EMD can derive distances between patients on the manifold of cells at least two orders of magnitude faster than equally accurate methods. This distance matrix between patients can be embedded into a higher level patient manifold which uncovers structure and heterogeneity in patients. More generally, Diffusion EMD is applicable to all datasets that are massively collected in parallel in many medical and biological systems. | Alexander Y Tong, Guillaume Huguet, Amine Natik, Kincaid Macdonald, Manik Kuchroo, Ronald Coifman, Guy Wolf, Smita Krishnaswamy | null | null | 2,021 | icml |
Deep Continuous Networks | null | CNNs and computational models of biological vision share some fundamental principles, which opened new avenues of research. However, fruitful cross-field research is hampered by conventional CNN architectures being based on spatially and depthwise discrete representations, which cannot accommodate certain aspects of biological complexity such as continuously varying receptive field sizes and dynamics of neuronal responses. Here we propose deep continuous networks (DCNs), which combine spatially continuous filters, with the continuous depth framework of neural ODEs. This allows us to learn the spatial support of the filters during training, as well as model the continuous evolution of feature maps, linking DCNs closely to biological models. We show that DCNs are versatile and highly applicable to standard image classification and reconstruction problems, where they improve parameter and data efficiency, and allow for meta-parametrization. We illustrate the biological plausibility of the scale distributions learned by DCNs and explore their performance in a neuroscientifically inspired pattern completion task. Finally, we investigate an efficient implementation of DCNs by changing input contrast. | Nergis Tomen, Silvia-Laura Pintea, Jan Van Gemert | null | null | 2,021 | icml |
Understanding self-supervised learning dynamics without contrastive pairs | null | While contrastive approaches of self-supervised learning (SSL) learn representations by minimizing the distance between two augmented views of the same data point (positive pairs) and maximizing views from different data points (negative pairs), recent \emph{non-contrastive} SSL (e.g., BYOL and SimSiam) show remarkable performance {\it without} negative pairs, with an extra learnable predictor and a stop-gradient operation. A fundamental question rises: why they do not collapse into trivial representation? In this paper, we answer this question via a simple theoretical study and propose a novel approach, \ourmethod{}, that \emph{directly} sets the linear predictor based on the statistics of its inputs, rather than trained with gradient update. On ImageNet, it performs comparably with more complex two-layer non-linear predictors that employ BatchNorm and outperforms linear predictor by $2.5%$ in 300-epoch training (and $5%$ in 60-epoch). \ourmethod{} is motivated by our theoretical study of the nonlinear learning dynamics of non-contrastive SSL in simple linear networks. Our study yields conceptual insights into how non-contrastive SSL methods learn, how they avoid representational collapse, and how multiple factors, like predictor networks, stop-gradients, exponential moving averages, and weight decay all come into play. Our simple theory recapitulates the results of real-world ablation studies in both STL-10 and ImageNet. Code is released\footnote{\url{https://github.com/facebookresearch/luckmatters/tree/master/ssl}}. | Yuandong Tian, Xinlei Chen, Surya Ganguli | null | null | 2,021 | icml |
On Disentangled Representations Learned from Correlated Data | null | The focus of disentanglement approaches has been on identifying independent factors of variation in data. However, the causal variables underlying real-world observations are often not statistically independent. In this work, we bridge the gap to real-world scenarios by analyzing the behavior of the most prominent disentanglement approaches on correlated data in a large-scale empirical study (including 4260 models). We show and quantify that systematically induced correlations in the dataset are being learned and reflected in the latent representations, which has implications for downstream applications of disentanglement such as fairness. We also demonstrate how to resolve these latent correlations, either using weak supervision during training or by post-hoc correcting a pre-trained model with a small number of labels. | Frederik Träuble, Elliot Creager, Niki Kilbertus, Francesco Locatello, Andrea Dittadi, Anirudh Goyal, Bernhard Schölkopf, Stefan Bauer | null | null | 2,021 | icml |
Efficient Generative Modelling of Protein Structure Fragments using a Deep Markov Model | null | Fragment libraries are often used in protein structure prediction, simulation and design as a means to significantly reduce the vast conformational search space. Current state-of-the-art methods for fragment library generation do not properly account for aleatory and epistemic uncertainty, respectively due to the dynamic nature of proteins and experimental errors in protein structures. Additionally, they typically rely on information that is not generally or readily available, such as homologous sequences, related protein structures and other complementary information. To address these issues, we developed BIFROST, a novel take on the fragment library problem based on a Deep Markov Model architecture combined with directional statistics for angular degrees of freedom, implemented in the deep probabilistic programming language Pyro. BIFROST is a probabilistic, generative model of the protein backbone dihedral angles conditioned solely on the amino acid sequence. BIFROST generates fragment libraries with a quality on par with current state-of-the-art methods at a fraction of the run-time, while requiring considerably less information and allowing efficient evaluation of probabilities. | Christian B Thygesen, Christian Skjødt Steenmans, Ahmad Salim Al-Sibahi, Lys Sanz Moreta, Anders Bundgård Sørensen, Thomas Hamelryck | null | null | 2,021 | icml |
Conservative Objective Models for Effective Offline Model-Based Optimization | null | In this paper, we aim to solve data-driven model-based optimization (MBO) problems, where the goal is to find a design input that maximizes an unknown objective function provided access to only a static dataset of inputs and their corresponding objective values. Such data-driven optimization procedures are the only practical methods in many real-world domains where active data collection is expensive (e.g., when optimizing over proteins) or dangerous (e.g., when optimizing over aircraft designs, actively evaluating malformed aircraft designs is unsafe). Typical methods for MBO that optimize the input against a learned model of the unknown score function are affected by erroneous overestimation in the learned model caused due to distributional shift, that drives the optimizer to low-scoring or invalid inputs. To overcome this, we propose conservative objective models (COMs), a method that learns a model of the objective function which lower bounds the actual value of the ground-truth objective on out-of-distribution inputs and uses it for optimization. In practice, COMs outperform a number existing methods on a wide range of MBO problems, including optimizing controller parameters, robot morphologies, and superconducting materials. | Brandon Trabucco, Aviral Kumar, Xinyang Geng, Sergey Levine | null | null | 2,021 | icml |
Training data-efficient image transformers & distillation through attention | null | Recently, neural networks purely based on attention were shown to address image understanding tasks such as image classification. These high-performing vision transformers are pre-trained with hundreds of millions of images using a large infrastructure, thereby limiting their adoption. In this work, we produce competitive convolution-free transformers trained on ImageNet only using a single computer in less than 3 days. Our reference vision transformer (86M parameters) achieves top-1 accuracy of 83.1% (single-crop) on ImageNet with no external data. We also introduce a teacher-student strategy specific to transformers. It relies on a distillation token ensuring that the student learns from the teacher through attention, typically from a convnet teacher. The learned transformers are competitive (85.2% top-1 acc.) with the state of the art on ImageNet, and similarly when transferred to other tasks. We will share our code and models. | Hugo Touvron, Matthieu Cord, Matthijs Douze, Francisco Massa, Alexandre Sablayrolles, Herve Jegou | null | null | 2,021 | icml |
Nonparametric Decomposition of Sparse Tensors | null | Tensor decomposition is a powerful framework for multiway data analysis. Despite the success of existing approaches, they ignore the sparse nature of the tensor data in many real-world applications, explicitly or implicitly assuming dense tensors. To address this model misspecification and to exploit the sparse tensor structures, we propose Nonparametric dEcomposition of Sparse Tensors (\ours), which can capture both the sparse structure properties and complex relationships between the tensor nodes to enhance the embedding estimation. Specifically, we first use completely random measures to construct tensor-valued random processes. We prove that the entry growth is much slower than that of the corresponding tensor size, which implies sparsity. Given finite observations (\ie projections), we then propose two nonparametric decomposition models that couple Dirichlet processes and Gaussian processes to jointly sample the sparse entry indices and the entry values (the latter as a nonlinear mapping of the embeddings), so as to encode both the structure properties and nonlinear relationships of the tensor nodes into the embeddings. Finally, we use the stick-breaking construction and random Fourier features to develop a scalable, stochastic variational learning algorithm. We show the advantage of our approach in sparse tensor generation, and entry index and value prediction in several real-world applications. | Conor Tillinghast, Shandian Zhe | null | null | 2,021 | icml |
Active Deep Probabilistic Subsampling | null | Subsampling a signal of interest can reduce costly data transfer, battery drain, radiation exposure and acquisition time in a wide range of problems. The recently proposed Deep Probabilistic Subsampling (DPS) method effectively integrates subsampling in an end-to-end deep learning model, but learns a static pattern for all datapoints. We generalize DPS to a sequential method that actively picks the next sample based on the information acquired so far; dubbed Active-DPS (A-DPS). We validate that A-DPS improves over DPS for MNIST classification at high subsampling rates. Moreover, we demonstrate strong performance in active acquisition Magnetic Resonance Image (MRI) reconstruction, outperforming DPS and other deep learning methods. | Hans Van Gorp, Iris Huijben, Bastiaan S Veeling, Nicola Pezzotti, Ruud J. G. Van Sloun | null | null | 2,021 | icml |
A Framework for Private Matrix Analysis in Sliding Window Model | null | We perform a rigorous study of private matrix analysis when only the last $W$ updates to matrices are considered useful for analysis. We show the existing framework in the non-private setting is not robust to noise required for privacy. We then propose a framework robust to noise and use it to give first efficient $o(W)$ space differentially private algorithms for spectral approximation, principal component analysis (PCA), multi-response linear regression, sparse PCA, and non-negative PCA. Prior to our work, no such result was known for sparse and non-negative differentially private PCA even in the static data setting. We also give a lower bound to demonstrate the cost of privacy in the sliding window model. | Jalaj Upadhyay, Sarvagya Upadhyay | null | null | 2,021 | icml |
Sparsifying Networks via Subdifferential Inclusion | null | Sparsifying deep neural networks is of paramount interest in many areas, especially when those networks have to be implemented on low-memory devices. In this article, we propose a new formulation of the problem of generating sparse weights for a pre-trained neural network. By leveraging the properties of standard nonlinear activation functions, we show that the problem is equivalent to an approximate subdifferential inclusion problem. The accuracy of the approximation controls the sparsity. We show that the proposed approach is valid for a broad class of activation functions (ReLU, sigmoid, softmax). We propose an iterative optimization algorithm to induce sparsity whose convergence is guaranteed. Because of the algorithm flexibility, the sparsity can be ensured from partial training data in a minibatch manner. To demonstrate the effectiveness of our method, we perform experiments on various networks in different applicative contexts: image classification, speech recognition, natural language processing, and time-series forecasting. | Sagar Verma, Jean-Christophe Pesquet | null | null | 2,021 | icml |
Fast Projection Onto Convex Smooth Constraints | null | The Euclidean projection onto a convex set is an important problem that arises in numerous constrained optimization tasks. Unfortunately, in many cases, computing projections is computationally demanding. In this work, we focus on projection problems where the constraints are smooth and the number of constraints is significantly smaller than the dimension. The runtime of existing approaches to solving such problems is either cubic in the dimension or polynomial in the inverse of the target accuracy. Conversely, we propose a simple and efficient primal-dual approach, with a runtime that scales only linearly with the dimension, and only logarithmically in the inverse of the target accuracy. We empirically demonstrate its performance, and compare it with standard baselines. | Ilnura Usmanova, Maryam Kamgarpour, Andreas Krause, Kfir Levy | null | null | 2,021 | icml |
Neuro-algorithmic Policies Enable Fast Combinatorial Generalization | null | Although model-based and model-free approaches to learning the control of systems have achieved impressive results on standard benchmarks, generalization to task variations is still lacking. Recent results suggest that generalization for standard architectures improves only after obtaining exhaustive amounts of data. We give evidence that generalization capabilities are in many cases bottlenecked by the inability to generalize on the combinatorial aspects of the problem. We show that, for a certain subclass of the MDP framework, this can be alleviated by a neuro-algorithmic policy architecture that embeds a time-dependent shortest path solver in a deep neural network. Trained end-to-end via blackbox-differentiation, this method leads to considerable improvement in generalization capabilities in the low-data regime. | Marin Vlastelica, Michal Rolinek, Georg Martius | null | null | 2,021 | icml |
Unbiased Gradient Estimation in Unrolled Computation Graphs with Persistent Evolution Strategies | null | Unrolled computation graphs arise in many scenarios, including training RNNs, tuning hyperparameters through unrolled optimization, and training learned optimizers. Current approaches to optimizing parameters in such computation graphs suffer from high variance gradients, bias, slow updates, or large memory usage. We introduce a method called Persistent Evolution Strategies (PES), which divides the computation graph into a series of truncated unrolls, and performs an evolution strategies-based update step after each unroll. PES eliminates bias from these truncations by accumulating correction terms over the entire sequence of unrolls. PES allows for rapid parameter updates, has low memory usage, is unbiased, and has reasonable variance characteristics. We experimentally demonstrate the advantages of PES compared to several other methods for gradient estimation on synthetic tasks, and show its applicability to training learned optimizers and tuning hyperparameters. | Paul Vicol, Luke Metz, Jascha Sohl-Dickstein | null | null | 2,021 | icml |
Bayesian Optimistic Optimisation with Exponentially Decaying Regret | null | Bayesian optimisation (BO) is a well known algorithm for finding the global optimum of expensive, black-box functions. The current practical BO algorithms have regret bounds ranging from $\mathcal{O}(\frac{logN}{\sqrt{N}})$ to $\mathcal O(e^{-\sqrt{N}})$, where $N$ is the number of evaluations. This paper explores the possibility of improving the regret bound in the noise-free setting by intertwining concepts from BO and optimistic optimisation methods which are based on partitioning the search space. We propose the BOO algorithm, a first practical approach which can achieve an exponential regret bound with order $\mathcal O(N^{-\sqrt{N}})$ under the assumption that the objective function is sampled from a Gaussian process with a Matérn kernel with smoothness parameter $\nu > 4 +\frac{D}{2}$, where $D$ is the number of dimensions. We perform experiments on optimisation of various synthetic functions and machine learning hyperparameter tuning tasks and show that our algorithm outperforms baselines. | Hung Tran-The, Sunil Gupta, Santu Rana, Svetha Venkatesh | null | null | 2,021 | icml |
Think Global and Act Local: Bayesian Optimisation over High-Dimensional Categorical and Mixed Search Spaces | null | High-dimensional black-box optimisation remains an important yet notoriously challenging problem. Despite the success of Bayesian optimisation methods on continuous domains, domains that are categorical, or that mix continuous and categorical variables, remain challenging. We propose a novel solution—we combine local optimisation with a tailored kernel design, effectively handling high-dimensional categorical and mixed search spaces, whilst retaining sample efficiency. We further derive convergence guarantee for the proposed approach. Finally, we demonstrate empirically that our method outperforms the current baselines on a variety of synthetic and real-world tasks in terms of performance, computational costs, or both. | Xingchen Wan, Vu Nguyen, Huong Ha, Binxin Ru, Cong Lu, Michael A. Osborne | null | null | 2,021 | icml |
Whitening and Second Order Optimization Both Make Information in the Dataset Unusable During Training, and Can Reduce or Prevent Generalization | null | Machine learning is predicated on the concept of generalization: a model achieving low error on a sufficiently large training set should also perform well on novel samples from the same distribution. We show that both data whitening and second order optimization can harm or entirely prevent generalization. In general, model training harnesses information contained in the sample-sample second moment matrix of a dataset. For a general class of models, namely models with a fully connected first layer, we prove that the information contained in this matrix is the only information which can be used to generalize. Models trained using whitened data, or with certain second order optimization schemes, have less access to this information, resulting in reduced or nonexistent generalization ability. We experimentally verify these predictions for several architectures, and further demonstrate that generalization continues to be harmed even when theoretical requirements are relaxed. However, we also show experimentally that regularized second order optimization can provide a practical tradeoff, where training is accelerated but less information is lost, and generalization can in some circumstances even improve. | Neha Wadia, Daniel Duckworth, Samuel S Schoenholz, Ethan Dyer, Jascha Sohl-Dickstein | null | null | 2,021 | icml |
Cumulants of Hawkes Processes are Robust to Observation Noise | null | Multivariate Hawkes processes (MHPs) are widely used in a variety of fields to model the occurrence of causally related discrete events in continuous time. Most state-of-the-art approaches address the problem of learning MHPs from perfect traces without noise. In practice, the process through which events are collected might introduce noise in the timestamps. In this work, we address the problem of learning the causal structure of MHPs when the observed timestamps of events are subject to random and unknown shifts, also known as random translations. We prove that the cumulants of MHPs are invariant to random translations, and therefore can be used to learn their underlying causal structure. Furthermore, we empirically characterize the effect of random translations on state-of-the-art learning methods. We show that maximum likelihood-based estimators are brittle, while cumulant-based estimators remain stable even in the presence of significant time shifts. | William Trouleau, Jalal Etesami, Matthias Grossglauser, Negar Kiyavash, Patrick Thiran | null | null | 2,021 | icml |
Explainable Automated Graph Representation Learning with Hyperparameter Importance | null | Current graph representation (GR) algorithms require huge demand of human experts in hyperparameter tuning, which significantly limits their practical applications, leading to an urge for automated graph representation without human intervention. Although automated machine learning (AutoML) serves as a good candidate for automatic hyperparameter tuning, little literature has been reported on automated graph presentation learning and the only existing work employs a black-box strategy, lacking insights into explaining the relative importance of different hyperparameters. To address this issue, we study explainable automated graph representation with hyperparameter importance in this paper. We propose an explainable AutoML approach for graph representation (e-AutoGR) which utilizes explainable graph features during performance estimation and learns decorrelated importance weights for different hyperparameters in affecting the model performance through a non-linear decorrelated weighting regression. These learned importance weights can in turn help to provide more insights in hyperparameter search procedure. We theoretically prove the soundness of the decorrelated weighting algorithm. Extensive experiments on real-world datasets demonstrate the superiority of our proposed e-AutoGR model against state-of-the-art methods in terms of both model performance and hyperparameter importance explainability. | Xin Wang, Shuyi Fan, Kun Kuang, Wenwu Zhu | null | null | 2,021 | icml |
A Proxy Variable View of Shared Confounding | null | Causal inference from observational data can be biased by unobserved confounders. Confounders{—}the variables that affect both the treatments and the outcome{—}induce spurious non-causal correlations between the two. Without additional conditions, unobserved confounders generally make causal quantities hard to identify. In this paper, we focus on the setting where there are many treatments with shared confounding, and we study under what conditions is causal identification possible. The key observation is that we can view subsets of treatments as proxies of the unobserved confounder and identify the intervention distributions of the rest. Moreover, while existing identification formulas for proxy variables involve solving integral equations, we show that one can circumvent the need for such solutions by directly modeling the data. Finally, we extend these results to an expanded class of causal graphs, those with other confounders and selection variables. | Yixin Wang, David Blei | null | null | 2,021 | icml |
Accelerate CNNs from Three Dimensions: A Comprehensive Pruning Framework | null | Most neural network pruning methods, such as filter-level and layer-level prunings, prune the network model along one dimension (depth, width, or resolution) solely to meet a computational budget. However, such a pruning policy often leads to excessive reduction of that dimension, thus inducing a huge accuracy loss. To alleviate this issue, we argue that pruning should be conducted along three dimensions comprehensively. For this purpose, our pruning framework formulates pruning as an optimization problem. Specifically, it first casts the relationships between a certain model’s accuracy and depth/width/resolution into a polynomial regression and then maximizes the polynomial to acquire the optimal values for the three dimensions. Finally, the model is pruned along the three optimal dimensions accordingly. In this framework, since collecting too much data for training the regression is very time-costly, we propose two approaches to lower the cost: 1) specializing the polynomial to ensure an accurate regression even with less training data; 2) employing iterative pruning and fine-tuning to collect the data faster. Extensive experiments show that our proposed algorithm surpasses state-of-the-art pruning algorithms and even neural architecture search-based algorithms. | Wenxiao Wang, Minghao Chen, Shuai Zhao, Long Chen, Jinming Hu, Haifeng Liu, Deng Cai, Xiaofei He, Wei Liu | null | null | 2,021 | icml |
AlphaNet: Improved Training of Supernets with Alpha-Divergence | null | Weight-sharing neural architecture search (NAS) is an effective technique for automating efficient neural architecture design. Weight-sharing NAS builds a supernet that assembles all the architectures as its sub-networks and jointly trains the supernet with the sub-networks. The success of weight-sharing NAS heavily relies on distilling the knowledge of the supernet to the sub-networks. However, we find that the widely used distillation divergence, i.e., KL divergence, may lead to student sub-networks that over-estimate or under-estimate the uncertainty of the teacher supernet, leading to inferior performance of the sub-networks. In this work, we propose to improve the supernet training with a more generalized alpha-divergence. By adaptively selecting the alpha-divergence, we simultaneously prevent the over-estimation or under-estimation of the uncertainty of the teacher model. We apply the proposed alpha-divergence based supernets training to both slimmable neural networks and weight-sharing NAS, and demonstrate significant improvements. Specifically, our discovered model family, AlphaNet, outperforms prior-art models on a wide range of FLOPs regimes, including BigNAS, Once-for-All networks, and AttentiveNAS. We achieve ImageNet top-1 accuracy of 80.0% with only 444M FLOPs. Our code and pretrained models are available at https://github.com/facebookresearch/AlphaNet. | Dilin Wang, Chengyue Gong, Meng Li, Qiang Liu, Vikas Chandra | null | null | 2,021 | icml |
Fast Algorithms for Stackelberg Prediction Game with Least Squares Loss | null | The Stackelberg prediction game (SPG) has been extensively used to model the interactions between the learner and data provider in the training process of various machine learning algorithms. Particularly, SPGs played prominent roles in cybersecurity applications, such as intrusion detection, banking fraud detection, spam filtering, and malware detection. Often formulated as NP-hard bi-level optimization problems, it is generally computationally intractable to find global solutions to SPGs. As an interesting progress in this area, a special class of SPGs with the least squares loss (SPG-LS) have recently been shown polynomially solvable by a bisection method. However, in each iteration of this method, a semidefinite program (SDP) needs to be solved. The resulted high computational costs prevent its applications for large-scale problems. In contrast, we propose a novel approach that reformulates a SPG-LS as a single SDP of a similar form and the same dimension as those solved in the bisection method. Our SDP reformulation is, evidenced by our numerical experiments, orders of magnitude faster than the existing bisection method. We further show that the obtained SDP can be reduced to a second order cone program (SOCP). This allows us to provide real-time response to large-scale SPG-LS problems. Numerical results on both synthetic and real world datasets indicate that the proposed SOCP method is up to 20,000+ times faster than the state of the art. | Jiali Wang, He Chen, Rujun Jiang, Xudong Li, Zihao Li | null | null | 2,021 | icml |
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