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Hemingway: Modeling Distributed Optimization Algorithms
cs.DC cs.AI cs.LG
Distributed optimization algorithms are widely used in many industrial machine learning applications. However choosing the appropriate algorithm and cluster size is often difficult for users as the performance and convergence rate of optimization algorithms vary with the size of the cluster. In this paper we make the case for an ML-optimizer that can select the appropriate algorithm and cluster size to use for a given problem. To do this we propose building two models: one that captures the system level characteristics of how computation, communication change as we increase cluster sizes and another that captures how convergence rates change with cluster sizes. We present preliminary results from our prototype implementation called Hemingway and discuss some of the challenges involved in developing such a system.
Xinghao Pan, Shivaram Venkataraman, Zizheng Tai, Joseph Gonzalez
null
1702.05865
null
null
Cosine Normalization: Using Cosine Similarity Instead of Dot Product in Neural Networks
cs.LG cs.AI stat.ML
Traditionally, multi-layer neural networks use dot product between the output vector of previous layer and the incoming weight vector as the input to activation function. The result of dot product is unbounded, thus increases the risk of large variance. Large variance of neuron makes the model sensitive to the change of input distribution, thus results in poor generalization, and aggravates the internal covariate shift which slows down the training. To bound dot product and decrease the variance, we propose to use cosine similarity or centered cosine similarity (Pearson Correlation Coefficient) instead of dot product in neural networks, which we call cosine normalization. We compare cosine normalization with batch, weight and layer normalization in fully-connected neural networks as well as convolutional networks on the data sets of MNIST, 20NEWS GROUP, CIFAR-10/100 and SVHN. Experiments show that cosine normalization achieves better performance than other normalization techniques.
Chunjie Luo, Jianfeng Zhan, Lei Wang, Qiang Yang
null
1702.0587
null
null
Phase Diagram of Restricted Boltzmann Machines and Generalised Hopfield Networks with Arbitrary Priors
cond-mat.dis-nn cs.LG physics.data-an stat.ML
Restricted Boltzmann Machines are described by the Gibbs measure of a bipartite spin glass, which in turn corresponds to the one of a generalised Hopfield network. This equivalence allows us to characterise the state of these systems in terms of retrieval capabilities, both at low and high load. We study the paramagnetic-spin glass and the spin glass-retrieval phase transitions, as the pattern (i.e. weight) distribution and spin (i.e. unit) priors vary smoothly from Gaussian real variables to Boolean discrete variables. Our analysis shows that the presence of a retrieval phase is robust and not peculiar to the standard Hopfield model with Boolean patterns. The retrieval region is larger when the pattern entries and retrieval units get more peaked and, conversely, when the hidden units acquire a broader prior and therefore have a stronger response to high fields. Moreover, at low load retrieval always exists below some critical temperature, for every pattern distribution ranging from the Boolean to the Gaussian case.
Adriano Barra, Giuseppe Genovese, Peter Sollich, Daniele Tantari
10.1103/PhysRevE.97.022310
1702.05882
null
null
The importance of stain normalization in colorectal tissue classification with convolutional networks
cs.CV cs.LG
The development of reliable imaging biomarkers for the analysis of colorectal cancer (CRC) in hematoxylin and eosin (H&E) stained histopathology images requires an accurate and reproducible classification of the main tissue components in the image. In this paper, we propose a system for CRC tissue classification based on convolutional networks (ConvNets). We investigate the importance of stain normalization in tissue classification of CRC tissue samples in H&E-stained images. Furthermore, we report the performance of ConvNets on a cohort of rectal cancer samples and on an independent publicly available dataset of colorectal H&E images.
Francesco Ciompi, Oscar Geessink, Babak Ehteshami Bejnordi, Gabriel Silva de Souza, Alexi Baidoshvili, Geert Litjens, Bram van Ginneken, Iris Nagtegaal, Jeroen van der Laak
null
1702.05931
null
null
Wages of wins: could an amateur make money from match outcome predictions?
stat.AP cs.LG
Evaluating the accuracies of models for match outcome predictions is nice and well but in the end the real proof is in the money to be made by betting. To evaluate the question whether the models developed by us could be used easily to make money via sports betting, we evaluate three cases: NCAAB post-season, NBA season, and NFL season, and find that it is possible yet not without its pitfalls. In particular, we illustrate that high accuracy does not automatically equal high pay-out, by looking at the type of match-ups that are predicted correctly by different models.
Albrecht Zimmermann
null
1702.05982
null
null
Generating Adversarial Malware Examples for Black-Box Attacks Based on GAN
cs.LG cs.CR
Machine learning has been used to detect new malware in recent years, while malware authors have strong motivation to attack such algorithms. Malware authors usually have no access to the detailed structures and parameters of the machine learning models used by malware detection systems, and therefore they can only perform black-box attacks. This paper proposes a generative adversarial network (GAN) based algorithm named MalGAN to generate adversarial malware examples, which are able to bypass black-box machine learning based detection models. MalGAN uses a substitute detector to fit the black-box malware detection system. A generative network is trained to minimize the generated adversarial examples' malicious probabilities predicted by the substitute detector. The superiority of MalGAN over traditional gradient based adversarial example generation algorithms is that MalGAN is able to decrease the detection rate to nearly zero and make the retraining based defensive method against adversarial examples hard to work.
Weiwei Hu and Ying Tan
null
1702.05983
null
null
An Extended Framework for Marginalized Domain Adaptation
cs.CV cs.LG
We propose an extended framework for marginalized domain adaptation, aimed at addressing unsupervised, supervised and semi-supervised scenarios. We argue that the denoising principle should be extended to explicitly promote domain-invariant features as well as help the classification task. Therefore we propose to jointly learn the data auto-encoders and the target classifiers. First, in order to make the denoised features domain-invariant, we propose a domain regularization that may be either a domain prediction loss or a maximum mean discrepancy between the source and target data. The noise marginalization in this case is reduced to solving the linear matrix system $AX=B$ which has a closed-form solution. Second, in order to help the classification, we include a class regularization term. Adding this component reduces the learning problem to solving a Sylvester linear matrix equation $AX+BX=C$, for which an efficient iterative procedure exists as well. We did an extensive study to assess how these regularization terms improve the baseline performance in the three domain adaptation scenarios and present experimental results on two image and one text benchmark datasets, conventionally used for validating domain adaptation methods. We report our findings and comparison with state-of-the-art methods.
Gabriela Csurka, Boris Chidlovski, Stephane Clinchant and Sophia Michel
null
1702.05993
null
null
Learning to Multi-Task by Active Sampling
cs.NE cs.LG
One of the long-standing challenges in Artificial Intelligence for learning goal-directed behavior is to build a single agent which can solve multiple tasks. Recent progress in multi-task learning for goal-directed sequential problems has been in the form of distillation based learning wherein a student network learns from multiple task-specific expert networks by mimicking the task-specific policies of the expert networks. While such approaches offer a promising solution to the multi-task learning problem, they require supervision from large expert networks which require extensive data and computation time for training. In this work, we propose an efficient multi-task learning framework which solves multiple goal-directed tasks in an on-line setup without the need for expert supervision. Our work uses active learning principles to achieve multi-task learning by sampling the harder tasks more than the easier ones. We propose three distinct models under our active sampling framework. An adaptive method with extremely competitive multi-tasking performance. A UCB-based meta-learner which casts the problem of picking the next task to train on as a multi-armed bandit problem. A meta-learning method that casts the next-task picking problem as a full Reinforcement Learning problem and uses actor critic methods for optimizing the multi-tasking performance directly. We demonstrate results in the Atari 2600 domain on seven multi-tasking instances: three 6-task instances, one 8-task instance, two 12-task instances and one 21-task instance.
Sahil Sharma, Ashutosh Jha, Parikshit Hegde, Balaraman Ravindran
null
1702.06053
null
null
Learning to Repeat: Fine Grained Action Repetition for Deep Reinforcement Learning
cs.LG cs.AI cs.NE
Reinforcement Learning algorithms can learn complex behavioral patterns for sequential decision making tasks wherein an agent interacts with an environment and acquires feedback in the form of rewards sampled from it. Traditionally, such algorithms make decisions, i.e., select actions to execute, at every single time step of the agent-environment interactions. In this paper, we propose a novel framework, Fine Grained Action Repetition (FiGAR), which enables the agent to decide the action as well as the time scale of repeating it. FiGAR can be used for improving any Deep Reinforcement Learning algorithm which maintains an explicit policy estimate by enabling temporal abstractions in the action space. We empirically demonstrate the efficacy of our framework by showing performance improvements on top of three policy search algorithms in different domains: Asynchronous Advantage Actor Critic in the Atari 2600 domain, Trust Region Policy Optimization in Mujoco domain and Deep Deterministic Policy Gradients in the TORCS car racing domain.
Sahil Sharma, Aravind Srinivas, Balaraman Ravindran
null
1702.06054
null
null
Learning Non-Discriminatory Predictors
cs.LG
We consider learning a predictor which is non-discriminatory with respect to a "protected attribute" according to the notion of "equalized odds" proposed by Hardt et al. [2016]. We study the problem of learning such a non-discriminatory predictor from a finite training set, both statistically and computationally. We show that a post-hoc correction approach, as suggested by Hardt et al, can be highly suboptimal, present a nearly-optimal statistical procedure, argue that the associated computational problem is intractable, and suggest a second moment relaxation of the non-discrimination definition for which learning is tractable.
Blake Woodworth, Suriya Gunasekar, Mesrob I. Ohannessian, Nathan Srebro
null
1702.06081
null
null
Label Distribution Learning Forests
cs.LG cs.CV
Label distribution learning (LDL) is a general learning framework, which assigns to an instance a distribution over a set of labels rather than a single label or multiple labels. Current LDL methods have either restricted assumptions on the expression form of the label distribution or limitations in representation learning, e.g., to learn deep features in an end-to-end manner. This paper presents label distribution learning forests (LDLFs) - a novel label distribution learning algorithm based on differentiable decision trees, which have several advantages: 1) Decision trees have the potential to model any general form of label distributions by a mixture of leaf node predictions. 2) The learning of differentiable decision trees can be combined with representation learning. We define a distribution-based loss function for a forest, enabling all the trees to be learned jointly, and show that an update function for leaf node predictions, which guarantees a strict decrease of the loss function, can be derived by variational bounding. The effectiveness of the proposed LDLFs is verified on several LDL tasks and a computer vision application, showing significant improvements to the state-of-the-art LDL methods.
Wei Shen, Kai Zhao, Yilu Guo, Alan Yuille
null
1702.06086
null
null
An Attention-Based Deep Net for Learning to Rank
cs.LG
In information retrieval, learning to rank constructs a machine-based ranking model which given a query, sorts the search results by their degree of relevance or importance to the query. Neural networks have been successfully applied to this problem, and in this paper, we propose an attention-based deep neural network which better incorporates different embeddings of the queries and search results with an attention-based mechanism. This model also applies a decoder mechanism to learn the ranks of the search results in a listwise fashion. The embeddings are trained with convolutional neural networks or the word2vec model. We demonstrate the performance of this model with image retrieval and text querying data sets.
Baiyang Wang, Diego Klabjan
null
1702.06106
null
null
On the Consistency of $k$-means++ algorithm
cs.LG
We prove in this paper that the expected value of the objective function of the $k$-means++ algorithm for samples converges to population expected value. As $k$-means++, for samples, provides with constant factor approximation for $k$-means objectives, such an approximation can be achieved for the population with increase of the sample size. This result is of potential practical relevance when one is considering using subsampling when clustering large data sets (large data bases).
Mieczys{\l}aw A. K{\l}opotek
null
1702.0612
null
null
Developing a comprehensive framework for multimodal feature extraction
cs.CV cs.IR cs.LG cs.MM
Feature extraction is a critical component of many applied data science workflows. In recent years, rapid advances in artificial intelligence and machine learning have led to an explosion of feature extraction tools and services that allow data scientists to cheaply and effectively annotate their data along a vast array of dimensions---ranging from detecting faces in images to analyzing the sentiment expressed in coherent text. Unfortunately, the proliferation of powerful feature extraction services has been mirrored by a corresponding expansion in the number of distinct interfaces to feature extraction services. In a world where nearly every new service has its own API, documentation, and/or client library, data scientists who need to combine diverse features obtained from multiple sources are often forced to write and maintain ever more elaborate feature extraction pipelines. To address this challenge, we introduce a new open-source framework for comprehensive multimodal feature extraction. Pliers is an open-source Python package that supports standardized annotation of diverse data types (video, images, audio, and text), and is expressly with both ease-of-use and extensibility in mind. Users can apply a wide range of pre-existing feature extraction tools to their data in just a few lines of Python code, and can also easily add their own custom extractors by writing modular classes. A graph-based API enables rapid development of complex feature extraction pipelines that output results in a single, standardized format. We describe the package's architecture, detail its major advantages over previous feature extraction toolboxes, and use a sample application to a large functional MRI dataset to illustrate how pliers can significantly reduce the time and effort required to construct sophisticated feature extraction workflows while increasing code clarity and maintainability.
Quinten McNamara, Alejandro de la Vega, and Tal Yarkoni
null
1702.06151
null
null
Bayesian Boolean Matrix Factorisation
stat.ML cs.LG cs.NA q-bio.GN q-bio.QM stat.ME
Boolean matrix factorisation aims to decompose a binary data matrix into an approximate Boolean product of two low rank, binary matrices: one containing meaningful patterns, the other quantifying how the observations can be expressed as a combination of these patterns. We introduce the OrMachine, a probabilistic generative model for Boolean matrix factorisation and derive a Metropolised Gibbs sampler that facilitates efficient parallel posterior inference. On real world and simulated data, our method outperforms all currently existing approaches for Boolean matrix factorisation and completion. This is the first method to provide full posterior inference for Boolean Matrix factorisation which is relevant in applications, e.g. for controlling false positive rates in collaborative filtering and, crucially, improves the interpretability of the inferred patterns. The proposed algorithm scales to large datasets as we demonstrate by analysing single cell gene expression data in 1.3 million mouse brain cells across 11 thousand genes on commodity hardware.
Tammo Rukat and Chris C. Holmes and Michalis K. Titsias and Christopher Yau
null
1702.06166
null
null
Structured signal recovery from quadratic measurements: Breaking sample complexity barriers via nonconvex optimization
cs.LG cs.IT math.FA math.IT math.OC stat.ML
This paper concerns the problem of recovering an unknown but structured signal $x \in R^n$ from $m$ quadratic measurements of the form $y_r=|<a_r,x>|^2$ for $r=1,2,...,m$. We focus on the under-determined setting where the number of measurements is significantly smaller than the dimension of the signal ($m<<n$). We formulate the recovery problem as a nonconvex optimization problem where prior structural information about the signal is enforced through constrains on the optimization variables. We prove that projected gradient descent, when initialized in a neighborhood of the desired signal, converges to the unknown signal at a linear rate. These results hold for any constraint set (convex or nonconvex) providing convergence guarantees to the global optimum even when the objective function and constraint set is nonconvex. Furthermore, these results hold with a number of measurements that is only a constant factor away from the minimal number of measurements required to uniquely identify the unknown signal. Our results provide the first provably tractable algorithm for this data-poor regime, breaking local sample complexity barriers that have emerged in recent literature. In a companion paper we demonstrate favorable properties for the optimization problem that may enable similar results to continue to hold more globally (over the entire ambient space). Collectively these two papers utilize and develop powerful tools for uniform convergence of empirical processes that may have broader implications for rigorous understanding of constrained nonconvex optimization heuristics. The mathematical results in this paper also pave the way for a new generation of data-driven phase-less imaging systems that can utilize prior information to significantly reduce acquisition time and enhance image reconstruction, enabling nano-scale imaging at unprecedented speeds and resolutions.
Mahdi Soltanolkotabi
null
1702.06175
null
null
Survey of reasoning using Neural networks
cs.LG cs.AI cs.NE
Reason and inference require process as well as memory skills by humans. Neural networks are able to process tasks like image recognition (better than humans) but in memory aspects are still limited (by attention mechanism, size). Recurrent Neural Network (RNN) and it's modified version LSTM are able to solve small memory contexts, but as context becomes larger than a threshold, it is difficult to use them. The Solution is to use large external memory. Still, it poses many challenges like, how to train neural networks for discrete memory representation, how to describe long term dependencies in sequential data etc. Most prominent neural architectures for such tasks are Memory networks: inference components combined with long term memory and Neural Turing Machines: neural networks using external memory resources. Also, additional techniques like attention mechanism, end to end gradient descent on discrete memory representation are needed to support these solutions. Preliminary results of above neural architectures on simple algorithms (sorting, copying) and Question Answering (based on story, dialogs) application are comparable with the state of the art. In this paper, I explain these architectures (in general), the additional techniques used and the results of their application.
Amit Sahu
null
1702.06186
null
null
Filtering Tweets for Social Unrest
cs.CL cs.IR cs.LG stat.ML
Since the events of the Arab Spring, there has been increased interest in using social media to anticipate social unrest. While efforts have been made toward automated unrest prediction, we focus on filtering the vast volume of tweets to identify tweets relevant to unrest, which can be provided to downstream users for further analysis. We train a supervised classifier that is able to label Arabic language tweets as relevant to unrest with high reliability. We examine the relationship between training data size and performance and investigate ways to optimize the model building process while minimizing cost. We also explore how confidence thresholds can be set to achieve desired levels of performance.
Alan Mishler, Kevin Wonus, Wendy Chambers and Michael Bloodgood
10.1109/ICSC.2017.75
1702.06216
null
null
Determination of hysteresis in finite-state random walks using Bayesian cross validation
stat.ME cs.LG physics.data-an q-bio.QM
Consider the problem of modeling hysteresis for finite-state random walks using higher-order Markov chains. This Letter introduces a Bayesian framework to determine, from data, the number of prior states of recent history upon which a trajectory is statistically dependent. The general recommendation is to use leave-one-out cross validation, using an easily-computable formula that is provided in closed form. Importantly, Bayes factors using flat model priors are biased in favor of too-complex a model (more hysteresis) when a large amount of data is present and the Akaike information criterion (AIC) is biased in favor of too-sparse a model (less hysteresis) when few data are present.
Joshua C. Chang
null
1702.06221
null
null
Beating the World's Best at Super Smash Bros. with Deep Reinforcement Learning
cs.LG cs.AI
There has been a recent explosion in the capabilities of game-playing artificial intelligence. Many classes of RL tasks, from Atari games to motor control to board games, are now solvable by fairly generic algorithms, based on deep learning, that learn to play from experience with minimal knowledge of the specific domain of interest. In this work, we will investigate the performance of these methods on Super Smash Bros. Melee (SSBM), a popular console fighting game. The SSBM environment has complex dynamics and partial observability, making it challenging for human and machine alike. The multi-player aspect poses an additional challenge, as the vast majority of recent advances in RL have focused on single-agent environments. Nonetheless, we will show that it is possible to train agents that are competitive against and even surpass human professionals, a new result for the multi-player video game setting.
Vlad Firoiu, William F. Whitney, Joshua B. Tenenbaum
null
1702.0623
null
null
Exact tensor completion with sum-of-squares
cs.LG cs.CC cs.DS cs.IT math.IT stat.ML
We obtain the first polynomial-time algorithm for exact tensor completion that improves over the bound implied by reduction to matrix completion. The algorithm recovers an unknown 3-tensor with $r$ incoherent, orthogonal components in $\mathbb R^n$ from $r\cdot \tilde O(n^{1.5})$ randomly observed entries of the tensor. This bound improves over the previous best one of $r\cdot \tilde O(n^{2})$ by reduction to exact matrix completion. Our bound also matches the best known results for the easier problem of approximate tensor completion (Barak & Moitra, 2015). Our algorithm and analysis extends seminal results for exact matrix completion (Candes & Recht, 2009) to the tensor setting via the sum-of-squares method. The main technical challenge is to show that a small number of randomly chosen monomials are enough to construct a degree-3 polynomial with precisely planted orthogonal global optima over the sphere and that this fact can be certified within the sum-of-squares proof system.
Aaron Potechin, David Steurer
null
1702.06237
null
null
Sample Efficient Policy Search for Optimal Stopping Domains
cs.AI cs.LG
Optimal stopping problems consider the question of deciding when to stop an observation-generating process in order to maximize a return. We examine the problem of simultaneously learning and planning in such domains, when data is collected directly from the environment. We propose GFSE, a simple and flexible model-free policy search method that reuses data for sample efficiency by leveraging problem structure. We bound the sample complexity of our approach to guarantee uniform convergence of policy value estimates, tightening existing PAC bounds to achieve logarithmic dependence on horizon length for our setting. We also examine the benefit of our method against prevalent model-based and model-free approaches on 3 domains taken from diverse fields.
Karan Goel, Christoph Dann and Emma Brunskill
null
1702.06238
null
null
SAR: Semantic Analysis for Recommendation
cs.IR cs.LG
Recommendation system is a common demand in daily life and matrix completion is a widely adopted technique for this task. However, most matrix completion methods lack semantic interpretation and usually result in weak-semantic recommendations. To this end, this paper proposes a $S$emantic $A$nalysis approach for $R$ecommendation systems $(SAR)$, which applies a two-level hierarchical generative process that assigns semantic properties and categories for user and item. $SAR$ learns semantic representations of users/items merely from user ratings on items, which offers a new path to recommendation by semantic matching with the learned representations. Extensive experiments demonstrate $SAR$ outperforms other state-of-the-art baselines substantially.
Han Xiao, Lian Meng
null
1702.06247
null
null
Memory and Communication Efficient Distributed Stochastic Optimization with Minibatch-Prox
cs.LG
We present and analyze an approach for distributed stochastic optimization which is statistically optimal and achieves near-linear speedups (up to logarithmic factors). Our approach allows a communication-memory tradeoff, with either logarithmic communication but linear memory, or polynomial communication and a corresponding polynomial reduction in required memory. This communication-memory tradeoff is achieved through minibatch-prox iterations (minibatch passive-aggressive updates), where a subproblem on a minibatch is solved at each iteration. We provide a novel analysis for such a minibatch-prox procedure which achieves the statistical optimal rate regardless of minibatch size and smoothness, thus significantly improving on prior work.
Jialei Wang, Weiran Wang, Nathan Srebro
null
1702.06269
null
null
On the (Statistical) Detection of Adversarial Examples
cs.CR cs.LG stat.ML
Machine Learning (ML) models are applied in a variety of tasks such as network intrusion detection or Malware classification. Yet, these models are vulnerable to a class of malicious inputs known as adversarial examples. These are slightly perturbed inputs that are classified incorrectly by the ML model. The mitigation of these adversarial inputs remains an open problem. As a step towards understanding adversarial examples, we show that they are not drawn from the same distribution than the original data, and can thus be detected using statistical tests. Using thus knowledge, we introduce a complimentary approach to identify specific inputs that are adversarial. Specifically, we augment our ML model with an additional output, in which the model is trained to classify all adversarial inputs. We evaluate our approach on multiple adversarial example crafting methods (including the fast gradient sign and saliency map methods) with several datasets. The statistical test flags sample sets containing adversarial inputs confidently at sample sizes between 10 and 100 data points. Furthermore, our augmented model either detects adversarial examples as outliers with high accuracy (> 80%) or increases the adversary's cost - the perturbation added - by more than 150%. In this way, we show that statistical properties of adversarial examples are essential to their detection.
Kathrin Grosse, Praveen Manoharan, Nicolas Papernot, Michael Backes, Patrick McDaniel
null
1702.0628
null
null
Convolutional Recurrent Neural Networks for Polyphonic Sound Event Detection
cs.LG cs.SD
Sound events often occur in unstructured environments where they exhibit wide variations in their frequency content and temporal structure. Convolutional neural networks (CNN) are able to extract higher level features that are invariant to local spectral and temporal variations. Recurrent neural networks (RNNs) are powerful in learning the longer term temporal context in the audio signals. CNNs and RNNs as classifiers have recently shown improved performances over established methods in various sound recognition tasks. We combine these two approaches in a Convolutional Recurrent Neural Network (CRNN) and apply it on a polyphonic sound event detection task. We compare the performance of the proposed CRNN method with CNN, RNN, and other established methods, and observe a considerable improvement for four different datasets consisting of everyday sound events.
Emre \c{C}ak{\i}r, Giambattista Parascandolo, Toni Heittola, Heikki Huttunen and Tuomas Virtanen
10.1109/TASLP.2017.2690575
1702.06286
null
null
Convolution Aware Initialization
cs.LG stat.ML
Initialization of parameters in deep neural networks has been shown to have a big impact on the performance of the networks (Mishkin & Matas, 2015). The initialization scheme devised by He et al, allowed convolution activations to carry a constrained mean which allowed deep networks to be trained effectively (He et al., 2015a). Orthogonal initializations and more generally orthogonal matrices in standard recurrent networks have been proved to eradicate the vanishing and exploding gradient problem (Pascanu et al., 2012). Majority of current initialization schemes do not take fully into account the intrinsic structure of the convolution operator. Using the duality of the Fourier transform and the convolution operator, Convolution Aware Initialization builds orthogonal filters in the Fourier space, and using the inverse Fourier transform represents them in the standard space. With Convolution Aware Initialization we noticed not only higher accuracy and lower loss, but faster convergence. We achieve new state of the art on the CIFAR10 dataset, and achieve close to state of the art on various other tasks.
Armen Aghajanyan
null
1702.06295
null
null
Towards a Common Implementation of Reinforcement Learning for Multiple Robotic Tasks
cs.AI cs.LG cs.RO
Mobile robots are increasingly being employed for performing complex tasks in dynamic environments. Reinforcement learning (RL) methods are recognized to be promising for specifying such tasks in a relatively simple manner. However, the strong dependency between the learning method and the task to learn is a well-known problem that restricts practical implementations of RL in robotics, often requiring major modifications of parameters and adding other techniques for each particular task. In this paper we present a practical core implementation of RL which enables the learning process for multiple robotic tasks with minimal per-task tuning or none. Based on value iteration methods, this implementation includes a novel approach for action selection, called Q-biased softmax regression (QBIASSR), which avoids poor performance of the learning process when the robot reaches new unexplored states. Our approach takes advantage of the structure of the state space by attending the physical variables involved (e.g., distances to obstacles, X,Y,{\theta} pose, etc.), thus experienced sets of states may favor the decision-making process of unexplored or rarely-explored states. This improvement has a relevant role in reducing the tuning of the algorithm for particular tasks. Experiments with real and simulated robots, performed with the software framework also introduced here, show that our implementation is effectively able to learn different robotic tasks without tuning the learning method. Results also suggest that the combination of true online SARSA({\lambda}) with QBIASSR can outperform the existing RL core algorithms in low-dimensional robotic tasks.
Angel Mart\'inez-Tenor, Juan Antonio Fern\'andez-Madrigal, Ana Cruz-Mart\'in and Javier Gonz\'alez-Jim\'enez
10.1016/j.eswa.2017.11.011
1702.06329
null
null
Fast rates for online learning in Linearly Solvable Markov Decision Processes
cs.LG math.OC stat.ML
We study the problem of online learning in a class of Markov decision processes known as linearly solvable MDPs. In the stationary version of this problem, a learner interacts with its environment by directly controlling the state transitions, attempting to balance a fixed state-dependent cost and a certain smooth cost penalizing extreme control inputs. In the current paper, we consider an online setting where the state costs may change arbitrarily between consecutive rounds, and the learner only observes the costs at the end of each respective round. We are interested in constructing algorithms for the learner that guarantee small regret against the best stationary control policy chosen in full knowledge of the cost sequence. Our main result is showing that the smoothness of the control cost enables the simple algorithm of following the leader to achieve a regret of order $\log^2 T$ after $T$ rounds, vastly improving on the best known regret bound of order $T^{3/4}$ for this setting.
Gergely Neu and Vicen\c{c} G\'omez
null
1702.06341
null
null
Scalable Demand-Aware Recommendation
cs.LG
Recommendation for e-commerce with a mix of durable and nondurable goods has characteristics that distinguish it from the well-studied media recommendation problem. The demand for items is a combined effect of form utility and time utility, i.e., a product must both be intrinsically appealing to a consumer and the time must be right for purchase. In particular for durable goods, time utility is a function of inter-purchase duration within product category because consumers are unlikely to purchase two items in the same category in close temporal succession. Moreover, purchase data, in contrast to ratings data, is implicit with non-purchases not necessarily indicating dislike. Together, these issues give rise to the positive-unlabeled demand-aware recommendation problem that we pose via joint low-rank tensor completion and product category inter-purchase duration vector estimation. We further relax this problem and propose a highly scalable alternating minimization approach with which we can solve problems with millions of users and millions of items in a single thread. We also show superior prediction accuracies on multiple real-world data sets.
Jinfeng Yi, Cho-Jui Hsieh, Kush Varshney, Lijun Zhang, Yao Li
null
1702.06347
null
null
Interpreting Outliers: Localized Logistic Regression for Density Ratio Estimation
stat.ML cs.LG
We propose an inlier-based outlier detection method capable of both identifying the outliers and explaining why they are outliers, by identifying the outlier-specific features. Specifically, we employ an inlier-based outlier detection criterion, which uses the ratio of inlier and test probability densities as a measure of plausibility of being an outlier. For estimating the density ratio function, we propose a localized logistic regression algorithm. Thanks to the locality of the model, variable selection can be outlier-specific, and will help interpret why points are outliers in a high-dimensional space. Through synthetic experiments, we show that the proposed algorithm can successfully detect the important features for outliers. Moreover, we show that the proposed algorithm tends to outperform existing algorithms in benchmark datasets.
Makoto Yamada, Song Liu, Samuel Kaski
null
1702.06354
null
null
Negative-Unlabeled Tensor Factorization for Location Category Inference from Highly Inaccurate Mobility Data
cs.LG
Identifying significant location categories visited by mobile users is the key to a variety of applications. This is an extremely challenging task due to the possible deviation between the estimated location coordinate and the actual location, which could be on the order of kilometers. To estimate the actual location category more precisely, we propose a novel tensor factorization framework, through several key observations including the intrinsic correlations between users, to infer the most likely location categories within the location uncertainty circle. In addition, the proposed algorithm can also predict where users are even in the absence of location information. In order to efficiently solve the proposed framework, we propose a parameter-free and scalable optimization algorithm by effectively exploring the sparse and low-rank structure of the tensor. Our empirical studies show that the proposed algorithm is both efficient and effective: it can solve problems with millions of users and billions of location updates, and also provides superior prediction accuracies on real-world location updates and check-in data sets.
Jinfeng Yi, Qi Lei, Wesley Gifford, Ji Liu, Junchi Yan
null
1702.06362
null
null
Causal Inference on Multivariate and Mixed-Type Data
stat.ML cs.LG
Given data over the joint distribution of two random variables $X$ and $Y$, we consider the problem of inferring the most likely causal direction between $X$ and $Y$. In particular, we consider the general case where both $X$ and $Y$ may be univariate or multivariate, and of the same or mixed data types. We take an information theoretic approach, based on Kolmogorov complexity, from which it follows that first describing the data over cause and then that of effect given cause is shorter than the reverse direction. The ideal score is not computable, but can be approximated through the Minimum Description Length (MDL) principle. Based on MDL, we propose two scores, one for when both $X$ and $Y$ are of the same single data type, and one for when they are mixed-type. We model dependencies between $X$ and $Y$ using classification and regression trees. As inferring the optimal model is NP-hard, we propose Crack, a fast greedy algorithm to determine the most likely causal direction directly from the data. Empirical evaluation on a wide range of data shows that Crack reliably, and with high accuracy, infers the correct causal direction on both univariate and multivariate cause-effect pairs over both single and mixed-type data.
Alexander Marx and Jilles Vreeken
null
1702.06385
null
null
A GPU-Outperforming FPGA Accelerator Architecture for Binary Convolutional Neural Networks
cs.DC cs.AR cs.CV cs.LG
FPGA-based hardware accelerators for convolutional neural networks (CNNs) have obtained great attentions due to their higher energy efficiency than GPUs. However, it is challenging for FPGA-based solutions to achieve a higher throughput than GPU counterparts. In this paper, we demonstrate that FPGA acceleration can be a superior solution in terms of both throughput and energy efficiency when a CNN is trained with binary constraints on weights and activations. Specifically, we propose an optimized FPGA accelerator architecture tailored for bitwise convolution and normalization that features massive spatial parallelism with deep pipelines stages. A key advantage of the FPGA accelerator is that its performance is insensitive to data batch size, while the performance of GPU acceleration varies largely depending on the batch size of the data. Experiment results show that the proposed accelerator architecture for binary CNNs running on a Virtex-7 FPGA is 8.3x faster and 75x more energy-efficient than a Titan X GPU for processing online individual requests in small batch sizes. For processing static data in large batch sizes, the proposed solution is on a par with a Titan X GPU in terms of throughput while delivering 9.5x higher energy efficiency.
Yixing Li, Zichuan Liu, Kai Xu, Hao Yu and Fengbo Ren
null
1702.06392
null
null
A Unified Optimization View on Generalized Matching Pursuit and Frank-Wolfe
cs.LG stat.ML
Two of the most fundamental prototypes of greedy optimization are the matching pursuit and Frank-Wolfe algorithms. In this paper, we take a unified view on both classes of methods, leading to the first explicit convergence rates of matching pursuit methods in an optimization sense, for general sets of atoms. We derive sublinear ($1/t$) convergence for both classes on general smooth objectives, and linear convergence on strongly convex objectives, as well as a clear correspondence of algorithm variants. Our presented algorithms and rates are affine invariant, and do not need any incoherence or sparsity assumptions.
Francesco Locatello, Rajiv Khanna, Michael Tschannen, Martin Jaggi
null
1702.06457
null
null
Predicting non-linear dynamics by stable local learning in a recurrent spiking neural network
q-bio.NC cs.LG cs.NE cs.SY
Brains need to predict how the body reacts to motor commands. It is an open question how networks of spiking neurons can learn to reproduce the non-linear body dynamics caused by motor commands, using local, online and stable learning rules. Here, we present a supervised learning scheme for the feedforward and recurrent connections in a network of heterogeneous spiking neurons. The error in the output is fed back through fixed random connections with a negative gain, causing the network to follow the desired dynamics, while an online and local rule changes the weights. The rule for Feedback-based Online Local Learning Of Weights (FOLLOW) is local in the sense that weight changes depend on the presynaptic activity and the error signal projected onto the postsynaptic neuron. We provide examples of learning linear, non-linear and chaotic dynamics, as well as the dynamics of a two-link arm. Using the Lyapunov method, and under reasonable assumptions and approximations, we show that FOLLOW learning is stable uniformly, with the error going to zero asymptotically.
Aditya Gilra, Wulfram Gerstner
10.7554/eLife.28295
1702.06463
null
null
PixelNet: Representation of the pixels, by the pixels, and for the pixels
cs.CV cs.LG cs.RO
We explore design principles for general pixel-level prediction problems, from low-level edge detection to mid-level surface normal estimation to high-level semantic segmentation. Convolutional predictors, such as the fully-convolutional network (FCN), have achieved remarkable success by exploiting the spatial redundancy of neighboring pixels through convolutional processing. Though computationally efficient, we point out that such approaches are not statistically efficient during learning precisely because spatial redundancy limits the information learned from neighboring pixels. We demonstrate that stratified sampling of pixels allows one to (1) add diversity during batch updates, speeding up learning; (2) explore complex nonlinear predictors, improving accuracy; and (3) efficiently train state-of-the-art models tabula rasa (i.e., "from scratch") for diverse pixel-labeling tasks. Our single architecture produces state-of-the-art results for semantic segmentation on PASCAL-Context dataset, surface normal estimation on NYUDv2 depth dataset, and edge detection on BSDS.
Aayush Bansal, Xinlei Chen, Bryan Russell, Abhinav Gupta, Deva Ramanan
null
1702.06506
null
null
Stochastic Canonical Correlation Analysis
cs.LG stat.ML
We study the sample complexity of canonical correlation analysis (CCA), \ie, the number of samples needed to estimate the population canonical correlation and directions up to arbitrarily small error. With mild assumptions on the data distribution, we show that in order to achieve $\epsilon$-suboptimality in a properly defined measure of alignment between the estimated canonical directions and the population solution, we can solve the empirical objective exactly with $N(\epsilon, \Delta, \gamma)$ samples, where $\Delta$ is the singular value gap of the whitened cross-covariance matrix and $1/\gamma$ is an upper bound of the condition number of auto-covariance matrices. Moreover, we can achieve the same learning accuracy by drawing the same level of samples and solving the empirical objective approximately with a stochastic optimization algorithm; this algorithm is based on the shift-and-invert power iterations and only needs to process the dataset for $\mathcal{O}\left(\log \frac{1}{\epsilon} \right)$ passes. Finally, we show that, given an estimate of the canonical correlation, the streaming version of the shift-and-invert power iterations achieves the same learning accuracy with the same level of sample complexity, by processing the data only once.
Chao Gao, Dan Garber, Nathan Srebro, Jialei Wang, Weiran Wang
null
1702.06533
null
null
Active One-shot Learning
cs.LG
Recent advances in one-shot learning have produced models that can learn from a handful of labeled examples, for passive classification and regression tasks. This paper combines reinforcement learning with one-shot learning, allowing the model to decide, during classification, which examples are worth labeling. We introduce a classification task in which a stream of images are presented and, on each time step, a decision must be made to either predict a label or pay to receive the correct label. We present a recurrent neural network based action-value function, and demonstrate its ability to learn how and when to request labels. Through the choice of reward function, the model can achieve a higher prediction accuracy than a similar model on a purely supervised task, or trade prediction accuracy for fewer label requests.
Mark Woodward and Chelsea Finn
null
1702.06559
null
null
Exemplar-Centered Supervised Shallow Parametric Data Embedding
cs.LG stat.ML
Metric learning methods for dimensionality reduction in combination with k-Nearest Neighbors (kNN) have been extensively deployed in many classification, data embedding, and information retrieval applications. However, most of these approaches involve pairwise training data comparisons, and thus have quadratic computational complexity with respect to the size of training set, preventing them from scaling to fairly big datasets. Moreover, during testing, comparing test data against all the training data points is also expensive in terms of both computational cost and resources required. Furthermore, previous metrics are either too constrained or too expressive to be well learned. To effectively solve these issues, we present an exemplar-centered supervised shallow parametric data embedding model, using a Maximally Collapsing Metric Learning (MCML) objective. Our strategy learns a shallow high-order parametric embedding function and compares training/test data only with learned or precomputed exemplars, resulting in a cost function with linear computational complexity for both training and testing. We also empirically demonstrate, using several benchmark datasets, that for classification in two-dimensional embedding space, our approach not only gains speedup of kNN by hundreds of times, but also outperforms state-of-the-art supervised embedding approaches.
Martin Renqiang Min, Hongyu Guo, Dongjin Song
null
1702.06602
null
null
Counterfactual Control for Free from Generative Models
cs.LG stat.ML
We introduce a method by which a generative model learning the joint distribution between actions and future states can be used to automatically infer a control scheme for any desired reward function, which may be altered on the fly without retraining the model. In this method, the problem of action selection is reduced to one of gradient descent on the latent space of the generative model, with the model itself providing the means of evaluating outcomes and finding the gradient, much like how the reward network in Deep Q-Networks (DQN) provides gradient information for the action generator. Unlike DQN or Actor-Critic, which are conditional models for a specific reward, using a generative model of the full joint distribution permits the reward to be changed on the fly. In addition, the generated futures can be inspected to gain insight in to what the network 'thinks' will happen, and to what went wrong when the outcomes deviate from prediction.
Nicholas Guttenberg, Yen Yu, Ryota Kanai
null
1702.06676
null
null
Ensembles of Randomized Time Series Shapelets Provide Improved Accuracy while Reducing Computational Costs
cs.LG
Shapelets are discriminative time series subsequences that allow generation of interpretable classification models, which provide faster and generally better classification than the nearest neighbor approach. However, the shapelet discovery process requires the evaluation of all possible subsequences of all time series in the training set, making it extremely computation intensive. Consequently, shapelet discovery for large time series datasets quickly becomes intractable. A number of improvements have been proposed to reduce the training time. These techniques use approximation or discretization and often lead to reduced classification accuracy compared to the exact method. We are proposing the use of ensembles of shapelet-based classifiers obtained using random sampling of the shapelet candidates. Using random sampling reduces the number of evaluated candidates and consequently the required computational cost, while the classification accuracy of the resulting models is also not significantly different than that of the exact algorithm. The combination of randomized classifiers rectifies the inaccuracies of individual models because of the diversity of the solutions. Based on the experiments performed, it is shown that the proposed approach of using an ensemble of inexpensive classifiers provides better classification accuracy compared to the exact method at a significantly lesser computational cost.
Atif Raza and Stefan Kramer
null
1702.06712
null
null
Memory Matching Networks for Genomic Sequence Classification
cs.LG q-bio.GN stat.ML
When analyzing the genome, researchers have discovered that proteins bind to DNA based on certain patterns of the DNA sequence known as "motifs". However, it is difficult to manually construct motifs due to their complexity. Recently, externally learned memory models have proven to be effective methods for reasoning over inputs and supporting sets. In this work, we present memory matching networks (MMN) for classifying DNA sequences as protein binding sites. Our model learns a memory bank of encoded motifs, which are dynamic memory modules, and then matches a new test sequence to each of the motifs to classify the sequence as a binding or nonbinding site.
Jack Lanchantin, Ritambhara Singh, Yanjun Qi
null
1702.0676
null
null
Style Transfer Generative Adversarial Networks: Learning to Play Chess Differently
cs.LG
The idea of style transfer has largely only been explored in image-based tasks, which we attribute in part to the specific nature of loss functions used for style transfer. We propose a general formulation of style transfer as an extension of generative adversarial networks, by using a discriminator to regularize a generator with an otherwise separate loss function. We apply our approach to the task of learning to play chess in the style of a specific player, and present empirical evidence for the viability of our approach.
Muthuraman Chidambaram, Yanjun Qi
null
1702.06762
null
null
DeepCloak: Masking Deep Neural Network Models for Robustness Against Adversarial Samples
cs.LG cs.AI cs.CR
Recent studies have shown that deep neural networks (DNN) are vulnerable to adversarial samples: maliciously-perturbed samples crafted to yield incorrect model outputs. Such attacks can severely undermine DNN systems, particularly in security-sensitive settings. It was observed that an adversary could easily generate adversarial samples by making a small perturbation on irrelevant feature dimensions that are unnecessary for the current classification task. To overcome this problem, we introduce a defensive mechanism called DeepCloak. By identifying and removing unnecessary features in a DNN model, DeepCloak limits the capacity an attacker can use generating adversarial samples and therefore increase the robustness against such inputs. Comparing with other defensive approaches, DeepCloak is easy to implement and computationally efficient. Experimental results show that DeepCloak can increase the performance of state-of-the-art DNN models against adversarial samples.
Ji Gao, Beilun Wang, Zeming Lin, Weilin Xu, Yanjun Qi
null
1702.06763
null
null
Causal Inference by Stochastic Complexity
cs.LG cs.AI
The algorithmic Markov condition states that the most likely causal direction between two random variables X and Y can be identified as that direction with the lowest Kolmogorov complexity. Due to the halting problem, however, this notion is not computable. We hence propose to do causal inference by stochastic complexity. That is, we propose to approximate Kolmogorov complexity via the Minimum Description Length (MDL) principle, using a score that is mini-max optimal with regard to the model class under consideration. This means that even in an adversarial setting, such as when the true distribution is not in this class, we still obtain the optimal encoding for the data relative to the class. We instantiate this framework, which we call CISC, for pairs of univariate discrete variables, using the class of multinomial distributions. Experiments show that CISC is highly accurate on synthetic, benchmark, as well as real-world data, outperforming the state of the art by a margin, and scales extremely well with regard to sample and domain sizes.
Kailash Budhathoki and Jilles Vreeken
null
1702.06776
null
null
Stochastic Approximation for Canonical Correlation Analysis
cs.LG stat.ML
We propose novel first-order stochastic approximation algorithms for canonical correlation analysis (CCA). Algorithms presented are instances of inexact matrix stochastic gradient (MSG) and inexact matrix exponentiated gradient (MEG), and achieve $\epsilon$-suboptimality in the population objective in $\operatorname{poly}(\frac{1}{\epsilon})$ iterations. We also consider practical variants of the proposed algorithms and compare them with other methods for CCA both theoretically and empirically.
Raman Arora and Teodor V. Marinov and Poorya Mianjy and Nathan Srebro
null
1702.06818
null
null
Distributed Representations of Signed Networks
stat.ML cs.LG cs.SI
Recent successes in word embedding and document embedding have motivated researchers to explore similar representations for networks and to use such representations for tasks such as edge prediction, node label prediction, and community detection. Such network embedding methods are largely focused on finding distributed representations for unsigned networks and are unable to discover embeddings that respect polarities inherent in edges. We propose SIGNet, a fast scalable embedding method suitable for signed networks. Our proposed objective function aims to carefully model the social structure implicit in signed networks by reinforcing the principles of social balance theory. Our method builds upon the traditional word2vec family of embedding approaches and adds a new targeted node sampling strategy to maintain structural balance in higher-order neighborhoods. We demonstrate the superiority of SIGNet over state-of-the-art methods proposed for both signed and unsigned networks on several real world datasets from different domains. In particular, SIGNet offers an approach to generate a richer vocabulary of features of signed networks to support representation and reasoning.
Mohammad Raihanul Islam and B. Aditya Prakash and Naren Ramakrishnan
10.1007/978-3-319-93037-4_13
1702.06819
null
null
Adversarial examples for generative models
stat.ML cs.LG
We explore methods of producing adversarial examples on deep generative models such as the variational autoencoder (VAE) and the VAE-GAN. Deep learning architectures are known to be vulnerable to adversarial examples, but previous work has focused on the application of adversarial examples to classification tasks. Deep generative models have recently become popular due to their ability to model input data distributions and generate realistic examples from those distributions. We present three classes of attacks on the VAE and VAE-GAN architectures and demonstrate them against networks trained on MNIST, SVHN and CelebA. Our first attack leverages classification-based adversaries by attaching a classifier to the trained encoder of the target generative model, which can then be used to indirectly manipulate the latent representation. Our second attack directly uses the VAE loss function to generate a target reconstruction image from the adversarial example. Our third attack moves beyond relying on classification or the standard loss for the gradient and directly optimizes against differences in source and target latent representations. We also motivate why an attacker might be interested in deploying such techniques against a target generative network.
Jernej Kos, Ian Fischer, Dawn Song
null
1702.06832
null
null
Scene Recognition by Combining Local and Global Image Descriptors
cs.CV cs.LG
Object recognition is an important problem in computer vision, having diverse applications. In this work, we construct an end-to-end scene recognition pipeline consisting of feature extraction, encoding, pooling and classification. Our approach simultaneously utilize global feature descriptors as well as local feature descriptors from images, to form a hybrid feature descriptor corresponding to each image. We utilize DAISY features associated with key points within images as our local feature descriptor and histogram of oriented gradients (HOG) corresponding to an entire image as a global descriptor. We make use of a bag-of-visual-words encoding and apply Mini- Batch K-Means algorithm to reduce the complexity of our feature encoding scheme. A 2-level pooling procedure is used to combine DAISY and HOG features corresponding to each image. Finally, we experiment with a multi-class SVM classifier with several kernels, in a cross-validation setting, and tabulate our results on the fifteen scene categories dataset. The average accuracy of our model was 76.4% in the case of a 40%-60% random split of images into training and testing datasets respectively. The primary objective of this work is to clearly outline the practical implementation of a basic screne-recognition pipeline having a reasonable accuracy, in python, using open-source libraries. A full implementation of the proposed model is available in our github repository.
Jobin Wilson and Muhammad Arif
null
1702.0685
null
null
Robustness to Adversarial Examples through an Ensemble of Specialists
cs.NE cs.LG
We are proposing to use an ensemble of diverse specialists, where speciality is defined according to the confusion matrix. Indeed, we observed that for adversarial instances originating from a given class, labeling tend to be done into a small subset of (incorrect) classes. Therefore, we argue that an ensemble of specialists should be better able to identify and reject fooling instances, with a high entropy (i.e., disagreement) over the decisions in the presence of adversaries. Experimental results obtained confirm that interpretation, opening a way to make the system more robust to adversarial examples through a rejection mechanism, rather than trying to classify them properly at any cost.
Mahdieh Abbasi and Christian Gagn\'e
null
1702.06856
null
null
On the Power of Truncated SVD for General High-rank Matrix Estimation Problems
stat.ML cs.LG math.NA
We show that given an estimate $\widehat{A}$ that is close to a general high-rank positive semi-definite (PSD) matrix $A$ in spectral norm (i.e., $\|\widehat{A}-A\|_2 \leq \delta$), the simple truncated SVD of $\widehat{A}$ produces a multiplicative approximation of $A$ in Frobenius norm. This observation leads to many interesting results on general high-rank matrix estimation problems, which we briefly summarize below ($A$ is an $n\times n$ high-rank PSD matrix and $A_k$ is the best rank-$k$ approximation of $A$): (1) High-rank matrix completion: By observing $\Omega(\frac{n\max\{\epsilon^{-4},k^2\}\mu_0^2\|A\|_F^2\log n}{\sigma_{k+1}(A)^2})$ elements of $A$ where $\sigma_{k+1}\left(A\right)$ is the $\left(k+1\right)$-th singular value of $A$ and $\mu_0$ is the incoherence, the truncated SVD on a zero-filled matrix satisfies $\|\widehat{A}_k-A\|_F \leq (1+O(\epsilon))\|A-A_k\|_F$ with high probability. (2)High-rank matrix de-noising: Let $\widehat{A}=A+E$ where $E$ is a Gaussian random noise matrix with zero mean and $\nu^2/n$ variance on each entry. Then the truncated SVD of $\widehat{A}$ satisfies $\|\widehat{A}_k-A\|_F \leq (1+O(\sqrt{\nu/\sigma_{k+1}(A)}))\|A-A_k\|_F + O(\sqrt{k}\nu)$. (3) Low-rank Estimation of high-dimensional covariance: Given $N$ i.i.d.~samples $X_1,\cdots,X_N\sim\mathcal N_n(0,A)$, can we estimate $A$ with a relative-error Frobenius norm bound? We show that if $N = \Omega\left(n\max\{\epsilon^{-4},k^2\}\gamma_k(A)^2\log N\right)$ for $\gamma_k(A)=\sigma_1(A)/\sigma_{k+1}(A)$, then $\|\widehat{A}_k-A\|_F \leq (1+O(\epsilon))\|A-A_k\|_F$ with high probability, where $\widehat{A}=\frac{1}{N}\sum_{i=1}^N{X_iX_i^\top}$ is the sample covariance.
Simon S. Du and Yining Wang and Aarti Singh
null
1702.06861
null
null
Knowledge Graph Completion via Complex Tensor Factorization
cs.AI cs.LG math.SP stat.ML
In statistical relational learning, knowledge graph completion deals with automatically understanding the structure of large knowledge graphs---labeled directed graphs---and predicting missing relationships---labeled edges. State-of-the-art embedding models propose different trade-offs between modeling expressiveness, and time and space complexity. We reconcile both expressiveness and complexity through the use of complex-valued embeddings and explore the link between such complex-valued embeddings and unitary diagonalization. We corroborate our approach theoretically and show that all real square matrices---thus all possible relation/adjacency matrices---are the real part of some unitarily diagonalizable matrix. This results opens the door to a lot of other applications of square matrices factorization. Our approach based on complex embeddings is arguably simple, as it only involves a Hermitian dot product, the complex counterpart of the standard dot product between real vectors, whereas other methods resort to more and more complicated composition functions to increase their expressiveness. The proposed complex embeddings are scalable to large data sets as it remains linear in both space and time, while consistently outperforming alternative approaches on standard link prediction benchmarks.
Th\'eo Trouillon, Christopher R. Dance, Johannes Welbl, Sebastian Riedel, \'Eric Gaussier, Guillaume Bouchard
null
1702.06879
null
null
Learning Deep Features via Congenerous Cosine Loss for Person Recognition
cs.CV cs.LG stat.ML
Person recognition aims at recognizing the same identity across time and space with complicated scenes and similar appearance. In this paper, we propose a novel method to address this task by training a network to obtain robust and representative features. The intuition is that we directly compare and optimize the cosine distance between two features - enlarging inter-class distinction as well as alleviating inner-class variance. We propose a congenerous cosine loss by minimizing the cosine distance between samples and their cluster centroid in a cooperative way. Such a design reduces the complexity and could be implemented via softmax with normalized inputs. Our method also differs from previous work in person recognition that we do not conduct a second training on the test subset. The identity of a person is determined by measuring the similarity from several body regions in the reference set. Experimental results show that the proposed approach achieves better classification accuracy against previous state-of-the-arts.
Yu Liu and Hongyang Li and Xiaogang Wang
null
1702.0689
null
null
liquidSVM: A Fast and Versatile SVM package
stat.ML cs.LG
liquidSVM is a package written in C++ that provides SVM-type solvers for various classification and regression tasks. Because of a fully integrated hyper-parameter selection, very carefully implemented solvers, multi-threading and GPU support, and several built-in data decomposition strategies it provides unprecedented speed for small training sizes as well as for data sets of tens of millions of samples. Besides the C++ API and a command line interface, bindings to R, MATLAB, Java, Python, and Spark are available. We present a brief description of the package and report experimental comparisons to other SVM packages.
Ingo Steinwart and Philipp Thomann
null
1702.06899
null
null
Training a Subsampling Mechanism in Expectation
cs.LG
We describe a mechanism for subsampling sequences and show how to compute its expected output so that it can be trained with standard backpropagation. We test this approach on a simple toy problem and discuss its shortcomings.
Colin Raffel and Dieterich Lawson
null
1702.06914
null
null
Fast Rates for Bandit Optimization with Upper-Confidence Frank-Wolfe
cs.LG math.OC stat.ML
We consider the problem of bandit optimization, inspired by stochastic optimization and online learning problems with bandit feedback. In this problem, the objective is to minimize a global loss function of all the actions, not necessarily a cumulative loss. This framework allows us to study a very general class of problems, with applications in statistics, machine learning, and other fields. To solve this problem, we analyze the Upper-Confidence Frank-Wolfe algorithm, inspired by techniques for bandits and convex optimization. We give theoretical guarantees for the performance of this algorithm over various classes of functions, and discuss the optimality of these results.
Quentin Berthet, Vianney Perchet
null
1702.06917
null
null
Distributed Representation of Subgraphs
cs.SI cs.LG stat.ML
Network embeddings have become very popular in learning effective feature representations of networks. Motivated by the recent successes of embeddings in natural language processing, researchers have tried to find network embeddings in order to exploit machine learning algorithms for mining tasks like node classification and edge prediction. However, most of the work focuses on finding distributed representations of nodes, which are inherently ill-suited to tasks such as community detection which are intuitively dependent on subgraphs. Here, we propose sub2vec, an unsupervised scalable algorithm to learn feature representations of arbitrary subgraphs. We provide means to characterize similarties between subgraphs and provide theoretical analysis of sub2vec and demonstrate that it preserves the so-called local proximity. We also highlight the usability of sub2vec by leveraging it for network mining tasks, like community detection. We show that sub2vec gets significant gains over state-of-the-art methods and node-embedding methods. In particular, sub2vec offers an approach to generate a richer vocabulary of features of subgraphs to support representation and reasoning.
Bijaya Adhikari, Yao Zhang, Naren Ramakrishnan, and B. Aditya Prakash
null
1702.06921
null
null
Regularizing Face Verification Nets For Pain Intensity Regression
cs.CV cs.AI cs.LG cs.MM
Limited labeled data are available for the research of estimating facial expression intensities. For instance, the ability to train deep networks for automated pain assessment is limited by small datasets with labels of patient-reported pain intensities. Fortunately, fine-tuning from a data-extensive pre-trained domain, such as face verification, can alleviate this problem. In this paper, we propose a network that fine-tunes a state-of-the-art face verification network using a regularized regression loss and additional data with expression labels. In this way, the expression intensity regression task can benefit from the rich feature representations trained on a huge amount of data for face verification. The proposed regularized deep regressor is applied to estimate the pain expression intensity and verified on the widely-used UNBC-McMaster Shoulder-Pain dataset, achieving the state-of-the-art performance. A weighted evaluation metric is also proposed to address the imbalance issue of different pain intensities.
Feng Wang, Xiang Xiang, Chang Liu, Trac D. Tran, Austin Reiter, Gregory D. Hager, Harry Quon, Jian Cheng, Alan L. Yuille
10.13140/RG.2.2.20841.49765
1702.06925
null
null
An Algebraic Formalization of Forward and Forward-backward Algorithms
cs.LG
In this paper, we propose an algebraic formalization of the two important classes of dynamic programming algorithms called forward and forward-backward algorithms. They are generalized extensively in this study so that a wide range of other existing algorithms is subsumed. Forward algorithms generalized in this study subsume the ordinary forward algorithm on trellises for sequence labeling, the inside algorithm on derivation forests for CYK parsing, a unidirectional message passing on acyclic factor graphs, the forward mode of automatic differentiation on computation graphs with addition and multiplication, and so on. In addition, we reveal algebraic structures underlying complicated computation with forward algorithms. By the aid of the revealed algebraic structures, we also propose a systematic framework to design complicated variants of forward algorithms. Forward-backward algorithms generalized in this study subsume the ordinary forward-backward algorithm on trellises for sequence labeling, the inside-outside algorithm on derivation forests for CYK parsing, the sum-product algorithm on acyclic factor graphs, the reverse mode of automatic differentiation (a.k.a. back propagation) on computation graphs with addition and multiplication, and so on. We also propose an algebraic characterization of what can be computed by forward-backward algorithms and elucidate the relationship between forward and forward-backward algorithms.
Ai Azuma, Masashi Shimbo, Yuji Matsumoto
null
1702.06941
null
null
Tuple-oriented Compression for Large-scale Mini-batch Stochastic Gradient Descent
cs.LG cs.DB stat.ML
Data compression is a popular technique for improving the efficiency of data processing workloads such as SQL queries and more recently, machine learning (ML) with classical batch gradient methods. But the efficacy of such ideas for mini-batch stochastic gradient descent (MGD), arguably the workhorse algorithm of modern ML, is an open question. MGD's unique data access pattern renders prior art, including those designed for batch gradient methods, less effective. We fill this crucial research gap by proposing a new lossless compression scheme we call tuple-oriented compression (TOC) that is inspired by an unlikely source, the string/text compression scheme Lempel-Ziv-Welch, but tailored to MGD in a way that preserves tuple boundaries within mini-batches. We then present a suite of novel compressed matrix operation execution techniques tailored to the TOC compression scheme that operate directly over the compressed data representation and avoid decompression overheads. An extensive empirical evaluation with real-world datasets shows that TOC consistently achieves substantial compression ratios by up to 51x and reduces runtimes for MGD workloads by up to 10.2x in popular ML systems.
Fengan Li, Lingjiao Chen, Yijing Zeng, Arun Kumar, Jeffrey F. Naughton, Jignesh M. Patel, Xi Wu
10.1145/3299869.3300070
1702.06943
null
null
Approximations of the Restless Bandit Problem
math.ST cs.LG math.PR stat.ML stat.TH
The multi-armed restless bandit problem is studied in the case where the pay-off distributions are stationary $\varphi$-mixing. This version of the problem provides a more realistic model for most real-world applications, but cannot be optimally solved in practice, since it is known to be PSPACE-hard. The objective of this paper is to characterize a sub-class of the problem where {\em good} approximate solutions can be found using tractable approaches. Specifically, it is shown that under some conditions on the $\varphi$-mixing coefficients, a modified version of UCB can prove effective. The main challenge is that, unlike in the i.i.d. setting, the distributions of the sampled pay-offs may not have the same characteristics as those of the original bandit arms. In particular, the $\varphi$-mixing property does not necessarily carry over. This is overcome by carefully controlling the effect of a sampling policy on the pay-off distributions. Some of the proof techniques developed in this paper can be more generally used in the context of online sampling under dependence. Proposed algorithms are accompanied with corresponding regret analysis.
Steffen Grunewalder and Azadeh Khaleghi
null
1702.06972
null
null
Heavy-Tailed Analogues of the Covariance Matrix for ICA
cs.LG stat.ML
Independent Component Analysis (ICA) is the problem of learning a square matrix $A$, given samples of $X=AS$, where $S$ is a random vector with independent coordinates. Most existing algorithms are provably efficient only when each $S_i$ has finite and moderately valued fourth moment. However, there are practical applications where this assumption need not be true, such as speech and finance. Algorithms have been proposed for heavy-tailed ICA, but they are not practical, using random walks and the full power of the ellipsoid algorithm multiple times. The main contributions of this paper are: (1) A practical algorithm for heavy-tailed ICA that we call HTICA. We provide theoretical guarantees and show that it outperforms other algorithms in some heavy-tailed regimes, both on real and synthetic data. Like the current state-of-the-art, the new algorithm is based on the centroid body (a first moment analogue of the covariance matrix). Unlike the state-of-the-art, our algorithm is practically efficient. To achieve this, we use explicit analytic representations of the centroid body, which bypasses the use of the ellipsoid method and random walks. (2) We study how heavy tails affect different ICA algorithms, including HTICA. Somewhat surprisingly, we show that some algorithms that use the covariance matrix or higher moments can successfully solve a range of ICA instances with infinite second moment. We study this theoretically and experimentally, with both synthetic and real-world heavy-tailed data.
Joseph Anderson and Navin Goyal and Anupama Nandi and Luis Rademacher
null
1702.06976
null
null
On Polynomial Time Methods for Exact Low Rank Tensor Completion
stat.ML cs.IT cs.LG math.IT
In this paper, we investigate the sample size requirement for exact recovery of a high order tensor of low rank from a subset of its entries. We show that a gradient descent algorithm with initial value obtained from a spectral method can, in particular, reconstruct a ${d\times d\times d}$ tensor of multilinear ranks $(r,r,r)$ with high probability from as few as $O(r^{7/2}d^{3/2}\log^{7/2}d+r^7d\log^6d)$ entries. In the case when the ranks $r=O(1)$, our sample size requirement matches those for nuclear norm minimization (Yuan and Zhang, 2016a), or alternating least squares assuming orthogonal decomposability (Jain and Oh, 2014). Unlike these earlier approaches, however, our method is efficient to compute, easy to implement, and does not impose extra structures on the tensor. Numerical results are presented to further demonstrate the merits of the proposed approach.
Dong Xia and Ming Yuan
null
1702.0698
null
null
Large-Scale Stochastic Learning using GPUs
cs.LG cs.DC
In this work we propose an accelerated stochastic learning system for very large-scale applications. Acceleration is achieved by mapping the training algorithm onto massively parallel processors: we demonstrate a parallel, asynchronous GPU implementation of the widely used stochastic coordinate descent/ascent algorithm that can provide up to 35x speed-up over a sequential CPU implementation. In order to train on very large datasets that do not fit inside the memory of a single GPU, we then consider techniques for distributed stochastic learning. We propose a novel method for optimally aggregating model updates from worker nodes when the training data is distributed either by example or by feature. Using this technique, we demonstrate that one can scale out stochastic learning across up to 8 worker nodes without any significant loss of training time. Finally, we combine GPU acceleration with the optimized distributed method to train on a dataset consisting of 200 million training examples and 75 million features. We show by scaling out across 4 GPUs, one can attain a high degree of training accuracy in around 4 seconds: a 20x speed-up in training time compared to a multi-threaded, distributed implementation across 4 CPUs.
Thomas Parnell, Celestine D\"unner, Kubilay Atasu, Manolis Sifalakis and Haris Pozidis
null
1702.07005
null
null
Learning Hawkes Processes from Short Doubly-Censored Event Sequences
cs.LG math.PR stat.ML
Many real-world applications require robust algorithms to learn point processes based on a type of incomplete data --- the so-called short doubly-censored (SDC) event sequences. We study this critical problem of quantitative asynchronous event sequence analysis under the framework of Hawkes processes by leveraging the idea of data synthesis. Given SDC event sequences observed in a variety of time intervals, we propose a sampling-stitching data synthesis method --- sampling predecessors and successors for each SDC event sequence from potential candidates and stitching them together to synthesize long training sequences. The rationality and the feasibility of our method are discussed in terms of arguments based on likelihood. Experiments on both synthetic and real-world data demonstrate that the proposed data synthesis method improves learning results indeed for both time-invariant and time-varying Hawkes processes.
Hongteng Xu, Dixin Luo, Hongyuan Zha
null
1702.07013
null
null
One Size Fits Many: Column Bundle for Multi-X Learning
stat.ML cs.LG
Much recent machine learning research has been directed towards leveraging shared statistics among labels, instances and data views, commonly referred to as multi-label, multi-instance and multi-view learning. The underlying premises are that there exist correlations among input parts and among output targets, and the predictive performance would increase when the correlations are incorporated. In this paper, we propose Column Bundle (CLB), a novel deep neural network for capturing the shared statistics in data. CLB is generic that the same architecture can be applied for various types of shared statistics by changing only input and output handling. CLB is capable of scaling to thousands of input parts and output labels by avoiding explicit modeling of pairwise relations. We evaluate CLB on different types of data: (a) multi-label, (b) multi-view, (c) multi-view/multi-label and (d) multi-instance. CLB demonstrates a comparable and competitive performance in all datasets against state-of-the-art methods designed specifically for each type.
Trang Pham, Truyen Tran, Svetha Venkatesh
null
1702.07021
null
null
On the ability of neural nets to express distributions
cs.LG
Deep neural nets have caused a revolution in many classification tasks. A related ongoing revolution -- also theoretically not understood -- concerns their ability to serve as generative models for complicated types of data such as images and texts. These models are trained using ideas like variational autoencoders and Generative Adversarial Networks. We take a first cut at explaining the expressivity of multilayer nets by giving a sufficient criterion for a function to be approximable by a neural network with $n$ hidden layers. A key ingredient is Barron's Theorem \cite{Barron1993}, which gives a Fourier criterion for approximability of a function by a neural network with 1 hidden layer. We show that a composition of $n$ functions which satisfy certain Fourier conditions ("Barron functions") can be approximated by a $n+1$-layer neural network. For probability distributions, this translates into a criterion for a probability distribution to be approximable in Wasserstein distance -- a natural metric on probability distributions -- by a neural network applied to a fixed base distribution (e.g., multivariate gaussian). Building up recent lower bound work, we also give an example function that shows that composition of Barron functions is more expressive than Barron functions alone.
Holden Lee, Rong Ge, Tengyu Ma, Andrej Risteski, Sanjeev Arora
null
1702.07028
null
null
Learning Model Predictive Control for Iterative Tasks: A Computationally Efficient Approach for Linear System
math.OC cs.LG
A Learning Model Predictive Controller (LMPC) for linear system in presented. The proposed controller is an extension of the LMPC [1] and it aims to decrease the computational burden. The control scheme is reference-free and is able to improve its performance by learning from previous iterations. A convex safe set and a terminal cost function are used in order to guarantee recursive feasibility and non-increasing performance at each iteration. The paper presents the control design approach, and shows how to recursively construct the convex terminal set and the terminal cost from state and input trajectories of previous iterations. Simulation results show the effectiveness of the proposed control logic.
Ugo Rosolia and Francesco Borrelli
null
1702.07064
null
null
Scalable Inference for Nested Chinese Restaurant Process Topic Models
stat.ML cs.DC cs.IR cs.LG
Nested Chinese Restaurant Process (nCRP) topic models are powerful nonparametric Bayesian methods to extract a topic hierarchy from a given text corpus, where the hierarchical structure is automatically determined by the data. Hierarchical Latent Dirichlet Allocation (hLDA) is a popular instance of nCRP topic models. However, hLDA has only been evaluated at small scale, because the existing collapsed Gibbs sampling and instantiated weight variational inference algorithms either are not scalable or sacrifice inference quality with mean-field assumptions. Moreover, an efficient distributed implementation of the data structures, such as dynamically growing count matrices and trees, is challenging. In this paper, we propose a novel partially collapsed Gibbs sampling (PCGS) algorithm, which combines the advantages of collapsed and instantiated weight algorithms to achieve good scalability as well as high model quality. An initialization strategy is presented to further improve the model quality. Finally, we propose an efficient distributed implementation of PCGS through vectorization, pre-processing, and a careful design of the concurrent data structures and communication strategy. Empirical studies show that our algorithm is 111 times more efficient than the previous open-source implementation for hLDA, with comparable or even better model quality. Our distributed implementation can extract 1,722 topics from a 131-million-document corpus with 28 billion tokens, which is 4-5 orders of magnitude larger than the previous largest corpus, with 50 machines in 7 hours.
Jianfei Chen, Jun Zhu, Jie Lu, Shixia Liu
null
1702.07083
null
null
Adaptive Bidirectional Backpropagation: Towards Biologically Plausible Error Signal Transmission in Neural Networks
cs.NE cs.LG
The back-propagation (BP) algorithm has been considered the de-facto method for training deep neural networks. It back-propagates errors from the output layer to the hidden layers in an exact manner using the transpose of the feedforward weights. However, it has been argued that this is not biologically plausible because back-propagating error signals with the exact incoming weights are not considered possible in biological neural systems. In this work, we propose a biologically plausible paradigm of neural architecture based on related literature in neuroscience and asymmetric BP-like methods. Specifically, we propose two bidirectional learning algorithms with trainable feedforward and feedback weights. The feedforward weights are used to relay activations from the inputs to target outputs. The feedback weights pass the error signals from the output layer to the hidden layers. Different from other asymmetric BP-like methods, the feedback weights are also plastic in our framework and are trained to approximate the forward activations. Preliminary results show that our models outperform other asymmetric BP-like methods on the MNIST and the CIFAR-10 datasets.
Hongyin Luo, Jie Fu, James Glass
null
1702.07097
null
null
Discriminating Traces with Time
cs.PL cs.CR cs.FL cs.LG cs.SE
What properties about the internals of a program explain the possible differences in its overall running time for different inputs? In this paper, we propose a formal framework for considering this question we dub trace-set discrimination. We show that even though the algorithmic problem of computing maximum likelihood discriminants is NP-hard, approaches based on integer linear programming (ILP) and decision tree learning can be useful in zeroing-in on the program internals. On a set of Java benchmarks, we find that compactly-represented decision trees scalably discriminate with high accuracy---more scalably than maximum likelihood discriminants and with comparable accuracy. We demonstrate on three larger case studies how decision-tree discriminants produced by our tool are useful for debugging timing side-channel vulnerabilities (i.e., where a malicious observer infers secrets simply from passively watching execution times) and availability vulnerabilities.
Saeid Tizpaz-Niari, Pavol Cerny, Bor-Yuh Evan Chang, Sriram Sankaranarayanan, Ashutosh Trivedi
null
1702.07103
null
null
Consistent On-Line Off-Policy Evaluation
stat.ML cs.LG
The problem of on-line off-policy evaluation (OPE) has been actively studied in the last decade due to its importance both as a stand-alone problem and as a module in a policy improvement scheme. However, most Temporal Difference (TD) based solutions ignore the discrepancy between the stationary distribution of the behavior and target policies and its effect on the convergence limit when function approximation is applied. In this paper we propose the Consistent Off-Policy Temporal Difference (COP-TD($\lambda$, $\beta$)) algorithm that addresses this issue and reduces this bias at some computational expense. We show that COP-TD($\lambda$, $\beta$) can be designed to converge to the same value that would have been obtained by using on-policy TD($\lambda$) with the target policy. Subsequently, the proposed scheme leads to a related and promising heuristic we call log-COP-TD($\lambda$, $\beta$). Both algorithms have favorable empirical results to the current state of the art on-line OPE algorithms. Finally, our formulation sheds some new light on the recently proposed Emphatic TD learning.
Assaf Hallak and Shie Mannor
null
1702.07121
null
null
Automatic Representation for Lifetime Value Recommender Systems
stat.ML cs.LG
Many modern commercial sites employ recommender systems to propose relevant content to users. While most systems are focused on maximizing the immediate gain (clicks, purchases or ratings), a better notion of success would be the lifetime value (LTV) of the user-system interaction. The LTV approach considers the future implications of the item recommendation, and seeks to maximize the cumulative gain over time. The Reinforcement Learning (RL) framework is the standard formulation for optimizing cumulative successes over time. However, RL is rarely used in practice due to its associated representation, optimization and validation techniques which can be complex. In this paper we propose a new architecture for combining RL with recommendation systems which obviates the need for hand-tuned features, thus automating the state-space representation construction process. We analyze the practical difficulties in this formulation and test our solutions on batch off-line real-world recommendation data.
Assaf Hallak, Yishay Mansour and Elad Yom-Tov
null
1702.07125
null
null
Stability of Topic Modeling via Matrix Factorization
cs.IR cs.CL cs.LG stat.ML
Topic models can provide us with an insight into the underlying latent structure of a large corpus of documents. A range of methods have been proposed in the literature, including probabilistic topic models and techniques based on matrix factorization. However, in both cases, standard implementations rely on stochastic elements in their initialization phase, which can potentially lead to different results being generated on the same corpus when using the same parameter values. This corresponds to the concept of "instability" which has previously been studied in the context of $k$-means clustering. In many applications of topic modeling, this problem of instability is not considered and topic models are treated as being definitive, even though the results may change considerably if the initialization process is altered. In this paper we demonstrate the inherent instability of popular topic modeling approaches, using a number of new measures to assess stability. To address this issue in the context of matrix factorization for topic modeling, we propose the use of ensemble learning strategies. Based on experiments performed on annotated text corpora, we show that a K-Fold ensemble strategy, combining both ensembles and structured initialization, can significantly reduce instability, while simultaneously yielding more accurate topic models.
Mark Belford and Brian Mac Namee and Derek Greene
null
1702.07186
null
null
A minimax and asymptotically optimal algorithm for stochastic bandits
stat.ML cs.LG math.ST stat.TH
We propose the kl-UCB ++ algorithm for regret minimization in stochastic bandit models with exponential families of distributions. We prove that it is simultaneously asymptotically optimal (in the sense of Lai and Robbins' lower bound) and minimax optimal. This is the first algorithm proved to enjoy these two properties at the same time. This work thus merges two different lines of research with simple and clear proofs.
Pierre M\'enard (1), Aur\'elien Garivier (1) ((1) IMT)
null
1702.07211
null
null
Rotting Bandits
stat.ML cs.LG
The Multi-Armed Bandits (MAB) framework highlights the tension between acquiring new knowledge (Exploration) and leveraging available knowledge (Exploitation). In the classical MAB problem, a decision maker must choose an arm at each time step, upon which she receives a reward. The decision maker's objective is to maximize her cumulative expected reward over the time horizon. The MAB problem has been studied extensively, specifically under the assumption of the arms' rewards distributions being stationary, or quasi-stationary, over time. We consider a variant of the MAB framework, which we termed Rotting Bandits, where each arm's expected reward decays as a function of the number of times it has been pulled. We are motivated by many real-world scenarios such as online advertising, content recommendation, crowdsourcing, and more. We present algorithms, accompanied by simulations, and derive theoretical guarantees.
Nir Levine, Koby Crammer, Shie Mannor
null
1702.07274
null
null
Online Multiclass Boosting
stat.ML cs.LG
Recent work has extended the theoretical analysis of boosting algorithms to multiclass problems and to online settings. However, the multiclass extension is in the batch setting and the online extensions only consider binary classification. We fill this gap in the literature by defining, and justifying, a weak learning condition for online multiclass boosting. This condition leads to an optimal boosting algorithm that requires the minimal number of weak learners to achieve a certain accuracy. Additionally, we propose an adaptive algorithm which is near optimal and enjoys an excellent performance on real data due to its adaptive property.
Young Hun Jung, Jack Goetz, Ambuj Tewari
null
1702.07305
null
null
Causal Discovery Using Proxy Variables
stat.ML cs.LG
Discovering causal relations is fundamental to reasoning and intelligence. In particular, observational causal discovery algorithms estimate the cause-effect relation between two random entities $X$ and $Y$, given $n$ samples from $P(X,Y)$. In this paper, we develop a framework to estimate the cause-effect relation between two static entities $x$ and $y$: for instance, an art masterpiece $x$ and its fraudulent copy $y$. To this end, we introduce the notion of proxy variables, which allow the construction of a pair of random entities $(A,B)$ from the pair of static entities $(x,y)$. Then, estimating the cause-effect relation between $A$ and $B$ using an observational causal discovery algorithm leads to an estimation of the cause-effect relation between $x$ and $y$. For example, our framework detects the causal relation between unprocessed photographs and their modifications, and orders in time a set of shuffled frames from a video. As our main case study, we introduce a human-elicited dataset of 10,000 pairs of casually-linked pairs of words from natural language. Our methods discover 75% of these causal relations. Finally, we discuss the role of proxy variables in machine learning, as a general tool to incorporate static knowledge into prediction tasks.
Mateo Rojas-Carulla, Marco Baroni, David Lopez-Paz
null
1702.07306
null
null
A Goal-Based Movement Model for Continuous Multi-Agent Tasks
q-bio.NC cs.LG stat.ML
Despite increasing attention paid to the need for fast, scalable methods to analyze next-generation neuroscience data, comparatively little attention has been paid to the development of similar methods for behavioral analysis. Just as the volume and complexity of brain data have grown, behavioral paradigms in systems neuroscience have likewise become more naturalistic and less constrained, necessitating an increase in the flexibility and scalability of the models used to study them. In particular, key assumptions made in the analysis of typical decision paradigms --- optimality; analytic tractability; discrete, low-dimensional action spaces --- may be untenable in richer tasks. Here, using the case of a two-player, real-time, continuous strategic game as an example, we show how the use of modern machine learning methods allows us to relax each of these assumptions. Following an inverse reinforcement learning approach, we are able to succinctly characterize the joint distribution over players' actions via a generative model that allows us to simulate realistic game play. We compare simulated play from a number of generative time series models and show that ours successfully resists mode collapse while generating trajectories with the rich variability of real behavior. Together, these methods offer a rich class of models for the analysis of continuous action tasks at the single-trial level.
Shariq Iqbal and John Pearson
null
1702.07319
null
null
A Converse to Banach's Fixed Point Theorem and its CLS Completeness
cs.CC cs.LG math.GN stat.ML
Banach's fixed point theorem for contraction maps has been widely used to analyze the convergence of iterative methods in non-convex problems. It is a common experience, however, that iterative maps fail to be globally contracting under the natural metric in their domain, making the applicability of Banach's theorem limited. We explore how generally we can apply Banach's fixed point theorem to establish the convergence of iterative methods when pairing it with carefully designed metrics. Our first result is a strong converse of Banach's theorem, showing that it is a universal analysis tool for establishing global convergence of iterative methods to unique fixed points, and for bounding their convergence rate. In other words, we show that, whenever an iterative map globally converges to a unique fixed point, there exists a metric under which the iterative map is contracting and which can be used to bound the number of iterations until convergence. We illustrate our approach in the widely used power method, providing a new way of bounding its convergence rate through contraction arguments. We next consider the computational complexity of Banach's fixed point theorem. Making the proof of our converse theorem constructive, we show that computing a fixed point whose existence is guaranteed by Banach's fixed point theorem is CLS-complete. We thus provide the first natural complete problem for the class CLS, which was defined in [Daskalakis, Papadimitriou 2011] to capture the complexity of problems such as P-matrix LCP, computing KKT-points, and finding mixed Nash equilibria in congestion and network coordination games.
Constantinos Daskalakis, Christos Tzamos, Manolis Zampetakis
null
1702.07339
null
null
Neural Decision Trees
stat.ML cs.LG
In this paper we propose a synergistic melting of neural networks and decision trees (DT) we call neural decision trees (NDT). NDT is an architecture a la decision tree where each splitting node is an independent multilayer perceptron allowing oblique decision functions or arbritrary nonlinear decision function if more than one layer is used. This way, each MLP can be seen as a node of the tree. We then show that with the weight sharing asumption among those units, we end up with a Hashing Neural Network (HNN) which is a multilayer perceptron with sigmoid activation function for the last layer as opposed to the standard softmax. The output units then jointly represent the probability to be in a particular region. The proposed framework allows for global optimization as opposed to greedy in DT and differentiability w.r.t. all parameters and the input, allowing easy integration in any learnable pipeline, for example after CNNs for computer vision tasks. We also demonstrate the modeling power of HNN allowing to learn union of disjoint regions for final clustering or classification making it more general and powerful than standard softmax MLP requiring linear separability thus reducing the need on the inner layer to perform complex data transformations. We finally show experiments for supervised, semi-suppervised and unsupervised tasks and compare results with standard DTs and MLPs.
Randall Balestriero
null
1702.0736
null
null
Bandits with Movement Costs and Adaptive Pricing
cs.LG cs.GT
We extend the model of Multi-armed Bandit with unit switching cost to incorporate a metric between the actions. We consider the case where the metric over the actions can be modeled by a complete binary tree, and the distance between two leaves is the size of the subtree of their least common ancestor, which abstracts the case that the actions are points on the continuous interval $[0,1]$ and the switching cost is their distance. In this setting, we give a new algorithm that establishes a regret of $\widetilde{O}(\sqrt{kT} + T/k)$, where $k$ is the number of actions and $T$ is the time horizon. When the set of actions corresponds to whole $[0,1]$ interval we can exploit our method for the task of bandit learning with Lipschitz loss functions, where our algorithm achieves an optimal regret rate of $\widetilde{\Theta}(T^{2/3})$, which is the same rate one obtains when there is no penalty for movements. As our main application, we use our new algorithm to solve an adaptive pricing problem. Specifically, we consider the case of a single seller faced with a stream of patient buyers. Each buyer has a private value and a window of time in which they are interested in buying, and they buy at the lowest price in the window, if it is below their value. We show that with an appropriate discretization of the prices, the seller can achieve a regret of $\widetilde{O}(T^{2/3})$ compared to the best fixed price in hindsight, which outperform the previous regret bound of $\widetilde{O}(T^{3/4})$ for the problem.
Tomer Koren, Roi Livni, Yishay Mansour
null
1702.07444
null
null
Strongly-Typed Agents are Guaranteed to Interact Safely
cs.LG cs.AI cs.GT
As artificial agents proliferate, it is becoming increasingly important to ensure that their interactions with one another are well-behaved. In this paper, we formalize a common-sense notion of when algorithms are well-behaved: an algorithm is safe if it does no harm. Motivated by recent progress in deep learning, we focus on the specific case where agents update their actions according to gradient descent. The paper shows that that gradient descent converges to a Nash equilibrium in safe games. The main contribution is to define strongly-typed agents and show they are guaranteed to interact safely, thereby providing sufficient conditions to guarantee safe interactions. A series of examples show that strong-typing generalizes certain key features of convexity, is closely related to blind source separation, and introduces a new perspective on classical multilinear games based on tensor decomposition.
David Balduzzi
null
1702.0745
null
null
Sequence Modeling via Segmentations
stat.ML cs.LG
Segmental structure is a common pattern in many types of sequences such as phrases in human languages. In this paper, we present a probabilistic model for sequences via their segmentations. The probability of a segmented sequence is calculated as the product of the probabilities of all its segments, where each segment is modeled using existing tools such as recurrent neural networks. Since the segmentation of a sequence is usually unknown in advance, we sum over all valid segmentations to obtain the final probability for the sequence. An efficient dynamic programming algorithm is developed for forward and backward computations without resorting to any approximation. We demonstrate our approach on text segmentation and speech recognition tasks. In addition to quantitative results, we also show that our approach can discover meaningful segments in their respective application contexts.
Chong Wang and Yining Wang and Po-Sen Huang and Abdelrahman Mohamed and Dengyong Zhou and Li Deng
null
1702.07463
null
null
Deep Models Under the GAN: Information Leakage from Collaborative Deep Learning
cs.CR cs.LG stat.ML
Deep Learning has recently become hugely popular in machine learning, providing significant improvements in classification accuracy in the presence of highly-structured and large databases. Researchers have also considered privacy implications of deep learning. Models are typically trained in a centralized manner with all the data being processed by the same training algorithm. If the data is a collection of users' private data, including habits, personal pictures, geographical positions, interests, and more, the centralized server will have access to sensitive information that could potentially be mishandled. To tackle this problem, collaborative deep learning models have recently been proposed where parties locally train their deep learning structures and only share a subset of the parameters in the attempt to keep their respective training sets private. Parameters can also be obfuscated via differential privacy (DP) to make information extraction even more challenging, as proposed by Shokri and Shmatikov at CCS'15. Unfortunately, we show that any privacy-preserving collaborative deep learning is susceptible to a powerful attack that we devise in this paper. In particular, we show that a distributed, federated, or decentralized deep learning approach is fundamentally broken and does not protect the training sets of honest participants. The attack we developed exploits the real-time nature of the learning process that allows the adversary to train a Generative Adversarial Network (GAN) that generates prototypical samples of the targeted training set that was meant to be private (the samples generated by the GAN are intended to come from the same distribution as the training data). Interestingly, we show that record-level DP applied to the shared parameters of the model, as suggested in previous work, is ineffective (i.e., record-level DP is not designed to address our attack).
Briland Hitaj, Giuseppe Ateniese, Fernando Perez-Cruz
null
1702.07464
null
null
Online Meta-learning by Parallel Algorithm Competition
cs.LG
The efficiency of reinforcement learning algorithms depends critically on a few meta-parameters that modulates the learning updates and the trade-off between exploration and exploitation. The adaptation of the meta-parameters is an open question in reinforcement learning, which arguably has become more of an issue recently with the success of deep reinforcement learning in high-dimensional state spaces. The long learning times in domains such as Atari 2600 video games makes it not feasible to perform comprehensive searches of appropriate meta-parameter values. We propose the Online Meta-learning by Parallel Algorithm Competition (OMPAC) method. In the OMPAC method, several instances of a reinforcement learning algorithm are run in parallel with small differences in the initial values of the meta-parameters. After a fixed number of episodes, the instances are selected based on their performance in the task at hand. Before continuing the learning, Gaussian noise is added to the meta-parameters with a predefined probability. We validate the OMPAC method by improving the state-of-the-art results in stochastic SZ-Tetris and in standard Tetris with a smaller, 10$\times$10, board, by 31% and 84%, respectively, and by improving the results for deep Sarsa($\lambda$) agents in three Atari 2600 games by 62% or more. The experiments also show the ability of the OMPAC method to adapt the meta-parameters according to the learning progress in different tasks.
Stefan Elfwing, Eiji Uchibe, Kenji Doya
null
1702.0749
null
null
Tight Bounds for Bandit Combinatorial Optimization
cs.LG
We revisit the study of optimal regret rates in bandit combinatorial optimization---a fundamental framework for sequential decision making under uncertainty that abstracts numerous combinatorial prediction problems. We prove that the attainable regret in this setting grows as $\widetilde{\Theta}(k^{3/2}\sqrt{dT})$ where $d$ is the dimension of the problem and $k$ is a bound over the maximal instantaneous loss, disproving a conjecture of Audibert, Bubeck, and Lugosi (2013) who argued that the optimal rate should be of the form $\widetilde{\Theta}(k\sqrt{dT})$. Our bounds apply to several important instances of the framework, and in particular, imply a tight bound for the well-studied bandit shortest path problem. By that, we also resolve an open problem posed by Cesa-Bianchi and Lugosi (2012).
Alon Cohen, Tamir Hazan, Tomer Koren
null
1702.07539
null
null
Learning Rates for Kernel-Based Expectile Regression
stat.ML cs.LG
Conditional expectiles are becoming an increasingly important tool in finance as well as in other areas of applications. We analyse a support vector machine type approach for estimating conditional expectiles and establish learning rates that are minimax optimal modulo a logarithmic factor if Gaussian RBF kernels are used and the desired expectile is smooth in a Besov sense. As a special case, our learning rates improve the best known rates for kernel-based least squares regression in this scenario. Key ingredients of our statistical analysis are a general calibration inequality for the asymmetric least squares loss, a corresponding variance bound as well as an improved entropy number bound for Gaussian RBF kernels.
Muhammad Farooq and Ingo Steinwart
null
1702.07552
null
null
RNN Decoding of Linear Block Codes
cs.IT cs.LG cs.NE math.IT
Designing a practical, low complexity, close to optimal, channel decoder for powerful algebraic codes with short to moderate block length is an open research problem. Recently it has been shown that a feed-forward neural network architecture can improve on standard belief propagation decoding, despite the large example space. In this paper we introduce a recurrent neural network architecture for decoding linear block codes. Our method shows comparable bit error rate results compared to the feed-forward neural network with significantly less parameters. We also demonstrate improved performance over belief propagation on sparser Tanner graph representations of the codes. Furthermore, we demonstrate that the RNN decoder can be used to improve the performance or alternatively reduce the computational complexity of the mRRD algorithm for low complexity, close to optimal, decoding of short BCH codes.
Eliya Nachmani, Elad Marciano, David Burshtein and Yair Be'ery
null
1702.0756
null
null
Control of Gene Regulatory Networks with Noisy Measurements and Uncertain Inputs
q-bio.MN cs.LG stat.ML
This paper is concerned with the problem of stochastic control of gene regulatory networks (GRNs) observed indirectly through noisy measurements and with uncertainty in the intervention inputs. The partial observability of the gene states and uncertainty in the intervention process are accounted for by modeling GRNs using the partially-observed Boolean dynamical system (POBDS) signal model with noisy gene expression measurements. Obtaining the optimal infinite-horizon control strategy for this problem is not attainable in general, and we apply reinforcement learning and Gaussian process techniques to find a near-optimal solution. The POBDS is first transformed to a directly-observed Markov Decision Process in a continuous belief space, and the Gaussian process is used for modeling the cost function over the belief and intervention spaces. Reinforcement learning then is used to learn the cost function from the available gene expression data. In addition, we employ sparsification, which enables the control of large partially-observed GRNs. The performance of the resulting algorithm is studied through a comprehensive set of numerical experiments using synthetic gene expression data generated from a melanoma gene regulatory network.
Mahdi Imani and Ulisses Braga-Neto
null
1702.07652
null
null
How ConvNets model Non-linear Transformations
cs.CV cs.LG
In this paper, we theoretically address three fundamental problems involving deep convolutional networks regarding invariance, depth and hierarchy. We introduce the paradigm of Transformation Networks (TN) which are a direct generalization of Convolutional Networks (ConvNets). Theoretically, we show that TNs (and thereby ConvNets) are can be invariant to non-linear transformations of the input despite pooling over mere local translations. Our analysis provides clear insights into the increase in invariance with depth in these networks. Deeper networks are able to model much richer classes of transformations. We also find that a hierarchical architecture allows the network to generate invariance much more efficiently than a non-hierarchical network. Our results provide useful insight into these three fundamental problems in deep learning using ConvNets.
Dipan K. Pal, Marios Savvides
null
1702.07664
null
null
Bayes-Optimal Entropy Pursuit for Active Choice-Based Preference Learning
stat.ML cs.IT cs.LG math.IT
We analyze the problem of learning a single user's preferences in an active learning setting, sequentially and adaptively querying the user over a finite time horizon. Learning is conducted via choice-based queries, where the user selects her preferred option among a small subset of offered alternatives. These queries have been shown to be a robust and efficient way to learn an individual's preferences. We take a parametric approach and model the user's preferences through a linear classifier, using a Bayesian prior to encode our current knowledge of this classifier. The rate at which we learn depends on the alternatives offered at every time epoch. Under certain noise assumptions, we show that the Bayes-optimal policy for maximally reducing entropy of the posterior distribution of this linear classifier is a greedy policy, and that this policy achieves a linear lower bound when alternatives can be constructed from the continuum. Further, we analyze a different metric called misclassification error, proving that the performance of the optimal policy that minimizes misclassification error is bounded below by a linear function of differential entropy. Lastly, we numerically compare the greedy entropy reduction policy with a knowledge gradient policy under a number of scenarios, examining their performance under both differential entropy and misclassification error.
Stephen N. Pallone, Peter I. Frazier, and Shane G. Henderson
null
1702.07694
null
null
Computationally Efficient Robust Estimation of Sparse Functionals
stat.ML cs.DS cs.LG
Many conventional statistical procedures are extremely sensitive to seemingly minor deviations from modeling assumptions. This problem is exacerbated in modern high-dimensional settings, where the problem dimension can grow with and possibly exceed the sample size. We consider the problem of robust estimation of sparse functionals, and provide a computationally and statistically efficient algorithm in the high-dimensional setting. Our theory identifies a unified set of deterministic conditions under which our algorithm guarantees accurate recovery. By further establishing that these deterministic conditions hold with high-probability for a wide range of statistical models, our theory applies to many problems of considerable interest including sparse mean and covariance estimation; sparse linear regression; and sparse generalized linear models.
Simon S. Du, Sivaraman Balakrishnan, Aarti Singh
null
1702.07709
null
null
A supervised approach to time scale detection in dynamic networks
cs.SI cs.LG
For any stream of time-stamped edges that form a dynamic network, an important choice is the aggregation granularity that an analyst uses to bin the data. Picking such a windowing of the data is often done by hand, or left up to the technology that is collecting the data. However, the choice can make a big difference in the properties of the dynamic network. This is the time scale detection problem. In previous work, this problem is often solved with a heuristic as an unsupervised task. As an unsupervised problem, it is difficult to measure how well a given algorithm performs. In addition, we show that the quality of the windowing is dependent on which task an analyst wants to perform on the network after windowing. Therefore the time scale detection problem should not be handled independently from the rest of the analysis of the network. We introduce a framework that tackles both of these issues: By measuring the performance of the time scale detection algorithm based on how well a given task is accomplished on the resulting network, we are for the first time able to directly compare different time scale detection algorithms to each other. Using this framework, we introduce time scale detection algorithms that take a supervised approach: they leverage ground truth on training data to find a good windowing of the test data. We compare the supervised approach to previous approaches and several baselines on real data.
Benjamin Fish, Rajmonda S. Caceres
null
1702.07752
null
null
Changing Model Behavior at Test-Time Using Reinforcement Learning
stat.ML cs.LG
Machine learning models are often used at test-time subject to constraints and trade-offs not present at training-time. For example, a computer vision model operating on an embedded device may need to perform real-time inference, or a translation model operating on a cell phone may wish to bound its average compute time in order to be power-efficient. In this work we describe a mixture-of-experts model and show how to change its test-time resource-usage on a per-input basis using reinforcement learning. We test our method on a small MNIST-based example.
Augustus Odena, Dieterich Lawson, Christopher Olah
null
1702.0778
null
null
Convolutional Gated Recurrent Neural Network Incorporating Spatial Features for Audio Tagging
cs.SD cs.LG cs.NE
Environmental audio tagging is a newly proposed task to predict the presence or absence of a specific audio event in a chunk. Deep neural network (DNN) based methods have been successfully adopted for predicting the audio tags in the domestic audio scene. In this paper, we propose to use a convolutional neural network (CNN) to extract robust features from mel-filter banks (MFBs), spectrograms or even raw waveforms for audio tagging. Gated recurrent unit (GRU) based recurrent neural networks (RNNs) are then cascaded to model the long-term temporal structure of the audio signal. To complement the input information, an auxiliary CNN is designed to learn on the spatial features of stereo recordings. We evaluate our proposed methods on Task 4 (audio tagging) of the Detection and Classification of Acoustic Scenes and Events 2016 (DCASE 2016) challenge. Compared with our recent DNN-based method, the proposed structure can reduce the equal error rate (EER) from 0.13 to 0.11 on the development set. The spatial features can further reduce the EER to 0.10. The performance of the end-to-end learning on raw waveforms is also comparable. Finally, on the evaluation set, we get the state-of-the-art performance with 0.12 EER while the performance of the best existing system is 0.15 EER.
Yong Xu and Qiuqiang Kong and Qiang Huang and Wenwu Wang and Mark D. Plumbley
null
1702.07787
null
null
Activation Ensembles for Deep Neural Networks
stat.ML cs.LG
Many activation functions have been proposed in the past, but selecting an adequate one requires trial and error. We propose a new methodology of designing activation functions within a neural network at each layer. We call this technique an "activation ensemble" because it allows the use of multiple activation functions at each layer. This is done by introducing additional variables, $\alpha$, at each activation layer of a network to allow for multiple activation functions to be active at each neuron. By design, activations with larger $\alpha$ values at a neuron is equivalent to having the largest magnitude. Hence, those higher magnitude activations are "chosen" by the network. We implement the activation ensembles on a variety of datasets using an array of Feed Forward and Convolutional Neural Networks. By using the activation ensemble, we achieve superior results compared to traditional techniques. In addition, because of the flexibility of this methodology, we more deeply explore activation functions and the features that they capture.
Mark Harmon, Diego Klabjan
null
1702.0779
null
null
Rank-to-engage: New Listwise Approaches to Maximize Engagement
stat.ML cs.LG
For many internet businesses, presenting a given list of items in an order that maximizes a certain metric of interest (e.g., click-through-rate, average engagement time etc.) is crucial. We approach the aforementioned task from a learning-to-rank perspective which reveals a new problem setup. In traditional learning-to-rank literature, it is implicitly assumed that during the training data generation one has access to the \emph{best or desired} order for the given list of items. In this work, we consider a problem setup where we do not observe the desired ranking. We present two novel solutions: the first solution is an extension of already existing listwise learning-to-rank technique--Listwise maximum likelihood estimation (ListMLE)--while the second one is a generic machine learning based framework that tackles the problem in its entire generality. We discuss several challenges associated with this generic framework, and propose a simple \emph{item-payoff} and \emph{positional-gain} model that addresses these challenges. We provide training algorithms, inference procedures, and demonstrate the effectiveness of the two approaches over traditional ListMLE on synthetic as well as on real-life setting of ranking news articles for increased dwell time.
Swayambhoo Jain, Akshay Soni, Nikolay Laptev, and Yashar Mehdad
null
1702.07798
null
null
On the Origin of Deep Learning
cs.LG cs.NE stat.ML
This paper is a review of the evolutionary history of deep learning models. It covers from the genesis of neural networks when associationism modeling of the brain is studied, to the models that dominate the last decade of research in deep learning like convolutional neural networks, deep belief networks, and recurrent neural networks. In addition to a review of these models, this paper primarily focuses on the precedents of the models above, examining how the initial ideas are assembled to construct the early models and how these preliminary models are developed into their current forms. Many of these evolutionary paths last more than half a century and have a diversity of directions. For example, CNN is built on prior knowledge of biological vision system; DBN is evolved from a trade-off of modeling power and computation complexity of graphical models and many nowadays models are neural counterparts of ancient linear models. This paper reviews these evolutionary paths and offers a concise thought flow of how these models are developed, and aims to provide a thorough background for deep learning. More importantly, along with the path, this paper summarizes the gist behind these milestones and proposes many directions to guide the future research of deep learning.
Haohan Wang and Bhiksha Raj
null
1702.078
null
null