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Training Deep Convolutional Neural Networks with Resistive Cross-Point
Devices | cs.LG cs.NE stat.ML | In a previous work we have detailed the requirements to obtain a maximal
performance benefit by implementing fully connected deep neural networks (DNN)
in form of arrays of resistive devices for deep learning. This concept of
Resistive Processing Unit (RPU) devices we extend here towards convolutional
neural networks (CNNs). We show how to map the convolutional layers to RPU
arrays such that the parallelism of the hardware can be fully utilized in all
three cycles of the backpropagation algorithm. We find that the noise and bound
limitations imposed due to analog nature of the computations performed on the
arrays effect the training accuracy of the CNNs. Noise and bound management
techniques are presented that mitigate these problems without introducing any
additional complexity in the analog circuits and can be addressed by the
digital circuits. In addition, we discuss digitally programmable update
management and device variability reduction techniques that can be used
selectively for some of the layers in a CNN. We show that combination of all
those techniques enables a successful application of the RPU concept for
training CNNs. The techniques discussed here are more general and can be
applied beyond CNN architectures and therefore enables applicability of RPU
approach for large class of neural network architectures.
| Tayfun Gokmen, O. Murat Onen, Wilfried Haensch | null | 1705.08014 | null | null |
Parallel Stochastic Gradient Descent with Sound Combiners | cs.LG stat.ML | Stochastic gradient descent (SGD) is a well known method for regression and
classification tasks. However, it is an inherently sequential algorithm at each
step, the processing of the current example depends on the parameters learned
from the previous examples. Prior approaches to parallelizing linear learners
using SGD, such as HOGWILD! and ALLREDUCE, do not honor these dependencies
across threads and thus can potentially suffer poor convergence rates and/or
poor scalability. This paper proposes SYMSGD, a parallel SGD algorithm that, to
a first-order approximation, retains the sequential semantics of SGD. Each
thread learns a local model in addition to a model combiner, which allows local
models to be combined to produce the same result as what a sequential SGD would
have produced. This paper evaluates SYMSGD's accuracy and performance on 6
datasets on a shared-memory machine shows upto 11x speedup over our heavily
optimized sequential baseline on 16 cores and 2.2x, on average, faster than
HOGWILD!.
| Saeed Maleki, Madanlal Musuvathi, Todd Mytkowicz | null | 1705.0803 | null | null |
Poincar\'e Embeddings for Learning Hierarchical Representations | cs.AI cs.LG stat.ML | Representation learning has become an invaluable approach for learning from
symbolic data such as text and graphs. However, while complex symbolic datasets
often exhibit a latent hierarchical structure, state-of-the-art methods
typically learn embeddings in Euclidean vector spaces, which do not account for
this property. For this purpose, we introduce a new approach for learning
hierarchical representations of symbolic data by embedding them into hyperbolic
space -- or more precisely into an n-dimensional Poincar\'e ball. Due to the
underlying hyperbolic geometry, this allows us to learn parsimonious
representations of symbolic data by simultaneously capturing hierarchy and
similarity. We introduce an efficient algorithm to learn the embeddings based
on Riemannian optimization and show experimentally that Poincar\'e embeddings
outperform Euclidean embeddings significantly on data with latent hierarchies,
both in terms of representation capacity and in terms of generalization
ability.
| Maximilian Nickel, Douwe Kiela | null | 1705.08039 | null | null |
Detection Algorithms for Communication Systems Using Deep Learning | cs.LG cs.AI cs.ET | The design and analysis of communication systems typically rely on the
development of mathematical models that describe the underlying communication
channel, which dictates the relationship between the transmitted and the
received signals. However, in some systems, such as molecular communication
systems where chemical signals are used for transfer of information, it is not
possible to accurately model this relationship. In these scenarios, because of
the lack of mathematical channel models, a completely new approach to design
and analysis is required. In this work, we focus on one important aspect of
communication systems, the detection algorithms, and demonstrate that by
borrowing tools from deep learning, it is possible to train detectors that
perform well, without any knowledge of the underlying channel models. We
evaluate these algorithms using experimental data that is collected by a
chemical communication platform, where the channel model is unknown and
difficult to model analytically. We show that deep learning algorithms perform
significantly better than a simple detector that was used in previous works,
which also did not assume any knowledge of the channel.
| Nariman Farsad and Andrea Goldsmith | null | 1705.08044 | null | null |
Neural Network Memory Architectures for Autonomous Robot Navigation | cs.RO cs.LG | This paper highlights the significance of including memory structures in
neural networks when the latter are used to learn perception-action loops for
autonomous robot navigation. Traditional navigation approaches rely on global
maps of the environment to overcome cul-de-sacs and plan feasible motions. Yet,
maintaining an accurate global map may be challenging in real-world settings. A
possible way to mitigate this limitation is to use learning techniques that
forgo hand-engineered map representations and infer appropriate control
responses directly from sensed information. An important but unexplored aspect
of such approaches is the effect of memory on their performance. This work is a
first thorough study of memory structures for deep-neural-network-based robot
navigation, and offers novel tools to train such networks from supervision and
quantify their ability to generalize to unseen scenarios. We analyze the
separation and generalization abilities of feedforward, long short-term memory,
and differentiable neural computer networks. We introduce a new method to
evaluate the generalization ability by estimating the VC-dimension of networks
with a final linear readout layer. We validate that the VC estimates are good
predictors of actual test performance. The reported method can be applied to
deep learning problems beyond robotics.
| Steven W Chen, Nikolay Atanasov, Arbaaz Khan, Konstantinos Karydis,
Daniel D. Lee, and Vijay Kumar | null | 1705.08049 | null | null |
Wasserstein Learning of Deep Generative Point Process Models | cs.LG stat.ML | Point processes are becoming very popular in modeling asynchronous sequential
data due to their sound mathematical foundation and strength in modeling a
variety of real-world phenomena. Currently, they are often characterized via
intensity function which limits model's expressiveness due to unrealistic
assumptions on its parametric form used in practice. Furthermore, they are
learned via maximum likelihood approach which is prone to failure in
multi-modal distributions of sequences. In this paper, we propose an
intensity-free approach for point processes modeling that transforms nuisance
processes to a target one. Furthermore, we train the model using a
likelihood-free leveraging Wasserstein distance between point processes.
Experiments on various synthetic and real-world data substantiate the
superiority of the proposed point process model over conventional ones.
| Shuai Xiao, Mehrdad Farajtabar, Xiaojing Ye, Junchi Yan, Le Song,
Hongyuan Zha | null | 1705.08051 | null | null |
Compressing Recurrent Neural Network with Tensor Train | cs.LG | Recurrent Neural Network (RNN) are a popular choice for modeling temporal and
sequential tasks and achieve many state-of-the-art performance on various
complex problems. However, most of the state-of-the-art RNNs have millions of
parameters and require many computational resources for training and predicting
new data. This paper proposes an alternative RNN model to reduce the number of
parameters significantly by representing the weight parameters based on Tensor
Train (TT) format. In this paper, we implement the TT-format representation for
several RNN architectures such as simple RNN and Gated Recurrent Unit (GRU). We
compare and evaluate our proposed RNN model with uncompressed RNN model on
sequence classification and sequence prediction tasks. Our proposed RNNs with
TT-format are able to preserve the performance while reducing the number of RNN
parameters significantly up to 40 times smaller.
| Andros Tjandra, Sakriani Sakti, Satoshi Nakamura | 10.1109/IJCNN.2017.7966420 | 1705.08052 | null | null |
Ambiguity set and learning via Bregman and Wasserstein | stat.ML cs.LG | Construction of ambiguity set in robust optimization relies on the choice of
divergences between probability distributions. In distribution learning,
choosing appropriate probability distributions based on observed data is
critical for approximating the true distribution. To improve the performance of
machine learning models, there has recently been interest in designing
objective functions based on Lp-Wasserstein distance rather than the classical
Kullback-Leibler (KL) divergence. In this paper, we derive concentration and
asymptotic results using Bregman divergence. We propose a novel asymmetric
statistical divergence called Wasserstein-Bregman divergence as a
generalization of L2-Wasserstein distance. We discuss how these results can be
applied to the construction of ambiguity set in robust optimization.
| Xin Guo, Johnny Hong, Nan Yang | null | 1705.08056 | null | null |
Learning from partial correction | cs.LG | We introduce a new model of interactive learning in which an expert examines
the predictions of a learner and partially fixes them if they are wrong.
Although this kind of feedback is not i.i.d., we show statistical
generalization bounds on the quality of the learned model.
| Sanjoy Dasgupta and Michael Luby | null | 1705.08076 | null | null |
Visual Semantic Planning using Deep Successor Representations | cs.CV cs.LG cs.RO | A crucial capability of real-world intelligent agents is their ability to
plan a sequence of actions to achieve their goals in the visual world. In this
work, we address the problem of visual semantic planning: the task of
predicting a sequence of actions from visual observations that transform a
dynamic environment from an initial state to a goal state. Doing so entails
knowledge about objects and their affordances, as well as actions and their
preconditions and effects. We propose learning these through interacting with a
visual and dynamic environment. Our proposed solution involves bootstrapping
reinforcement learning with imitation learning. To ensure cross task
generalization, we develop a deep predictive model based on successor
representations. Our experimental results show near optimal results across a
wide range of tasks in the challenging THOR environment.
| Yuke Zhu, Daniel Gordon, Eric Kolve, Dieter Fox, Li Fei-Fei, Abhinav
Gupta, Roozbeh Mottaghi, Ali Farhadi | null | 1705.0808 | null | null |
Combinatorial Semi-Bandits with Knapsacks | cs.LG | We unify two prominent lines of work on multi-armed bandits: bandits with
knapsacks (BwK) and combinatorial semi-bandits. The former concerns limited
"resources" consumed by the algorithm, e.g., limited supply in dynamic pricing.
The latter allows a huge number of actions but assumes combinatorial structure
and additional feedback to make the problem tractable. We define a common
generalization, support it with several motivating examples, and design an
algorithm for it. Our regret bounds are comparable with those for BwK and
combinatorial semi- bandits.
| Karthik Abinav Sankararaman, Aleksandrs Slivkins | null | 1705.0811 | null | null |
Consistent Multitask Learning with Nonlinear Output Relations | cs.LG stat.ML | Key to multitask learning is exploiting relationships between different tasks
to improve prediction performance. If the relations are linear, regularization
approaches can be used successfully. However, in practice assuming the tasks to
be linearly related might be restrictive, and allowing for nonlinear structures
is a challenge. In this paper, we tackle this issue by casting the problem
within the framework of structured prediction. Our main contribution is a novel
algorithm for learning multiple tasks which are related by a system of
nonlinear equations that their joint outputs need to satisfy. We show that the
algorithm is consistent and can be efficiently implemented. Experimental
results show the potential of the proposed method.
| Carlo Ciliberto, Alessandro Rudi, Lorenzo Rosasco, Massimiliano Pontil | null | 1705.08118 | null | null |
Black-Box Attacks against RNN based Malware Detection Algorithms | cs.LG cs.CR | Recent researches have shown that machine learning based malware detection
algorithms are very vulnerable under the attacks of adversarial examples. These
works mainly focused on the detection algorithms which use features with fixed
dimension, while some researchers have begun to use recurrent neural networks
(RNN) to detect malware based on sequential API features. This paper proposes a
novel algorithm to generate sequential adversarial examples, which are used to
attack a RNN based malware detection system. It is usually hard for malicious
attackers to know the exact structures and weights of the victim RNN. A
substitute RNN is trained to approximate the victim RNN. Then we propose a
generative RNN to output sequential adversarial examples from the original
sequential malware inputs. Experimental results showed that RNN based malware
detection algorithms fail to detect most of the generated malicious adversarial
examples, which means the proposed model is able to effectively bypass the
detection algorithms.
| Weiwei Hu and Ying Tan | null | 1705.08131 | null | null |
Latent Multi-task Architecture Learning | stat.ML cs.AI cs.CL cs.LG cs.NE | Multi-task learning (MTL) allows deep neural networks to learn from related
tasks by sharing parameters with other networks. In practice, however, MTL
involves searching an enormous space of possible parameter sharing
architectures to find (a) the layers or subspaces that benefit from sharing,
(b) the appropriate amount of sharing, and (c) the appropriate relative weights
of the different task losses. Recent work has addressed each of the above
problems in isolation. In this work we present an approach that learns a latent
multi-task architecture that jointly addresses (a)--(c). We present experiments
on synthetic data and data from OntoNotes 5.0, including four different tasks
and seven different domains. Our extension consistently outperforms previous
approaches to learning latent architectures for multi-task problems and
achieves up to 15% average error reductions over common approaches to MTL.
| Sebastian Ruder, Joachim Bingel, Isabelle Augenstein, Anders
S{\o}gaard | null | 1705.08142 | null | null |
Techniques for visualizing LSTMs applied to electrocardiograms | stat.ML cs.LG | This paper explores four different visualization techniques for long
short-term memory (LSTM) networks applied to continuous-valued time series. On
the datasets analysed, we find that the best visualization technique is to
learn an input deletion mask that optimally reduces the true class score. With
a specific focus on single-lead electrocardiograms from the MIT-BIH arrhythmia
dataset, we show that salient input features for the LSTM classifier align well
with medical theory.
| Jos van der Westhuizen and Joan Lasenby | null | 1705.08153 | null | null |
Look, Listen and Learn | cs.CV cs.LG | We consider the question: what can be learnt by looking at and listening to a
large number of unlabelled videos? There is a valuable, but so far untapped,
source of information contained in the video itself -- the correspondence
between the visual and the audio streams, and we introduce a novel
"Audio-Visual Correspondence" learning task that makes use of this. Training
visual and audio networks from scratch, without any additional supervision
other than the raw unconstrained videos themselves, is shown to successfully
solve this task, and, more interestingly, result in good visual and audio
representations. These features set the new state-of-the-art on two sound
classification benchmarks, and perform on par with the state-of-the-art
self-supervised approaches on ImageNet classification. We also demonstrate that
the network is able to localize objects in both modalities, as well as perform
fine-grained recognition tasks.
| Relja Arandjelovi\'c, Andrew Zisserman | null | 1705.08168 | null | null |
Nearest-Neighbor Sample Compression: Efficiency, Consistency, Infinite
Dimensions | cs.LG math.ST stat.TH | We examine the Bayes-consistency of a recently proposed
1-nearest-neighbor-based multiclass learning algorithm. This algorithm is
derived from sample compression bounds and enjoys the statistical advantages of
tight, fully empirical generalization bounds, as well as the algorithmic
advantages of a faster runtime and memory savings. We prove that this algorithm
is strongly Bayes-consistent in metric spaces with finite doubling dimension
--- the first consistency result for an efficient nearest-neighbor sample
compression scheme. Rather surprisingly, we discover that this algorithm
continues to be Bayes-consistent even in a certain infinite-dimensional
setting, in which the basic measure-theoretic conditions on which classic
consistency proofs hinge are violated. This is all the more surprising, since
it is known that $k$-NN is not Bayes-consistent in this setting. We pose
several challenging open problems for future research.
| Aryeh Kontorovich, Sivan Sabato, Roi Weiss | null | 1705.08184 | null | null |
Learning to Succeed while Teaching to Fail: Privacy in Closed Machine
Learning Systems | stat.ML cs.LG | Security, privacy, and fairness have become critical in the era of data
science and machine learning. More and more we see that achieving universally
secure, private, and fair systems is practically impossible. We have seen for
example how generative adversarial networks can be used to learn about the
expected private training data; how the exploitation of additional data can
reveal private information in the original one; and how what looks like
unrelated features can teach us about each other. Confronted with this
challenge, in this paper we open a new line of research, where the security,
privacy, and fairness is learned and used in a closed environment. The goal is
to ensure that a given entity (e.g., the company or the government), trusted to
infer certain information with our data, is blocked from inferring protected
information from it. For example, a hospital might be allowed to produce
diagnosis on the patient (the positive task), without being able to infer the
gender of the subject (negative task). Similarly, a company can guarantee that
internally it is not using the provided data for any undesired task, an
important goal that is not contradicting the virtually impossible challenge of
blocking everybody from the undesired task. We design a system that learns to
succeed on the positive task while simultaneously fail at the negative one, and
illustrate this with challenging cases where the positive task is actually
harder than the negative one being blocked. Fairness, to the information in the
negative task, is often automatically obtained as a result of this proposed
approach. The particular framework and examples open the door to security,
privacy, and fairness in very important closed scenarios, ranging from private
data accumulation companies like social networks to law-enforcement and
hospitals.
| Jure Sokolic, Qiang Qiu, Miguel R. D. Rodrigues, Guillermo Sapiro | null | 1705.08197 | null | null |
Unbiasing Truncated Backpropagation Through Time | cs.NE cs.LG | Truncated Backpropagation Through Time (truncated BPTT) is a widespread
method for learning recurrent computational graphs. Truncated BPTT keeps the
computational benefits of Backpropagation Through Time (BPTT) while relieving
the need for a complete backtrack through the whole data sequence at every
step. However, truncation favors short-term dependencies: the gradient estimate
of truncated BPTT is biased, so that it does not benefit from the convergence
guarantees from stochastic gradient theory. We introduce Anticipated Reweighted
Truncated Backpropagation (ARTBP), an algorithm that keeps the computational
benefits of truncated BPTT, while providing unbiasedness. ARTBP works by using
variable truncation lengths together with carefully chosen compensation factors
in the backpropagation equation. We check the viability of ARTBP on two tasks.
First, a simple synthetic task where careful balancing of temporal dependencies
at different scales is needed: truncated BPTT displays unreliable performance,
and in worst case scenarios, divergence, while ARTBP converges reliably.
Second, on Penn Treebank character-level language modelling, ARTBP slightly
outperforms truncated BPTT.
| Corentin Tallec and Yann Ollivier | null | 1705.08209 | null | null |
Matching neural paths: transfer from recognition to correspondence
search | cs.CV cs.LG cs.NE | Many machine learning tasks require finding per-part correspondences between
objects. In this work we focus on low-level correspondences - a highly
ambiguous matching problem. We propose to use a hierarchical semantic
representation of the objects, coming from a convolutional neural network, to
solve this ambiguity. Training it for low-level correspondence prediction
directly might not be an option in some domains where the ground-truth
correspondences are hard to obtain. We show how transfer from recognition can
be used to avoid such training. Our idea is to mark parts as "matching" if
their features are close to each other at all the levels of convolutional
feature hierarchy (neural paths). Although the overall number of such paths is
exponential in the number of layers, we propose a polynomial algorithm for
aggregating all of them in a single backward pass. The empirical validation is
done on the task of stereo correspondence and demonstrates that we achieve
competitive results among the methods which do not use labeled target domain
data.
| Nikolay Savinov, Lubor Ladicky and Marc Pollefeys | null | 1705.08272 | null | null |
The Marginal Value of Adaptive Gradient Methods in Machine Learning | stat.ML cs.LG | Adaptive optimization methods, which perform local optimization with a metric
constructed from the history of iterates, are becoming increasingly popular for
training deep neural networks. Examples include AdaGrad, RMSProp, and Adam. We
show that for simple overparameterized problems, adaptive methods often find
drastically different solutions than gradient descent (GD) or stochastic
gradient descent (SGD). We construct an illustrative binary classification
problem where the data is linearly separable, GD and SGD achieve zero test
error, and AdaGrad, Adam, and RMSProp attain test errors arbitrarily close to
half. We additionally study the empirical generalization capability of adaptive
methods on several state-of-the-art deep learning models. We observe that the
solutions found by adaptive methods generalize worse (often significantly
worse) than SGD, even when these solutions have better training performance.
These results suggest that practitioners should reconsider the use of adaptive
methods to train neural networks.
| Ashia C. Wilson and Rebecca Roelofs and Mitchell Stern and Nathan
Srebro and Benjamin Recht | null | 1705.08292 | null | null |
Efficient and principled score estimation with Nystr\"om kernel
exponential families | stat.ML cs.LG stat.ME | We propose a fast method with statistical guarantees for learning an
exponential family density model where the natural parameter is in a
reproducing kernel Hilbert space, and may be infinite-dimensional. The model is
learned by fitting the derivative of the log density, the score, thus avoiding
the need to compute a normalization constant. Our approach improves the
computational efficiency of an earlier solution by using a low-rank,
Nystr\"om-like solution. The new solution retains the consistency and
convergence rates of the full-rank solution (exactly in Fisher distance, and
nearly in other distances), with guarantees on the degree of cost and storage
reduction. We evaluate the method in experiments on density estimation and in
the construction of an adaptive Hamiltonian Monte Carlo sampler. Compared to an
existing score learning approach using a denoising autoencoder, our estimator
is empirically more data-efficient when estimating the score, runs faster, and
has fewer parameters (which can be tuned in a principled and interpretable
way), in addition to providing statistical guarantees.
| Danica J. Sutherland, Heiko Strathmann, Michael Arbel, Arthur Gretton | null | 1705.0836 | null | null |
Detecting Adversarial Image Examples in Deep Networks with Adaptive
Noise Reduction | cs.CR cs.LG | Recently, many studies have demonstrated deep neural network (DNN)
classifiers can be fooled by the adversarial example, which is crafted via
introducing some perturbations into an original sample. Accordingly, some
powerful defense techniques were proposed. However, existing defense techniques
often require modifying the target model or depend on the prior knowledge of
attacks. In this paper, we propose a straightforward method for detecting
adversarial image examples, which can be directly deployed into unmodified
off-the-shelf DNN models. We consider the perturbation to images as a kind of
noise and introduce two classic image processing techniques, scalar
quantization and smoothing spatial filter, to reduce its effect. The image
entropy is employed as a metric to implement an adaptive noise reduction for
different kinds of images. Consequently, the adversarial example can be
effectively detected by comparing the classification results of a given sample
and its denoised version, without referring to any prior knowledge of attacks.
More than 20,000 adversarial examples against some state-of-the-art DNN models
are used to evaluate the proposed method, which are crafted with different
attack techniques. The experiments show that our detection method can achieve a
high overall F1 score of 96.39% and certainly raises the bar for defense-aware
attacks.
| Bin Liang, Hongcheng Li, Miaoqiang Su, Xirong Li, Wenchang Shi and
Xiaofeng Wang | 10.1109/TDSC.2018.2874243 | 1705.08378 | null | null |
Better Text Understanding Through Image-To-Text Transfer | cs.CL cs.CV cs.LG | Generic text embeddings are successfully used in a variety of tasks. However,
they are often learnt by capturing the co-occurrence structure from pure text
corpora, resulting in limitations of their ability to generalize. In this
paper, we explore models that incorporate visual information into the text
representation. Based on comprehensive ablation studies, we propose a
conceptually simple, yet well performing architecture. It outperforms previous
multimodal approaches on a set of well established benchmarks. We also improve
the state-of-the-art results for image-related text datasets, using orders of
magnitude less data.
| Karol Kurach, Sylvain Gelly, Michal Jastrzebski, Philip Haeusser,
Olivier Teytaud, Damien Vincent, Olivier Bousquet | null | 1705.08386 | null | null |
Continual Learning in Generative Adversarial Nets | cs.LG cs.AI stat.ML | Developments in deep generative models have allowed for tractable learning of
high-dimensional data distributions. While the employed learning procedures
typically assume that training data is drawn i.i.d. from the distribution of
interest, it may be desirable to model distinct distributions which are
observed sequentially, such as when different classes are encountered over
time. Although conditional variations of deep generative models permit multiple
distributions to be modeled by a single network in a disentangled fashion, they
are susceptible to catastrophic forgetting when the distributions are
encountered sequentially. In this paper, we adapt recent work in reducing
catastrophic forgetting to the task of training generative adversarial networks
on a sequence of distinct distributions, enabling continual generative
modeling.
| Ari Seff, Alex Beatson, Daniel Suo, Han Liu | null | 1705.08395 | null | null |
Ridesourcing Car Detection by Transfer Learning | cs.LG stat.ML | Ridesourcing platforms like Uber and Didi are getting more and more popular
around the world. However, unauthorized ridesourcing activities taking
advantages of the sharing economy can greatly impair the healthy development of
this emerging industry. As the first step to regulate on-demand ride services
and eliminate black market, we design a method to detect ridesourcing cars from
a pool of cars based on their trajectories. Since licensed ridesourcing car
traces are not openly available and may be completely missing in some cities
due to legal issues, we turn to transferring knowledge from public transport
open data, i.e, taxis and buses, to ridesourcing detection among ordinary
vehicles. We propose a two-stage transfer learning framework. In Stage 1, we
take taxi and bus data as input to learn a random forest (RF) classifier using
trajectory features shared by taxis/buses and ridesourcing/other cars. Then, we
use the RF to label all the candidate cars. In Stage 2, leveraging the subset
of high confident labels from the previous stage as input, we further learn a
convolutional neural network (CNN) classifier for ridesourcing detection, and
iteratively refine RF and CNN, as well as the feature set, via a co-training
process. Finally, we use the resulting ensemble of RF and CNN to identify the
ridesourcing cars in the candidate pool. Experiments on real car, taxi and bus
traces show that our transfer learning framework, with no need of a pre-labeled
ridesourcing dataset, can achieve similar accuracy as the supervised learning
methods.
| Leye Wang, Xu Geng, Jintao Ke, Chen Peng, Xiaojuan Ma, Daqing Zhang,
Qiang Yang | null | 1705.08409 | null | null |
Reinforcement Learning with a Corrupted Reward Channel | cs.AI cs.LG stat.ML | No real-world reward function is perfect. Sensory errors and software bugs
may result in RL agents observing higher (or lower) rewards than they should.
For example, a reinforcement learning agent may prefer states where a sensory
error gives it the maximum reward, but where the true reward is actually small.
We formalise this problem as a generalised Markov Decision Problem called
Corrupt Reward MDP. Traditional RL methods fare poorly in CRMDPs, even under
strong simplifying assumptions and when trying to compensate for the possibly
corrupt rewards. Two ways around the problem are investigated. First, by giving
the agent richer data, such as in inverse reinforcement learning and
semi-supervised reinforcement learning, reward corruption stemming from
systematic sensory errors may sometimes be completely managed. Second, by using
randomisation to blunt the agent's optimisation, reward corruption can be
partially managed under some assumptions.
| Tom Everitt, Victoria Krakovna, Laurent Orseau, Marcus Hutter, Shane
Legg | null | 1705.08417 | null | null |
Continuous State-Space Models for Optimal Sepsis Treatment - a Deep
Reinforcement Learning Approach | cs.LG | Sepsis is a leading cause of mortality in intensive care units (ICUs) and
costs hospitals billions annually. Treating a septic patient is highly
challenging, because individual patients respond very differently to medical
interventions and there is no universally agreed-upon treatment for sepsis.
Understanding more about a patient's physiological state at a given time could
hold the key to effective treatment policies. In this work, we propose a new
approach to deduce optimal treatment policies for septic patients by using
continuous state-space models and deep reinforcement learning. Learning
treatment policies over continuous spaces is important, because we retain more
of the patient's physiological information. Our model is able to learn
clinically interpretable treatment policies, similar in important aspects to
the treatment policies of physicians. Evaluating our algorithm on past ICU
patient data, we find that our model could reduce patient mortality in the
hospital by up to 3.6% over observed clinical policies, from a baseline
mortality of 13.7%. The learned treatment policies could be used to aid
intensive care clinicians in medical decision making and improve the likelihood
of patient survival.
| Aniruddh Raghu, Matthieu Komorowski, Leo Anthony Celi, Peter Szolovits
and Marzyeh Ghassemi | null | 1705.08422 | null | null |
Submultiplicative Glivenko-Cantelli and Uniform Convergence of Revenues | cs.LG cs.GT | In this work we derive a variant of the classic Glivenko-Cantelli Theorem,
which asserts uniform convergence of the empirical Cumulative Distribution
Function (CDF) to the CDF of the underlying distribution. Our variant allows
for tighter convergence bounds for extreme values of the CDF.
We apply our bound in the context of revenue learning, which is a
well-studied problem in economics and algorithmic game theory. We derive
sample-complexity bounds on the uniform convergence rate of the empirical
revenues to the true revenues, assuming a bound on the $k$th moment of the
valuations, for any (possibly fractional) $k>1$.
For uniform convergence in the limit, we give a complete characterization and
a zero-one law: if the first moment of the valuations is finite, then uniform
convergence almost surely occurs; conversely, if the first moment is infinite,
then uniform convergence almost never occurs.
| Noga Alon, Moshe Babaioff, Yannai A. Gonczarowski, Yishay Mansour,
Shay Moran, Amir Yehudayoff | null | 1705.0843 | null | null |
Personalized and Private Peer-to-Peer Machine Learning | cs.LG cs.CR cs.DC cs.SY stat.ML | The rise of connected personal devices together with privacy concerns call
for machine learning algorithms capable of leveraging the data of a large
number of agents to learn personalized models under strong privacy
requirements. In this paper, we introduce an efficient algorithm to address the
above problem in a fully decentralized (peer-to-peer) and asynchronous fashion,
with provable convergence rate. We show how to make the algorithm
differentially private to protect against the disclosure of information about
the personal datasets, and formally analyze the trade-off between utility and
privacy. Our experiments show that our approach dramatically outperforms
previous work in the non-private case, and that under privacy constraints, we
can significantly improve over models learned in isolation.
| Aur\'elien Bellet, Rachid Guerraoui, Mahsa Taziki, Marc Tommasi | null | 1705.08435 | null | null |
Formal Guarantees on the Robustness of a Classifier against Adversarial
Manipulation | cs.LG cs.AI cs.CV stat.ML | Recent work has shown that state-of-the-art classifiers are quite brittle, in
the sense that a small adversarial change of an originally with high confidence
correctly classified input leads to a wrong classification again with high
confidence. This raises concerns that such classifiers are vulnerable to
attacks and calls into question their usage in safety-critical systems. We show
in this paper for the first time formal guarantees on the robustness of a
classifier by giving instance-specific lower bounds on the norm of the input
manipulation required to change the classifier decision. Based on this analysis
we propose the Cross-Lipschitz regularization functional. We show that using
this form of regularization in kernel methods resp. neural networks improves
the robustness of the classifier without any loss in prediction performance.
| Matthias Hein, Maksym Andriushchenko | null | 1705.08475 | null | null |
Efficiently applying attention to sequential data with the Recurrent
Discounted Attention unit | cs.LG | Recurrent Neural Networks architectures excel at processing sequences by
modelling dependencies over different timescales. The recently introduced
Recurrent Weighted Average (RWA) unit captures long term dependencies far
better than an LSTM on several challenging tasks. The RWA achieves this by
applying attention to each input and computing a weighted average over the full
history of its computations. Unfortunately, the RWA cannot change the attention
it has assigned to previous timesteps, and so struggles with carrying out
consecutive tasks or tasks with changing requirements. We present the Recurrent
Discounted Attention (RDA) unit that builds on the RWA by additionally allowing
the discounting of the past.
We empirically compare our model to RWA, LSTM and GRU units on several
challenging tasks. On tasks with a single output the RWA, RDA and GRU units
learn much quicker than the LSTM and with better performance. On the multiple
sequence copy task our RDA unit learns the task three times as quickly as the
LSTM or GRU units while the RWA fails to learn at all. On the Wikipedia
character prediction task the LSTM performs best but it followed closely by our
RDA unit. Overall our RDA unit performs well and is sample efficient on a large
variety of sequence tasks.
| Brendan Maginnis, Pierre H. Richemond | null | 1705.0848 | null | null |
Bayesian Pool-based Active Learning With Abstention Feedbacks | stat.ML cs.LG | We study pool-based active learning with abstention feedbacks, where a
labeler can abstain from labeling a queried example with some unknown
abstention rate. This is an important problem with many useful applications. We
take a Bayesian approach to the problem and develop two new greedy algorithms
that learn both the classification problem and the unknown abstention rate at
the same time. These are achieved by simply incorporating the estimated
abstention rate into the greedy criteria. We prove that both of our algorithms
have near-optimality guarantees: they respectively achieve a
${(1-\frac{1}{e})}$ constant factor approximation of the optimal expected or
worst-case value of a useful utility function. Our experiments show the
algorithms perform well in various practical scenarios.
| Cuong V. Nguyen, Lam Si Tung Ho, Huan Xu, Vu Dinh, Binh Nguyen | null | 1705.08481 | null | null |
Clinical Intervention Prediction and Understanding using Deep Networks | cs.LG | Real-time prediction of clinical interventions remains a challenge within
intensive care units (ICUs). This task is complicated by data sources that are
noisy, sparse, heterogeneous and outcomes that are imbalanced. In this paper,
we integrate data from all available ICU sources (vitals, labs, notes,
demographics) and focus on learning rich representations of this data to
predict onset and weaning of multiple invasive interventions. In particular, we
compare both long short-term memory networks (LSTM) and convolutional neural
networks (CNN) for prediction of five intervention tasks: invasive ventilation,
non-invasive ventilation, vasopressors, colloid boluses, and crystalloid
boluses. Our predictions are done in a forward-facing manner to enable
"real-time" performance, and predictions are made with a six hour gap time to
support clinically actionable planning. We achieve state-of-the-art results on
our predictive tasks using deep architectures. We explore the use of feature
occlusion to interpret LSTM models, and compare this to the interpretability
gained from examining inputs that maximally activate CNN outputs. We show that
our models are able to significantly outperform baselines in intervention
prediction, and provide insight into model learning, which is crucial for the
adoption of such models in practice.
| Harini Suresh, Nathan Hunt, Alistair Johnson, Leo Anthony Celi, Peter
Szolovits and Marzyeh Ghassemi | null | 1705.08498 | null | null |
The Prediction Advantage: A Universally Meaningful Performance Measure
for Classification and Regression | cs.LG | We introduce the Prediction Advantage (PA), a novel performance measure for
prediction functions under any loss function (e.g., classification or
regression). The PA is defined as the performance advantage relative to the
Bayesian risk restricted to knowing only the distribution of the labels. We
derive the PA for well-known loss functions, including 0/1 loss, cross-entropy
loss, absolute loss, and squared loss. In the latter case, the PA is identical
to the well-known R-squared measure, widely used in statistics. The use of the
PA ensures meaningful quantification of prediction performance, which is not
guaranteed, for example, when dealing with noisy imbalanced classification
problems. We argue that among several known alternative performance measures,
PA is the best (and only) quantity ensuring meaningfulness for all noise and
imbalance levels.
| Ran El-Yaniv, Yonatan Geifman, Yair Wiener | null | 1705.08499 | null | null |
Selective Classification for Deep Neural Networks | cs.LG cs.AI | Selective classification techniques (also known as reject option) have not
yet been considered in the context of deep neural networks (DNNs). These
techniques can potentially significantly improve DNNs prediction performance by
trading-off coverage. In this paper we propose a method to construct a
selective classifier given a trained neural network. Our method allows a user
to set a desired risk level. At test time, the classifier rejects instances as
needed, to grant the desired risk (with high probability). Empirical results
over CIFAR and ImageNet convincingly demonstrate the viability of our method,
which opens up possibilities to operate DNNs in mission-critical applications.
For example, using our method an unprecedented 2% error in top-5 ImageNet
classification can be guaranteed with probability 99.9%, and almost 60% test
coverage.
| Yonatan Geifman, Ran El-Yaniv | null | 1705.085 | null | null |
Interpreting Blackbox Models via Model Extraction | cs.LG | Interpretability has become incredibly important as machine learning is
increasingly used to inform consequential decisions. We propose to construct
global explanations of complex, blackbox models in the form of a decision tree
approximating the original model---as long as the decision tree is a good
approximation, then it mirrors the computation performed by the blackbox model.
We devise a novel algorithm for extracting decision tree explanations that
actively samples new training points to avoid overfitting. We evaluate our
algorithm on a random forest to predict diabetes risk and a learned controller
for cart-pole. Compared to several baselines, our decision trees are both
substantially more accurate and equally or more interpretable based on a user
study. Finally, we describe several insights provided by our interpretations,
including a causal issue validated by a physician.
| Osbert Bastani, Carolyn Kim, Hamsa Bastani | null | 1705.08504 | null | null |
An effective algorithm for hyperparameter optimization of neural
networks | cs.AI cs.LG cs.NE | A major challenge in designing neural network (NN) systems is to determine
the best structure and parameters for the network given the data for the
machine learning problem at hand. Examples of parameters are the number of
layers and nodes, the learning rates, and the dropout rates. Typically, these
parameters are chosen based on heuristic rules and manually fine-tuned, which
may be very time-consuming, because evaluating the performance of a single
parametrization of the NN may require several hours. This paper addresses the
problem of choosing appropriate parameters for the NN by formulating it as a
box-constrained mathematical optimization problem, and applying a
derivative-free optimization tool that automatically and effectively searches
the parameter space. The optimization tool employs a radial basis function
model of the objective function (the prediction accuracy of the NN) to
accelerate the discovery of configurations yielding high accuracy. Candidate
configurations explored by the algorithm are trained to a small number of
epochs, and only the most promising candidates receive full training. The
performance of the proposed methodology is assessed on benchmark sets and in
the context of predicting drug-drug interactions, showing promising results.
The optimization tool used in this paper is open-source.
| Gonzalo Diaz, Achille Fokoue, Giacomo Nannicini, Horst Samulowitz | null | 1705.0852 | null | null |
Data-driven Random Fourier Features using Stein Effect | cs.LG stat.ML | Large-scale kernel approximation is an important problem in machine learning
research. Approaches using random Fourier features have become increasingly
popular [Rahimi and Recht, 2007], where kernel approximation is treated as
empirical mean estimation via Monte Carlo (MC) or Quasi-Monte Carlo (QMC)
integration [Yang et al., 2014]. A limitation of the current approaches is that
all the features receive an equal weight summing to 1. In this paper, we
propose a novel shrinkage estimator from "Stein effect", which provides a
data-driven weighting strategy for random features and enjoys theoretical
justifications in terms of lowering the empirical risk. We further present an
efficient randomized algorithm for large-scale applications of the proposed
method. Our empirical results on six benchmark data sets demonstrate the
advantageous performance of this approach over representative baselines in both
kernel approximation and supervised learning tasks.
| Wei-Cheng Chang, Chun-Liang Li, Yiming Yang, Barnabas Poczos | null | 1705.08525 | null | null |
Convergence Analysis of Gradient EM for Multi-component Gaussian Mixture | math.ST cs.LG stat.TH | In this paper, we study convergence properties of the gradient
Expectation-Maximization algorithm \cite{lange1995gradient} for Gaussian
Mixture Models for general number of clusters and mixing coefficients. We
derive the convergence rate depending on the mixing coefficients, minimum and
maximum pairwise distances between the true centers and dimensionality and
number of components; and obtain a near-optimal local contraction radius. While
there have been some recent notable works that derive local convergence rates
for EM in the two equal mixture symmetric GMM, in the more general case, the
derivations need structurally different and non-trivial arguments. We use
recent tools from learning theory and empirical processes to achieve our
theoretical results.
| Bowei Yan, Mingzhang Yin and Purnamrita Sarkar | null | 1705.0853 | null | null |
Safe Model-based Reinforcement Learning with Stability Guarantees | stat.ML cs.AI cs.LG cs.SY | Reinforcement learning is a powerful paradigm for learning optimal policies
from experimental data. However, to find optimal policies, most reinforcement
learning algorithms explore all possible actions, which may be harmful for
real-world systems. As a consequence, learning algorithms are rarely applied on
safety-critical systems in the real world. In this paper, we present a learning
algorithm that explicitly considers safety, defined in terms of stability
guarantees. Specifically, we extend control-theoretic results on Lyapunov
stability verification and show how to use statistical models of the dynamics
to obtain high-performance control policies with provable stability
certificates. Moreover, under additional regularity assumptions in terms of a
Gaussian process prior, we prove that one can effectively and safely collect
data in order to learn about the dynamics and thus both improve control
performance and expand the safe region of the state space. In our experiments,
we show how the resulting algorithm can safely optimize a neural network policy
on a simulated inverted pendulum, without the pendulum ever falling down.
| Felix Berkenkamp, Matteo Turchetta, Angela P. Schoellig, Andreas
Krause | null | 1705.08551 | null | null |
Grounded Recurrent Neural Networks | stat.ML cs.CL cs.LG cs.NE | In this work, we present the Grounded Recurrent Neural Network (GRNN), a
recurrent neural network architecture for multi-label prediction which
explicitly ties labels to specific dimensions of the recurrent hidden state (we
call this process "grounding"). The approach is particularly well-suited for
extracting large numbers of concepts from text. We apply the new model to
address an important problem in healthcare of understanding what medical
concepts are discussed in clinical text. Using a publicly available dataset
derived from Intensive Care Units, we learn to label a patient's diagnoses and
procedures from their discharge summary. Our evaluation shows a clear advantage
to using our proposed architecture over a variety of strong baselines.
| Ankit Vani, Yacine Jernite, David Sontag | null | 1705.08557 | null | null |
Hashing as Tie-Aware Learning to Rank | stat.ML cs.CV cs.LG | Hashing, or learning binary embeddings of data, is frequently used in nearest
neighbor retrieval. In this paper, we develop learning to rank formulations for
hashing, aimed at directly optimizing ranking-based evaluation metrics such as
Average Precision (AP) and Normalized Discounted Cumulative Gain (NDCG). We
first observe that the integer-valued Hamming distance often leads to tied
rankings, and propose to use tie-aware versions of AP and NDCG to evaluate
hashing for retrieval. Then, to optimize tie-aware ranking metrics, we derive
their continuous relaxations, and perform gradient-based optimization with deep
neural networks. Our results establish the new state-of-the-art for image
retrieval by Hamming ranking in common benchmarks.
| Kun He, Fatih Cakir, Sarah Adel Bargal, Stan Sclaroff | null | 1705.08562 | null | null |
Towards Interrogating Discriminative Machine Learning Models | cs.LG stat.ML | It is oftentimes impossible to understand how machine learning models reach a
decision. While recent research has proposed various technical approaches to
provide some clues as to how a learning model makes individual decisions, they
cannot provide users with ability to inspect a learning model as a complete
entity. In this work, we propose a new technical approach that augments a
Bayesian regression mixture model with multiple elastic nets. Using the
enhanced mixture model, we extract explanations for a target model through
global approximation. To demonstrate the utility of our approach, we evaluate
it on different learning models covering the tasks of text mining and image
recognition. Our results indicate that the proposed approach not only
outperforms the state-of-the-art technique in explaining individual decisions
but also provides users with an ability to discover the vulnerabilities of a
learning model.
| Wenbo Guo, Kaixuan Zhang, Lin Lin, Sui Huang, Xinyu Xing | null | 1705.08564 | null | null |
MMD GAN: Towards Deeper Understanding of Moment Matching Network | cs.LG cs.AI stat.ML | Generative moment matching network (GMMN) is a deep generative model that
differs from Generative Adversarial Network (GAN) by replacing the
discriminator in GAN with a two-sample test based on kernel maximum mean
discrepancy (MMD). Although some theoretical guarantees of MMD have been
studied, the empirical performance of GMMN is still not as competitive as that
of GAN on challenging and large benchmark datasets. The computational
efficiency of GMMN is also less desirable in comparison with GAN, partially due
to its requirement for a rather large batch size during the training. In this
paper, we propose to improve both the model expressiveness of GMMN and its
computational efficiency by introducing adversarial kernel learning techniques,
as the replacement of a fixed Gaussian kernel in the original GMMN. The new
approach combines the key ideas in both GMMN and GAN, hence we name it MMD GAN.
The new distance measure in MMD GAN is a meaningful loss that enjoys the
advantage of weak topology and can be optimized via gradient descent with
relatively small batch sizes. In our evaluation on multiple benchmark datasets,
including MNIST, CIFAR- 10, CelebA and LSUN, the performance of MMD-GAN
significantly outperforms GMMN, and is competitive with other representative
GAN works.
| Chun-Liang Li, Wei-Cheng Chang, Yu Cheng, Yiming Yang, Barnab\'as
P\'oczos | null | 1705.08584 | null | null |
Multi-Task Learning for Contextual Bandits | stat.ML cs.LG | Contextual bandits are a form of multi-armed bandit in which the agent has
access to predictive side information (known as the context) for each arm at
each time step, and have been used to model personalized news recommendation,
ad placement, and other applications. In this work, we propose a multi-task
learning framework for contextual bandit problems. Like multi-task learning in
the batch setting, the goal is to leverage similarities in contexts for
different arms so as to improve the agent's ability to predict rewards from
contexts. We propose an upper confidence bound-based multi-task learning
algorithm for contextual bandits, establish a corresponding regret bound, and
interpret this bound to quantify the advantages of learning in the presence of
high task (arm) similarity. We also describe an effective scheme for estimating
task similarity from data, and demonstrate our algorithm's performance on
several data sets.
| Aniket Anand Deshmukh, Urun Dogan, Clayton Scott | null | 1705.08618 | null | null |
Dictionary-based Monitoring of Premature Ventricular Contractions: An
Ultra-Low-Cost Point-of-Care Service | cs.LG | While cardiovascular diseases (CVDs) are prevalent across economic strata,
the economically disadvantaged population is disproportionately affected due to
the high cost of traditional CVD management. Accordingly, developing an
ultra-low-cost alternative, affordable even to groups at the bottom of the
economic pyramid, has emerged as a societal imperative. Against this backdrop,
we propose an inexpensive yet accurate home-based electrocardiogram(ECG)
monitoring service. Specifically, we seek to provide point-of-care monitoring
of premature ventricular contractions (PVCs), high frequency of which could
indicate the onset of potentially fatal arrhythmia. Note that a traditional
telecardiology system acquires the ECG, transmits it to a professional
diagnostic centre without processing, and nearly achieves the diagnostic
accuracy of a bedside setup, albeit at high bandwidth cost. In this context, we
aim at reducing cost without significantly sacrificing reliability. To this
end, we develop a dictionary-based algorithm that detects with high sensitivity
the anomalous beats only which are then transmitted. We further compress those
transmitted beats using class-specific dictionaries subject to suitable
reconstruction/diagnostic fidelity. Such a scheme would not only reduce the
overall bandwidth requirement, but also localising anomalous beats, thereby
reducing physicians' burden. Finally, using Monte Carlo cross validation on
MIT/BIH arrhythmia database, we evaluate the performance of the proposed
system. In particular, with a sensitivity target of at most one undetected PVC
in one hundred beats, and a percentage root mean squared difference less than
9% (a clinically acceptable level of fidelity), we achieved about 99.15%
reduction in bandwidth cost, equivalent to 118-fold savings over traditional
telecardiology.
| Bollepalli S. Chandra, Challa S. Sastry, Laxminarayana Anumandla and
Soumya Jana | null | 1705.08619 | null | null |
Nonparametric Preference Completion | stat.ML cs.LG | We consider the task of collaborative preference completion: given a pool of
items, a pool of users and a partially observed item-user rating matrix, the
goal is to recover the \emph{personalized ranking} of each user over all of the
items. Our approach is nonparametric: we assume that each item $i$ and each
user $u$ have unobserved features $x_i$ and $y_u$, and that the associated
rating is given by $g_u(f(x_i,y_u))$ where $f$ is Lipschitz and $g_u$ is a
monotonic transformation that depends on the user. We propose a $k$-nearest
neighbors-like algorithm and prove that it is consistent. To the best of our
knowledge, this is the first consistency result for the collaborative
preference completion problem in a nonparametric setting. Finally, we
demonstrate the performance of our algorithm with experiments on the Netflix
and Movielens datasets.
| Julian Katz-Samuels and Clayton Scott | null | 1705.08621 | null | null |
Towards Understanding the Invertibility of Convolutional Neural Networks | stat.ML cs.LG | Several recent works have empirically observed that Convolutional Neural Nets
(CNNs) are (approximately) invertible. To understand this approximate
invertibility phenomenon and how to leverage it more effectively, we focus on a
theoretical explanation and develop a mathematical model of sparse signal
recovery that is consistent with CNNs with random weights. We give an exact
connection to a particular model of model-based compressive sensing (and its
recovery algorithms) and random-weight CNNs. We show empirically that several
learned networks are consistent with our mathematical analysis and then
demonstrate that with such a simple theoretical framework, we can obtain
reasonable re- construction results on real images. We also discuss gaps
between our model assumptions and the CNN trained for classification in
practical scenarios.
| Anna C. Gilbert, Yi Zhang, Kibok Lee, Yuting Zhang, Honglak Lee | null | 1705.08664 | null | null |
Bayesian Compression for Deep Learning | stat.ML cs.LG | Compression and computational efficiency in deep learning have become a
problem of great significance. In this work, we argue that the most principled
and effective way to attack this problem is by adopting a Bayesian point of
view, where through sparsity inducing priors we prune large parts of the
network. We introduce two novelties in this paper: 1) we use hierarchical
priors to prune nodes instead of individual weights, and 2) we use the
posterior uncertainties to determine the optimal fixed point precision to
encode the weights. Both factors significantly contribute to achieving the
state of the art in terms of compression rates, while still staying competitive
with methods designed to optimize for speed or energy efficiency.
| Christos Louizos, Karen Ullrich and Max Welling | null | 1705.08665 | null | null |
Continual Learning with Deep Generative Replay | cs.AI cs.CV cs.LG | Attempts to train a comprehensive artificial intelligence capable of solving
multiple tasks have been impeded by a chronic problem called catastrophic
forgetting. Although simply replaying all previous data alleviates the problem,
it requires large memory and even worse, often infeasible in real world
applications where the access to past data is limited. Inspired by the
generative nature of hippocampus as a short-term memory system in primate
brain, we propose the Deep Generative Replay, a novel framework with a
cooperative dual model architecture consisting of a deep generative model
("generator") and a task solving model ("solver"). With only these two models,
training data for previous tasks can easily be sampled and interleaved with
those for a new task. We test our methods in several sequential learning
settings involving image classification tasks.
| Hanul Shin, Jung Kwon Lee, Jaehong Kim, Jiwon Kim | null | 1705.0869 | null | null |
Stochastic Sequential Neural Networks with Structured Inference | cs.LG cs.CV | Unsupervised structure learning in high-dimensional time series data has
attracted a lot of research interests. For example, segmenting and labelling
high dimensional time series can be helpful in behavior understanding and
medical diagnosis. Recent advances in generative sequential modeling have
suggested to combine recurrent neural networks with state space models (e.g.,
Hidden Markov Models). This combination can model not only the long term
dependency in sequential data, but also the uncertainty included in the hidden
states. Inheriting these advantages of stochastic neural sequential models, we
propose a structured and stochastic sequential neural network, which models
both the long-term dependencies via recurrent neural networks and the
uncertainty in the segmentation and labels via discrete random variables. For
accurate and efficient inference, we present a bi-directional inference network
by reparamterizing the categorical segmentation and labels with the recent
proposed Gumbel-Softmax approximation and resort to the Stochastic Gradient
Variational Bayes. We evaluate the proposed model in a number of tasks,
including speech modeling, automatic segmentation and labeling in behavior
understanding, and sequential multi-objects recognition. Experimental results
have demonstrated that our proposed model can achieve significant improvement
over the state-of-the-art methods.
| Hao Liu and Haoli Bai and Lirong He and Zenglin Xu | null | 1705.08695 | null | null |
Open-Category Classification by Adversarial Sample Generation | cs.LG | In real-world classification tasks, it is difficult to collect training
samples from all possible categories of the environment. Therefore, when an
instance of an unseen class appears in the prediction stage, a robust
classifier should be able to tell that it is from an unseen class, instead of
classifying it to be any known category. In this paper, adopting the idea of
adversarial learning, we propose the ASG framework for open-category
classification. ASG generates positive and negative samples of seen categories
in the unsupervised manner via an adversarial learning strategy. With the
generated samples, ASG then learns to tell seen from unseen in the supervised
manner. Experiments performed on several datasets show the effectiveness of
ASG.
| Yang Yu, Wei-Yang Qu, Nan Li, Zimin Guo | null | 1705.08722 | null | null |
Non-Stationary Spectral Kernels | stat.ML cs.LG | We propose non-stationary spectral kernels for Gaussian process regression.
We propose to model the spectral density of a non-stationary kernel function as
a mixture of input-dependent Gaussian process frequency density surfaces. We
solve the generalised Fourier transform with such a model, and present a family
of non-stationary and non-monotonic kernels that can learn input-dependent and
potentially long-range, non-monotonic covariances between inputs. We derive
efficient inference using model whitening and marginalized posterior, and show
with case studies that these kernels are necessary when modelling even rather
simple time series, image or geospatial data with non-stationary
characteristics.
| Sami Remes, Markus Heinonen, Samuel Kaski | null | 1705.08736 | null | null |
Train longer, generalize better: closing the generalization gap in large
batch training of neural networks | stat.ML cs.LG | Background: Deep learning models are typically trained using stochastic
gradient descent or one of its variants. These methods update the weights using
their gradient, estimated from a small fraction of the training data. It has
been observed that when using large batch sizes there is a persistent
degradation in generalization performance - known as the "generalization gap"
phenomena. Identifying the origin of this gap and closing it had remained an
open problem.
Contributions: We examine the initial high learning rate training phase. We
find that the weight distance from its initialization grows logarithmically
with the number of weight updates. We therefore propose a "random walk on
random landscape" statistical model which is known to exhibit similar
"ultra-slow" diffusion behavior. Following this hypothesis we conducted
experiments to show empirically that the "generalization gap" stems from the
relatively small number of updates rather than the batch size, and can be
completely eliminated by adapting the training regime used. We further
investigate different techniques to train models in the large-batch regime and
present a novel algorithm named "Ghost Batch Normalization" which enables
significant decrease in the generalization gap without increasing the number of
updates. To validate our findings we conduct several additional experiments on
MNIST, CIFAR-10, CIFAR-100 and ImageNet. Finally, we reassess common practices
and beliefs concerning training of deep models and suggest they may not be
optimal to achieve good generalization.
| Elad Hoffer, Itay Hubara, Daniel Soudry | null | 1705.08741 | null | null |
Beyond Parity: Fairness Objectives for Collaborative Filtering | cs.IR cs.AI cs.LG stat.ML | We study fairness in collaborative-filtering recommender systems, which are
sensitive to discrimination that exists in historical data. Biased data can
lead collaborative-filtering methods to make unfair predictions for users from
minority groups. We identify the insufficiency of existing fairness metrics and
propose four new metrics that address different forms of unfairness. These
fairness metrics can be optimized by adding fairness terms to the learning
objective. Experiments on synthetic and real data show that our new metrics can
better measure fairness than the baseline, and that the fairness objectives
effectively help reduce unfairness.
| Sirui Yao, Bert Huang | null | 1705.08804 | null | null |
Causal Effect Inference with Deep Latent-Variable Models | stat.ML cs.LG | Learning individual-level causal effects from observational data, such as
inferring the most effective medication for a specific patient, is a problem of
growing importance for policy makers. The most important aspect of inferring
causal effects from observational data is the handling of confounders, factors
that affect both an intervention and its outcome. A carefully designed
observational study attempts to measure all important confounders. However,
even if one does not have direct access to all confounders, there may exist
noisy and uncertain measurement of proxies for confounders. We build on recent
advances in latent variable modeling to simultaneously estimate the unknown
latent space summarizing the confounders and the causal effect. Our method is
based on Variational Autoencoders (VAE) which follow the causal structure of
inference with proxies. We show our method is significantly more robust than
existing methods, and matches the state-of-the-art on previous benchmarks
focused on individual treatment effects.
| Christos Louizos, Uri Shalit, Joris Mooij, David Sontag, Richard Zemel
and Max Welling | null | 1705.08821 | null | null |
Learning with Average Top-k Loss | stat.ML cs.LG | In this work, we introduce the {\em average top-$k$} (\atk) loss as a new
aggregate loss for supervised learning, which is the average over the $k$
largest individual losses over a training dataset. We show that the \atk loss
is a natural generalization of the two widely used aggregate losses, namely the
average loss and the maximum loss, but can combine their advantages and
mitigate their drawbacks to better adapt to different data distributions.
Furthermore, it remains a convex function over all individual losses, which can
lead to convex optimization problems that can be solved effectively with
conventional gradient-based methods. We provide an intuitive interpretation of
the \atk loss based on its equivalent effect on the continuous individual loss
functions, suggesting that it can reduce the penalty on correctly classified
data. We further give a learning theory analysis of \matk learning on the
classification calibration of the \atk loss and the error bounds of \atk-SVM.
We demonstrate the applicability of minimum average top-$k$ learning for binary
classification and regression using synthetic and real datasets.
| Yanbo Fan, Siwei Lyu, Yiming Ying, Bao-Gang Hu | null | 1705.08826 | null | null |
Multi-Level Variational Autoencoder: Learning Disentangled
Representations from Grouped Observations | cs.LG stat.ML | We would like to learn a representation of the data which decomposes an
observation into factors of variation which we can independently control.
Specifically, we want to use minimal supervision to learn a latent
representation that reflects the semantics behind a specific grouping of the
data, where within a group the samples share a common factor of variation. For
example, consider a collection of face images grouped by identity. We wish to
anchor the semantics of the grouping into a relevant and disentangled
representation that we can easily exploit. However, existing deep probabilistic
models often assume that the observations are independent and identically
distributed. We present the Multi-Level Variational Autoencoder (ML-VAE), a new
deep probabilistic model for learning a disentangled representation of a set of
grouped observations. The ML-VAE separates the latent representation into
semantically meaningful parts by working both at the group level and the
observation level, while retaining efficient test-time inference. Quantitative
and qualitative evaluations show that the ML-VAE model (i) learns a
semantically meaningful disentanglement of grouped data, (ii) enables
manipulation of the latent representation, and (iii) generalises to unseen
groups.
| Diane Bouchacourt, Ryota Tomioka, Sebastian Nowozin | null | 1705.08841 | null | null |
Joint Distribution Optimal Transportation for Domain Adaptation | stat.ML cs.LG | This paper deals with the unsupervised domain adaptation problem, where one
wants to estimate a prediction function $f$ in a given target domain without
any labeled sample by exploiting the knowledge available from a source domain
where labels are known. Our work makes the following assumption: there exists a
non-linear transformation between the joint feature/label space distributions
of the two domain $\mathcal{P}_s$ and $\mathcal{P}_t$. We propose a solution of
this problem with optimal transport, that allows to recover an estimated target
$\mathcal{P}^f_t=(X,f(X))$ by optimizing simultaneously the optimal coupling
and $f$. We show that our method corresponds to the minimization of a bound on
the target error, and provide an efficient algorithmic solution, for which
convergence is proved. The versatility of our approach, both in terms of class
of hypothesis or loss functions is demonstrated with real world classification
and regression problems, for which we reach or surpass state-of-the-art
results.
| Nicolas Courty, R\'emi Flamary, Amaury Habrard and Alain Rakotomamonjy | null | 1705.08848 | null | null |
Semi-supervised Learning with GANs: Manifold Invariance with Improved
Inference | cs.LG cs.AI cs.CV stat.ML | Semi-supervised learning methods using Generative Adversarial Networks (GANs)
have shown promising empirical success recently. Most of these methods use a
shared discriminator/classifier which discriminates real examples from fake
while also predicting the class label. Motivated by the ability of the GANs
generator to capture the data manifold well, we propose to estimate the tangent
space to the data manifold using GANs and employ it to inject invariances into
the classifier. In the process, we propose enhancements over existing methods
for learning the inverse mapping (i.e., the encoder) which greatly improves in
terms of semantic similarity of the reconstructed sample with the input sample.
We observe considerable empirical gains in semi-supervised learning over
baselines, particularly in the cases when the number of labeled examples is
low. We also provide insights into how fake examples influence the
semi-supervised learning procedure.
| Abhishek Kumar, Prasanna Sattigeri, P. Thomas Fletcher | null | 1705.0885 | null | null |
Audio-replay attack detection countermeasures | cs.SD cs.LG stat.ML | This paper presents the Speech Technology Center (STC) replay attack
detection systems proposed for Automatic Speaker Verification Spoofing and
Countermeasures Challenge 2017. In this study we focused on comparison of
different spoofing detection approaches. These were GMM based methods, high
level features extraction with simple classifier and deep learning frameworks.
Experiments performed on the development and evaluation parts of the challenge
dataset demonstrated stable efficiency of deep learning approaches in case of
changing acoustic conditions. At the same time SVM classifier with high level
features provided a substantial input in the efficiency of the resulting STC
systems according to the fusion systems results.
| Galina Lavrentyeva, Sergey Novoselov, Egor Malykh, Alexander Kozlov,
Oleg Kudashev and Vadim Shchemelinin | null | 1705.08858 | null | null |
Anti-spoofing Methods for Automatic SpeakerVerification System | cs.SD cs.LG stat.ML | Growing interest in automatic speaker verification (ASV)systems has lead to
significant quality improvement of spoofing attackson them. Many research works
confirm that despite the low equal er-ror rate (EER) ASV systems are still
vulnerable to spoofing attacks. Inthis work we overview different acoustic
feature spaces and classifiersto determine reliable and robust countermeasures
against spoofing at-tacks. We compared several spoofing detection systems,
presented so far,on the development and evaluation datasets of the Automatic
SpeakerVerification Spoofing and Countermeasures (ASVspoof) Challenge
2015.Experimental results presented in this paper demonstrate that the useof
magnitude and phase information combination provides a substantialinput into
the efficiency of the spoofing detection systems. Also wavelet-based features
show impressive results in terms of equal error rate. Inour overview we compare
spoofing performance for systems based on dif-ferent classifiers. Comparison
results demonstrate that the linear SVMclassifier outperforms the conventional
GMM approach. However, manyresearchers inspired by the great success of deep
neural networks (DNN)approaches in the automatic speech recognition, applied
DNN in thespoofing detection task and obtained quite low EER for known and
un-known type of spoofing attacks.
| Galina Lavrentyeva, Sergey Novoselov and Konstantin Simonchik | null | 1705.08865 | null | null |
Flow-GAN: Combining Maximum Likelihood and Adversarial Learning in
Generative Models | cs.LG cs.AI cs.NE stat.ML | Adversarial learning of probabilistic models has recently emerged as a
promising alternative to maximum likelihood. Implicit models such as generative
adversarial networks (GAN) often generate better samples compared to explicit
models trained by maximum likelihood. Yet, GANs sidestep the characterization
of an explicit density which makes quantitative evaluations challenging. To
bridge this gap, we propose Flow-GANs, a generative adversarial network for
which we can perform exact likelihood evaluation, thus supporting both
adversarial and maximum likelihood training. When trained adversarially,
Flow-GANs generate high-quality samples but attain extremely poor
log-likelihood scores, inferior even to a mixture model memorizing the training
data; the opposite is true when trained by maximum likelihood. Results on MNIST
and CIFAR-10 demonstrate that hybrid training can attain high held-out
likelihoods while retaining visual fidelity in the generated samples.
| Aditya Grover, Manik Dhar, Stefano Ermon | null | 1705.08868 | null | null |
Dense Transformer Networks | cs.CV cs.LG cs.NE stat.ML | The key idea of current deep learning methods for dense prediction is to
apply a model on a regular patch centered on each pixel to make pixel-wise
predictions. These methods are limited in the sense that the patches are
determined by network architecture instead of learned from data. In this work,
we propose the dense transformer networks, which can learn the shapes and sizes
of patches from data. The dense transformer networks employ an encoder-decoder
architecture, and a pair of dense transformer modules are inserted into each of
the encoder and decoder paths. The novelty of this work is that we provide
technical solutions for learning the shapes and sizes of patches from data and
efficiently restoring the spatial correspondence required for dense prediction.
The proposed dense transformer modules are differentiable, thus the entire
network can be trained. We apply the proposed networks on natural and
biological image segmentation tasks and show superior performance is achieved
in comparison to baseline methods.
| Jun Li, Yongjun Chen, Lei Cai, Ian Davidson, Shuiwang Ji | null | 1705.08881 | null | null |
Unsupervised Learning Layers for Video Analysis | cs.LG cs.CV stat.ML | This paper presents two unsupervised learning layers (UL layers) for
label-free video analysis: one for fully connected layers, and the other for
convolutional ones. The proposed UL layers can play two roles: they can be the
cost function layer for providing global training signal; meanwhile they can be
added to any regular neural network layers for providing local training signals
and combined with the training signals backpropagated from upper layers for
extracting both slow and fast changing features at layers of different depths.
Therefore, the UL layers can be used in either pure unsupervised or
semi-supervised settings. Both a closed-form solution and an online learning
algorithm for two UL layers are provided. Experiments with unlabeled synthetic
and real-world videos demonstrated that the neural networks equipped with UL
layers and trained with the proposed online learning algorithm can extract
shape and motion information from video sequences of moving objects. The
experiments demonstrated the potential applications of UL layers and online
learning algorithm to head orientation estimation and moving object
localization.
| Liang Zhao, Yang Wang, Yi Yang, Wei Xu | null | 1705.08918 | null | null |
Consistent Kernel Density Estimation with Non-Vanishing Bandwidth | stat.ML cs.LG | Consistency of the kernel density estimator requires that the kernel
bandwidth tends to zero as the sample size grows. In this paper we investigate
the question of whether consistency is possible when the bandwidth is fixed, if
we consider a more general class of weighted KDEs. To answer this question in
the affirmative, we introduce the fixed-bandwidth KDE (fbKDE), obtained by
solving a quadratic program, and prove that it consistently estimates any
continuous square-integrable density. We also establish rates of convergence
for the fbKDE with radial kernels and the box kernel under appropriate
smoothness assumptions. Furthermore, in an experimental study we demonstrate
that the fbKDE compares favorably to the standard KDE and the previously
proposed variable bandwidth KDE.
| Efr\'en Cruz Cort\'es, Clayton Scott | null | 1705.08921 | null | null |
Exploring the Regularity of Sparse Structure in Convolutional Neural
Networks | cs.LG stat.ML | Sparsity helps reduce the computational complexity of deep neural networks by
skipping zeros. Taking advantage of sparsity is listed as a high priority in
next generation DNN accelerators such as TPU. The structure of sparsity, i.e.,
the granularity of pruning, affects the efficiency of hardware accelerator
design as well as the prediction accuracy. Coarse-grained pruning creates
regular sparsity patterns, making it more amenable for hardware acceleration
but more challenging to maintain the same accuracy. In this paper we
quantitatively measure the trade-off between sparsity regularity and prediction
accuracy, providing insights in how to maintain accuracy while having more a
more structured sparsity pattern. Our experimental results show that
coarse-grained pruning can achieve a sparsity ratio similar to unstructured
pruning without loss of accuracy. Moreover, due to the index saving effect,
coarse-grained pruning is able to obtain a better compression ratio than
fine-grained sparsity at the same accuracy threshold. Based on the recent
sparse convolutional neural network accelerator (SCNN), our experiments further
demonstrate that coarse-grained sparsity saves about 2x the memory references
compared to fine-grained sparsity. Since memory reference is more than two
orders of magnitude more expensive than arithmetic operations, the regularity
of sparse structure leads to more efficient hardware design.
| Huizi Mao, Song Han, Jeff Pool, Wenshuo Li, Xingyu Liu, Yu Wang,
William J. Dally | null | 1705.08922 | null | null |
Proximity Variational Inference | stat.ML cs.LG stat.CO | Variational inference is a powerful approach for approximate posterior
inference. However, it is sensitive to initialization and can be subject to
poor local optima. In this paper, we develop proximity variational inference
(PVI). PVI is a new method for optimizing the variational objective that
constrains subsequent iterates of the variational parameters to robustify the
optimization path. Consequently, PVI is less sensitive to initialization and
optimization quirks and finds better local optima. We demonstrate our method on
three proximity statistics. We study PVI on a Bernoulli factor model and
sigmoid belief network with both real and synthetic data and compare to
deterministic annealing (Katahira et al., 2008). We highlight the flexibility
of PVI by designing a proximity statistic for Bayesian deep learning models
such as the variational autoencoder (Kingma and Welling, 2014; Rezende et al.,
2014). Empirically, we show that PVI consistently finds better local optima and
gives better predictive performance.
| Jaan Altosaar, Rajesh Ranganath, David M. Blei | null | 1705.08931 | null | null |
Optimal Cooperative Inference | cs.LG | Cooperative transmission of data fosters rapid accumulation of knowledge by
efficiently combining experiences across learners. Although well studied in
human learning and increasingly in machine learning, we lack formal frameworks
through which we may reason about the benefits and limitations of cooperative
inference. We present such a framework. We introduce novel indices for
measuring the effectiveness of probabilistic and cooperative information
transmission. We relate our indices to the well-known Teaching Dimension in
deterministic settings. We prove conditions under which optimal cooperative
inference can be achieved, including a representation theorem that constrains
the form of inductive biases for learners optimized for cooperative inference.
We conclude by demonstrating how these principles may inform the design of
machine learning algorithms and discuss implications for human and machine
learning.
| Scott Cheng-Hsin Yang, Yue Yu, Arash Givchi, Pei Wang, Wai Keen Vong,
and Patrick Shafto | null | 1705.08971 | null | null |
Modeling The Intensity Function Of Point Process Via Recurrent Neural
Networks | cs.LG cs.AI stat.ML | Event sequence, asynchronously generated with random timestamp, is ubiquitous
among applications. The precise and arbitrary timestamp can carry important
clues about the underlying dynamics, and has lent the event data fundamentally
different from the time-series whereby series is indexed with fixed and equal
time interval. One expressive mathematical tool for modeling event is point
process. The intensity functions of many point processes involve two
components: the background and the effect by the history. Due to its inherent
spontaneousness, the background can be treated as a time series while the other
need to handle the history events. In this paper, we model the background by a
Recurrent Neural Network (RNN) with its units aligned with time series indexes
while the history effect is modeled by another RNN whose units are aligned with
asynchronous events to capture the long-range dynamics. The whole model with
event type and timestamp prediction output layers can be trained end-to-end.
Our approach takes an RNN perspective to point process, and models its
background and history effect. For utility, our method allows a black-box
treatment for modeling the intensity which is often a pre-defined parametric
form in point processes. Meanwhile end-to-end training opens the venue for
reusing existing rich techniques in deep network for point process modeling. We
apply our model to the predictive maintenance problem using a log dataset by
more than 1000 ATMs from a global bank headquartered in North America.
| Shuai Xiao, Junchi Yan, Stephen M. Chu, Xiaokang Yang, Hongyuan Zha | null | 1705.08982 | null | null |
Approximation and Convergence Properties of Generative Adversarial
Learning | cs.LG stat.ML | Generative adversarial networks (GAN) approximate a target data distribution
by jointly optimizing an objective function through a "two-player game" between
a generator and a discriminator. Despite their empirical success, however, two
very basic questions on how well they can approximate the target distribution
remain unanswered. First, it is not known how restricting the discriminator
family affects the approximation quality. Second, while a number of different
objective functions have been proposed, we do not understand when convergence
to the global minima of the objective function leads to convergence to the
target distribution under various notions of distributional convergence.
In this paper, we address these questions in a broad and unified setting by
defining a notion of adversarial divergences that includes a number of recently
proposed objective functions. We show that if the objective function is an
adversarial divergence with some additional conditions, then using a restricted
discriminator family has a moment-matching effect. Additionally, we show that
for objective functions that are strict adversarial divergences, convergence in
the objective function implies weak convergence, thus generalizing previous
results.
| Shuang Liu, Olivier Bousquet, Kamalika Chaudhuri | null | 1705.08991 | null | null |
State Space Decomposition and Subgoal Creation for Transfer in Deep
Reinforcement Learning | cs.AI cs.LG stat.ML | Typical reinforcement learning (RL) agents learn to complete tasks specified
by reward functions tailored to their domain. As such, the policies they learn
do not generalize even to similar domains. To address this issue, we develop a
framework through which a deep RL agent learns to generalize policies from
smaller, simpler domains to more complex ones using a recurrent attention
mechanism. The task is presented to the agent as an image and an instruction
specifying the goal. This meta-controller guides the agent towards its goal by
designing a sequence of smaller subtasks on the part of the state space within
the attention, effectively decomposing it. As a baseline, we consider a setup
without attention as well. Our experiments show that the meta-controller learns
to create subgoals within the attention.
| Himanshu Sahni, Saurabh Kumar, Farhan Tejani, Yannick Schroecker,
Charles Isbell | null | 1705.08997 | null | null |
Principled Hybrids of Generative and Discriminative Domain Adaptation | cs.LG cs.AI | We propose a probabilistic framework for domain adaptation that blends both
generative and discriminative modeling in a principled way. Under this
framework, generative and discriminative models correspond to specific choices
of the prior over parameters. This provides us a very general way to
interpolate between generative and discriminative extremes through different
choices of priors. By maximizing both the marginal and the conditional
log-likelihoods, models derived from this framework can use both labeled
instances from the source domain as well as unlabeled instances from both
source and target domains. Under this framework, we show that the popular
reconstruction loss of autoencoder corresponds to an upper bound of the
negative marginal log-likelihoods of unlabeled instances, where marginal
distributions are given by proper kernel density estimations. This provides a
way to interpret the empirical success of autoencoders in domain adaptation and
semi-supervised learning. We instantiate our framework using neural networks,
and build a concrete model, DAuto. Empirically, we demonstrate the
effectiveness of DAuto on text, image and speech datasets, showing that it
outperforms related competitors when domain adaptation is possible.
| Han Zhao, Zhenyao Zhu, Junjie Hu, Adam Coates, Geoff Gordon | null | 1705.09011 | null | null |
Learning to Pour | cs.RO cs.LG | Pouring is a simple task people perform daily. It is the second most
frequently executed motion in cooking scenarios, after pick-and-place. We
present a pouring trajectory generation approach, which uses force feedback
from the cup to determine the future velocity of pouring. The approach uses
recurrent neural networks as its building blocks. We collected the pouring
demonstrations which we used for training. To test our approach in simulation,
we also created and trained a force estimation system. The simulated
experiments show that the system is able to generalize to single unseen element
of the pouring characteristics.
| Yongqiang Huang and Yu Sun | null | 1705.09021 | null | null |
Best-Choice Edge Grafting for Efficient Structure Learning of Markov
Random Fields | cs.LG cs.AI stat.ML | Incremental methods for structure learning of pairwise Markov random fields
(MRFs), such as grafting, improve scalability by avoiding inference over the
entire feature space in each optimization step. Instead, inference is performed
over an incrementally grown active set of features. In this paper, we address
key computational bottlenecks that current incremental techniques still suffer
by introducing best-choice edge grafting, an incremental, structured method
that activates edges as groups of features in a streaming setting. The method
uses a reservoir of edges that satisfy an activation condition, approximating
the search for the optimal edge to activate. It also reorganizes the search
space using search-history and structure heuristics. Experiments show a
significant speedup for structure learning and a controllable trade-off between
the speed and quality of learning.
| Walid Chaabene and Bert Huang | null | 1705.09026 | null | null |
Deriving Neural Architectures from Sequence and Graph Kernels | cs.NE cs.CL cs.LG | The design of neural architectures for structured objects is typically guided
by experimental insights rather than a formal process. In this work, we appeal
to kernels over combinatorial structures, such as sequences and graphs, to
derive appropriate neural operations. We introduce a class of deep recurrent
neural operations and formally characterize their associated kernel spaces. Our
recurrent modules compare the input to virtual reference objects (cf. filters
in CNN) via the kernels. Similar to traditional neural operations, these
reference objects are parameterized and directly optimized in end-to-end
training. We empirically evaluate the proposed class of neural architectures on
standard applications such as language modeling and molecular graph regression,
achieving state-of-the-art results across these applications.
| Tao Lei, Wengong Jin, Regina Barzilay and Tommi Jaakkola | null | 1705.09037 | null | null |
A Clustering-based Consistency Adaptation Strategy for Distributed SDN
Controllers | cs.NI cs.LG | Distributed controllers are oftentimes used in large-scale SDN deployments
where they run a myriad of network applications simultaneously. Such
applications could have different consistency and availability preferences.
These controllers need to communicate via east/west interfaces in order to
synchronize their state information. The consistency and the availability of
the distributed state information are governed by an underlying consistency
model. Earlier, we suggested the use of adaptively-consistent controllers that
can autonomously tune their consistency parameters in order to meet the
performance requirements of a certain application. In this paper, we examine
the feasibility of employing adaptive controllers that are built on-top of
tunable consistency models similar to that of Apache Cassandra. We present an
adaptation strategy that uses clustering techniques (sequential k-means and
incremental k-means) in order to map a given application performance indicator
into a feasible consistency level that can be used with the underlying tunable
consistency model. In the cases that we modeled and tested, our results show
that in the case of sequential k-means, with a reasonable number of clusters
(>= 50), a plausible mapping (low RMSE) could be estimated between the
application performance indicators and the consistency level indicator. In the
case of incremental k-means, the results also showed that a plausible mapping
(low RMSE) could be estimated using a similar number of clusters (>= 50) by
using a small threshold (~$ 0.01).
| Mohamed Aslan, Ashraf Matrawy | null | 1705.0905 | null | null |
The cost of fairness in classification | cs.LG | We study the problem of learning classifiers with a fairness constraint, with
three main contributions towards the goal of quantifying the problem's inherent
tradeoffs. First, we relate two existing fairness measures to cost-sensitive
risks. Second, we show that for cost-sensitive classification and fairness
measures, the optimal classifier is an instance-dependent thresholding of the
class-probability function. Third, we show how the tradeoff between accuracy
and fairness is determined by the alignment between the class-probabilities for
the target and sensitive features. Underpinning our analysis is a general
framework that casts the problem of learning with a fairness requirement as one
of minimising the difference of two statistical risks.
| Aditya Krishna Menon and Robert C. Williamson | null | 1705.09055 | null | null |
Can Decentralized Algorithms Outperform Centralized Algorithms? A Case
Study for Decentralized Parallel Stochastic Gradient Descent | math.OC cs.DC cs.LG stat.ML | Most distributed machine learning systems nowadays, including TensorFlow and
CNTK, are built in a centralized fashion. One bottleneck of centralized
algorithms lies on high communication cost on the central node. Motivated by
this, we ask, can decentralized algorithms be faster than its centralized
counterpart?
Although decentralized PSGD (D-PSGD) algorithms have been studied by the
control community, existing analysis and theory do not show any advantage over
centralized PSGD (C-PSGD) algorithms, simply assuming the application scenario
where only the decentralized network is available. In this paper, we study a
D-PSGD algorithm and provide the first theoretical analysis that indicates a
regime in which decentralized algorithms might outperform centralized
algorithms for distributed stochastic gradient descent. This is because D-PSGD
has comparable total computational complexities to C-PSGD but requires much
less communication cost on the busiest node. We further conduct an empirical
study to validate our theoretical analysis across multiple frameworks (CNTK and
Torch), different network configurations, and computation platforms up to 112
GPUs. On network configurations with low bandwidth or high latency, D-PSGD can
be up to one order of magnitude faster than its well-optimized centralized
counterparts.
| Xiangru Lian, Ce Zhang, Huan Zhang, Cho-Jui Hsieh, Wei Zhang, Ji Liu | null | 1705.09056 | null | null |
MagNet: a Two-Pronged Defense against Adversarial Examples | cs.CR cs.LG | Deep learning has shown promising results on hard perceptual problems in
recent years. However, deep learning systems are found to be vulnerable to
small adversarial perturbations that are nearly imperceptible to human. Such
specially crafted perturbations cause deep learning systems to output incorrect
decisions, with potentially disastrous consequences. These vulnerabilities
hinder the deployment of deep learning systems where safety or security is
important. Attempts to secure deep learning systems either target specific
attacks or have been shown to be ineffective.
In this paper, we propose MagNet, a framework for defending neural network
classifiers against adversarial examples. MagNet does not modify the protected
classifier or know the process for generating adversarial examples. MagNet
includes one or more separate detector networks and a reformer network.
Different from previous work, MagNet learns to differentiate between normal and
adversarial examples by approximating the manifold of normal examples. Since it
does not rely on any process for generating adversarial examples, it has
substantial generalization power. Moreover, MagNet reconstructs adversarial
examples by moving them towards the manifold, which is effective for helping
classify adversarial examples with small perturbation correctly. We discuss the
intrinsic difficulty in defending against whitebox attack and propose a
mechanism to defend against graybox attack. Inspired by the use of randomness
in cryptography, we propose to use diversity to strengthen MagNet. We show
empirically that MagNet is effective against most advanced state-of-the-art
attacks in blackbox and graybox scenarios while keeping false positive rate on
normal examples very low.
| Dongyu Meng, Hao Chen | null | 1705.09064 | null | null |
Investigation of Using VAE for i-Vector Speaker Verification | cs.SD cs.LG stat.ML | New system for i-vector speaker recognition based on variational autoencoder
(VAE) is investigated. VAE is a promising approach for developing accurate deep
nonlinear generative models of complex data. Experiments show that VAE provides
speaker embedding and can be effectively trained in an unsupervised manner. LLR
estimate for VAE is developed. Experiments on NIST SRE 2010 data demonstrate
its correctness. Additionally, we show that the performance of VAE-based system
in the i-vectors space is close to that of the diagonal PLDA. Several
interesting results are also observed in the experiments with $\beta$-VAE. In
particular, we found that for $\beta\ll 1$, VAE can be trained to capture the
features of complex input data distributions in an effective way, which is hard
to obtain in the standard VAE ($\beta=1$).
| Timur Pekhovsky, Maxim Korenevsky | null | 1705.09185 | null | null |
Classification of Quantitative Light-Induced Fluorescence Images Using
Convolutional Neural Network | cs.CV cs.LG | Images are an important data source for diagnosis and treatment of oral
diseases. The manual classification of images may lead to misdiagnosis or
mistreatment due to subjective errors. In this paper an image classification
model based on Convolutional Neural Network is applied to Quantitative
Light-induced Fluorescence images. The deep neural network outperforms other
state of the art shallow classification models in predicting labels derived
from three different dental plaque assessment scores. The model directly
benefits from multi-channel representation of the images resulting in improved
performance when, besides the Red colour channel, additional Green and Blue
colour channels are used.
| Sultan Imangaliyev, Monique H. van der Veen, Catherine M. C.
Volgenant, Bruno G. Loos, Bart J. F. Keijser, Wim Crielaard, Evgeni Levin | null | 1705.09193 | null | null |
Asynchronous Parallel Bayesian Optimisation via Thompson Sampling | stat.ML cs.LG | We design and analyse variations of the classical Thompson sampling (TS)
procedure for Bayesian optimisation (BO) in settings where function evaluations
are expensive, but can be performed in parallel. Our theoretical analysis shows
that a direct application of the sequential Thompson sampling algorithm in
either synchronous or asynchronous parallel settings yields a surprisingly
powerful result: making $n$ evaluations distributed among $M$ workers is
essentially equivalent to performing $n$ evaluations in sequence. Further, by
modeling the time taken to complete a function evaluation, we show that, under
a time constraint, asynchronously parallel TS achieves asymptotically lower
regret than both the synchronous and sequential versions. These results are
complemented by an experimental analysis, showing that asynchronous TS
outperforms a suite of existing parallel BO algorithms in simulations and in a
hyper-parameter tuning application in convolutional neural networks. In
addition to these, the proposed procedure is conceptually and computationally
much simpler than existing work for parallel BO.
| Kirthevasan Kandasamy, Akshay Krishnamurthy, Jeff Schneider and
Barnabas Poczos | null | 1705.09236 | null | null |
Geometric Methods for Robust Data Analysis in High Dimension | cs.LG | Machine learning and data analysis now finds both scientific and industrial
application in biology, chemistry, geology, medicine, and physics. These
applications rely on large quantities of data gathered from automated sensors
and user input. Furthermore, the dimensionality of many datasets is extreme:
more details are being gathered about single user interactions or sensor
readings. All of these applications encounter problems with a common theme: use
observed data to make inferences about the world. Our work obtains the first
provably efficient algorithms for Independent Component Analysis (ICA) in the
presence of heavy-tailed data. The main tool in this result is the centroid
body (a well-known topic in convex geometry), along with optimization and
random walks for sampling from a convex body. This is the first algorithmic use
of the centroid body and it is of independent theoretical interest, since it
effectively replaces the estimation of covariance from samples, and is more
generally accessible.
This reduction relies on a non-linear transformation of samples from such an
intersection of halfspaces (i.e. a simplex) to samples which are approximately
from a linearly transformed product distribution. Through this transformation
of samples, which can be done efficiently, one can then use an ICA algorithm to
recover the vertices of the intersection of halfspaces.
Finally, we again use ICA as an algorithmic primitive to construct an
efficient solution to the widely-studied problem of learning the parameters of
a Gaussian mixture model. Our algorithm again transforms samples from a
Gaussian mixture model into samples which fit into the ICA model and, when
processed by an ICA algorithm, result in recovery of the mixture parameters.
Our algorithm is effective even when the number of Gaussians in the mixture
grows polynomially with the ambient dimension
| Joseph Anderson | null | 1705.09269 | null | null |
Filtering Variational Objectives | cs.LG cs.AI cs.NE stat.ML | When used as a surrogate objective for maximum likelihood estimation in
latent variable models, the evidence lower bound (ELBO) produces
state-of-the-art results. Inspired by this, we consider the extension of the
ELBO to a family of lower bounds defined by a particle filter's estimator of
the marginal likelihood, the filtering variational objectives (FIVOs). FIVOs
take the same arguments as the ELBO, but can exploit a model's sequential
structure to form tighter bounds. We present results that relate the tightness
of FIVO's bound to the variance of the particle filter's estimator by
considering the generic case of bounds defined as log-transformed likelihood
estimators. Experimentally, we show that training with FIVO results in
substantial improvements over training the same model architecture with the
ELBO on sequential data.
| Chris J. Maddison, Dieterich Lawson, George Tucker, Nicolas Heess,
Mohammad Norouzi, Andriy Mnih, Arnaud Doucet, Yee Whye Teh | null | 1705.09279 | null | null |
Implicit Regularization in Matrix Factorization | stat.ML cs.LG | We study implicit regularization when optimizing an underdetermined quadratic
objective over a matrix $X$ with gradient descent on a factorization of $X$. We
conjecture and provide empirical and theoretical evidence that with small
enough step sizes and initialization close enough to the origin, gradient
descent on a full dimensional factorization converges to the minimum nuclear
norm solution.
| Suriya Gunasekar, Blake Woodworth, Srinadh Bhojanapalli, Behnam
Neyshabur, Nathan Srebro | null | 1705.0928 | null | null |
GXNOR-Net: Training deep neural networks with ternary weights and
activations without full-precision memory under a unified discretization
framework | cs.LG cs.CV stat.ML | There is a pressing need to build an architecture that could subsume these
networks under a unified framework that achieves both higher performance and
less overhead. To this end, two fundamental issues are yet to be addressed. The
first one is how to implement the back propagation when neuronal activations
are discrete. The second one is how to remove the full-precision hidden weights
in the training phase to break the bottlenecks of memory/computation
consumption. To address the first issue, we present a multi-step neuronal
activation discretization method and a derivative approximation technique that
enable the implementing the back propagation algorithm on discrete DNNs. While
for the second issue, we propose a discrete state transition (DST) methodology
to constrain the weights in a discrete space without saving the hidden weights.
Through this way, we build a unified framework that subsumes the binary or
ternary networks as its special cases, and under which a heuristic algorithm is
provided at the website https://github.com/AcrossV/Gated-XNOR. More
particularly, we find that when both the weights and activations become ternary
values, the DNNs can be reduced to sparse binary networks, termed as gated XNOR
networks (GXNOR-Nets) since only the event of non-zero weight and non-zero
activation enables the control gate to start the XNOR logic operations in the
original binary networks. This promises the event-driven hardware design for
efficient mobile intelligence. We achieve advanced performance compared with
state-of-the-art algorithms. Furthermore, the computational sparsity and the
number of states in the discrete space can be flexibly modified to make it
suitable for various hardware platforms.
| Lei Deng, Peng Jiao, Jing Pei, Zhenzhi Wu and Guoqi Li | null | 1705.09283 | null | null |
Latent Geometry and Memorization in Generative Models | cs.LG stat.ML | It can be difficult to tell whether a trained generative model has learned to
generate novel examples or has simply memorized a specific set of outputs. In
published work, it is common to attempt to address this visually, for example
by displaying a generated example and its nearest neighbor(s) in the training
set (in, for example, the L2 metric). As any generative model induces a
probability density on its output domain, we propose studying this density
directly. We first study the geometry of the latent representation and
generator, relate this to the output density, and then develop techniques to
compute and inspect the output density. As an application, we demonstrate that
"memorization" tends to a density made of delta functions concentrated on the
memorized examples. We note that without first understanding the geometry, the
measurement would be essentially impossible to make.
| Matt Feiszli | null | 1705.09303 | null | null |
Diagonal Rescaling For Neural Networks | cs.LG stat.ML | We define a second-order neural network stochastic gradient training
algorithm whose block-diagonal structure effectively amounts to normalizing the
unit activations. Investigating why this algorithm lacks in robustness then
reveals two interesting insights. The first insight suggests a new way to scale
the stepsizes, clarifying popular algorithms such as RMSProp as well as old
neural network tricks such as fanin stepsize scaling. The second insight
stresses the practical importance of dealing with fast changes of the curvature
of the cost.
| Jean Lafond, Nicolas Vasilache, L\'eon Bottou | null | 1705.09319 | null | null |
Convergent Tree Backup and Retrace with Function Approximation | cs.LG | Off-policy learning is key to scaling up reinforcement learning as it allows
to learn about a target policy from the experience generated by a different
behavior policy. Unfortunately, it has been challenging to combine off-policy
learning with function approximation and multi-step bootstrapping in a way that
leads to both stable and efficient algorithms. In this work, we show that the
\textsc{Tree Backup} and \textsc{Retrace} algorithms are unstable with linear
function approximation, both in theory and in practice with specific examples.
Based on our analysis, we then derive stable and efficient gradient-based
algorithms using a quadratic convex-concave saddle-point formulation. By
exploiting the problem structure proper to these algorithms, we are able to
provide convergence guarantees and finite-sample bounds. The applicability of
our new analysis also goes beyond \textsc{Tree Backup} and \textsc{Retrace} and
allows us to provide new convergence rates for the GTD and GTD2 algorithms
without having recourse to projections or Polyak averaging.
| Ahmed Touati, Pierre-Luc Bacon, Doina Precup, Pascal Vincent | null | 1705.09322 | null | null |
Generating Time-Based Label Refinements to Discover More Precise Process
Models | cs.LG cs.AI cs.DB | Process mining is a research field focused on the analysis of event data with
the aim of extracting insights related to dynamic behavior. Applying process
mining techniques on data from smart home environments has the potential to
provide valuable insights in (un)healthy habits and to contribute to ambient
assisted living solutions. Finding the right event labels to enable the
application of process mining techniques is however far from trivial, as simply
using the triggering sensor as the label for sensor events results in
uninformative models that allow for too much behavior (overgeneralizing).
Refinements of sensor level event labels suggested by domain experts have been
shown to enable discovery of more precise and insightful process models.
However, there exists no automated approach to generate refinements of event
labels in the context of process mining. In this paper we propose a framework
for the automated generation of label refinements based on the time attribute
of events, allowing us to distinguish behaviourally different instances of the
same event type based on their time attribute. We show on a case study with
real life smart home event data that using automatically generated refined
labels in process discovery, we can find more specific, and therefore more
insightful, process models. We observe that one label refinement could have an
effect on the usefulness of other label refinements when used together.
Therefore, we explore four strategies to generate useful combinations of
multiple label refinements and evaluate those on three real life smart home
event logs.
| Niek Tax, Emin Alasgarov, Natalia Sidorova, Wil M.P. van der Aalst,
Reinder Haakma | null | 1705.09359 | null | null |
Stabilizing Training of Generative Adversarial Networks through
Regularization | cs.LG stat.ML | Deep generative models based on Generative Adversarial Networks (GANs) have
demonstrated impressive sample quality but in order to work they require a
careful choice of architecture, parameter initialization, and selection of
hyper-parameters. This fragility is in part due to a dimensional mismatch or
non-overlapping support between the model distribution and the data
distribution, causing their density ratio and the associated f-divergence to be
undefined. We overcome this fundamental limitation and propose a new
regularization approach with low computational cost that yields a stable GAN
training procedure. We demonstrate the effectiveness of this regularizer across
several architectures trained on common benchmark image generation tasks. Our
regularization turns GAN models into reliable building blocks for deep
learning.
| Kevin Roth, Aurelien Lucchi, Sebastian Nowozin, Thomas Hofmann | null | 1705.09367 | null | null |
Approximate and Stochastic Greedy Optimization | math.OC cs.LG | We consider two greedy algorithms for minimizing a convex function in a
bounded convex set: an algorithm by Jones [1992] and the Frank-Wolfe (FW)
algorithm. We first consider approximate versions of these algorithms. For
smooth convex functions, we give sufficient conditions for convergence, a
unified analysis for the well-known convergence rate of O(1/k) together with a
result showing that this rate is the best obtainable from the proof technique,
and an equivalence result for the two algorithms. We also consider approximate
stochastic greedy algorithms for minimizing expectations. We show that
replacing the full gradient by a single stochastic gradient can fail even on
smooth convex functions. We give a convergent approximate stochastic Jones
algorithm and a convergent approximate stochastic FW algorithm for smooth
convex functions. In addition, we give a convergent approximate stochastic FW
algorithm for nonsmooth convex functions. Convergence rates for these
algorithms are given and proved.
| Nan Ye and Peter Bartlett | null | 1705.09396 | null | null |
Multimodal Machine Learning: A Survey and Taxonomy | cs.LG | Our experience of the world is multimodal - we see objects, hear sounds, feel
texture, smell odors, and taste flavors. Modality refers to the way in which
something happens or is experienced and a research problem is characterized as
multimodal when it includes multiple such modalities. In order for Artificial
Intelligence to make progress in understanding the world around us, it needs to
be able to interpret such multimodal signals together. Multimodal machine
learning aims to build models that can process and relate information from
multiple modalities. It is a vibrant multi-disciplinary field of increasing
importance and with extraordinary potential. Instead of focusing on specific
multimodal applications, this paper surveys the recent advances in multimodal
machine learning itself and presents them in a common taxonomy. We go beyond
the typical early and late fusion categorization and identify broader
challenges that are faced by multimodal machine learning, namely:
representation, translation, alignment, fusion, and co-learning. This new
taxonomy will enable researchers to better understand the state of the field
and identify directions for future research.
| Tadas Baltru\v{s}aitis, Chaitanya Ahuja, Louis-Philippe Morency | null | 1705.09406 | null | null |
An Efficient Algorithm for Bayesian Nearest Neighbours | cs.LG stat.ML | K-Nearest Neighbours (k-NN) is a popular classification and regression
algorithm, yet one of its main limitations is the difficulty in choosing the
number of neighbours. We present a Bayesian algorithm to compute the posterior
probability distribution for k given a target point within a data-set,
efficiently and without the use of Markov Chain Monte Carlo (MCMC) methods or
simulation - alongside an exact solution for distributions within the
exponential family. The central idea is that data points around our target are
generated by the same probability distribution, extending outwards over the
appropriate, though unknown, number of neighbours. Once the data is projected
onto a distance metric of choice, we can transform the choice of k into a
change-point detection problem, for which there is an efficient solution: we
recursively compute the probability of the last change-point as we move towards
our target, and thus de facto compute the posterior probability distribution
over k. Applying this approach to both a classification and a regression UCI
data-sets, we compare favourably and, most importantly, by removing the need
for simulation, we are able to compute the posterior probability of k exactly
and rapidly. As an example, the computational time for the Ripley data-set is a
few milliseconds compared to a few hours when using a MCMC approach.
| Giuseppe Nuti | null | 1705.09407 | null | null |
Human Trajectory Prediction using Spatially aware Deep Attention Models | cs.LG cs.AI | Trajectory Prediction of dynamic objects is a widely studied topic in the
field of artificial intelligence. Thanks to a large number of applications like
predicting abnormal events, navigation system for the blind, etc. there have
been many approaches to attempt learning patterns of motion directly from data
using a wide variety of techniques ranging from hand-crafted features to
sophisticated deep learning models for unsupervised feature learning. All these
approaches have been limited by problems like inefficient features in the case
of hand crafted features, large error propagation across the predicted
trajectory and no information of static artefacts around the dynamic moving
objects. We propose an end to end deep learning model to learn the motion
patterns of humans using different navigational modes directly from data using
the much popular sequence to sequence model coupled with a soft attention
mechanism. We also propose a novel approach to model the static artefacts in a
scene and using these to predict the dynamic trajectories. The proposed method,
tested on trajectories of pedestrians, consistently outperforms previously
proposed state of the art approaches on a variety of large scale data sets. We
also show how our architecture can be naturally extended to handle multiple
modes of movement (say pedestrians, skaters, bikers and buses) simultaneously.
| Daksh Varshneya, G. Srinivasaraghavan | null | 1705.09436 | null | null |
Taste or Addiction?: Using Play Logs to Infer Song Selection Motivation | cs.AI cs.LG | Online music services are increasing in popularity. They enable us to analyze
people's music listening behavior based on play logs. Although it is known that
people listen to music based on topic (e.g., rock or jazz), we assume that when
a user is addicted to an artist, s/he chooses the artist's songs regardless of
topic. Based on this assumption, in this paper, we propose a probabilistic
model to analyze people's music listening behavior. Our main contributions are
three-fold. First, to the best of our knowledge, this is the first study
modeling music listening behavior by taking into account the influence of
addiction to artists. Second, by using real-world datasets of play logs, we
showed the effectiveness of our proposed model. Third, we carried out
qualitative experiments and showed that taking addiction into account enables
us to analyze music listening behavior from a new viewpoint in terms of how
people listen to music according to the time of day, how an artist's songs are
listened to by people, etc. We also discuss the possibility of applying the
analysis results to applications such as artist similarity computation and song
recommendation.
| Kosetsu Tsukuda, Masataka Goto | null | 1705.09439 | null | null |
Learning Robust Features with Incremental Auto-Encoders | cs.LG cs.CV | Automatically learning features, especially robust features, has attracted
much attention in the machine learning community. In this paper, we propose a
new method to learn non-linear robust features by taking advantage of the data
manifold structure. We first follow the commonly used trick of the trade, that
is learning robust features with artificially corrupted data, which are
training samples with manually injected noise. Following the idea of the
auto-encoder, we first assume features should contain much information to well
reconstruct the input from its corrupted copies. However, merely reconstructing
clean input from its noisy copies could make data manifold in the feature space
noisy. To address this problem, we propose a new method, called Incremental
Auto-Encoders, to iteratively denoise the extracted features. We assume the
noisy manifold structure is caused by a diffusion process. Consequently, we
reverse this specific diffusion process to further contract this noisy
manifold, which results in an incremental optimization of model parameters .
Furthermore, we show these learned non-linear features can be stacked into a
hierarchy of features. Experimental results on real-world datasets demonstrate
the proposed method can achieve better classification performances.
| Yanan Li, Donghui Wang | null | 1705.09476 | null | null |
A Sampling Theory Perspective of Graph-based Semi-supervised Learning | cs.LG | Graph-based methods have been quite successful in solving unsupervised and
semi-supervised learning problems, as they provide a means to capture the
underlying geometry of the dataset. It is often desirable for the constructed
graph to satisfy two properties: first, data points that are similar in the
feature space should be strongly connected on the graph, and second, the class
label information should vary smoothly with respect to the graph, where
smoothness is measured using the spectral properties of the graph Laplacian
matrix. Recent works have justified some of these smoothness conditions by
showing that they are strongly linked to the semi-supervised smoothness
assumption and its variants. In this work, we reinforce this connection by
viewing the problem from a graph sampling theoretic perspective, where class
indicator functions are treated as bandlimited graph signals (in the
eigenvector basis of the graph Laplacian) and label prediction as a bandlimited
reconstruction problem. Our approach involves analyzing the bandwidth of class
indicator signals generated from statistical data models with separable and
nonseparable classes. These models are quite general and mimic the nature of
most real-world datasets. Our results show that in the asymptotic limit, the
bandwidth of any class indicator is also closely related to the geometry of the
dataset. This allows one to theoretically justify the assumption of
bandlimitedness of class indicator signals, thereby providing a sampling
theoretic interpretation of graph-based semi-supervised classification.
| Aamir Anis and Aly El Gamal and Salman Avestimehr and Antonio Ortega | 10.1109/TIT.2018.2879897 | 1705.09518 | null | null |
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