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A PARTAN-Accelerated Frank-Wolfe Algorithm for Large-Scale SVM
Classification | stat.ML cs.LG math.OC | Frank-Wolfe algorithms have recently regained the attention of the Machine
Learning community. Their solid theoretical properties and sparsity guarantees
make them a suitable choice for a wide range of problems in this field. In
addition, several variants of the basic procedure exist that improve its
theoretical properties and practical performance. In this paper, we investigate
the application of some of these techniques to Machine Learning, focusing in
particular on a Parallel Tangent (PARTAN) variant of the FW algorithm that has
not been previously suggested or studied for this type of problems. We provide
experiments both in a standard setting and using a stochastic speed-up
technique, showing that the considered algorithms obtain promising results on
several medium and large-scale benchmark datasets for SVM classification.
| Emanuele Frandi, Ricardo Nanculef, Johan A. K. Suykens | null | 1502.01563 | null | null |
A Simple Expression for Mill's Ratio of the Student's $t$-Distribution | cs.LG math.PR | I show a simple expression of the Mill's ratio of the Student's
t-Distribution. I use it to prove Conjecture 1 in P. Auer, N. Cesa-Bianchi, and
P. Fischer. Finite-time analysis of the multiarmed bandit problem. Mach.
Learn., 47(2-3):235--256, May 2002.
| Francesco Orabona | null | 1502.01632 | null | null |
Estimating Optimal Active Learning via Model Retraining Improvement | stat.ML cs.LG | A central question for active learning (AL) is: "what is the optimal
selection?" Defining optimality by classifier loss produces a new
characterisation of optimal AL behaviour, by treating expected loss reduction
as a statistical target for estimation. This target forms the basis of model
retraining improvement (MRI), a novel approach providing a statistical
estimation framework for AL. This framework is constructed to address the
central question of AL optimality, and to motivate the design of estimation
algorithms. MRI allows the exploration of optimal AL behaviour, and the
examination of AL heuristics, showing precisely how they make sub-optimal
selections. The abstract formulation of MRI is used to provide a new guarantee
for AL, that an unbiased MRI estimator should outperform random selection. This
MRI framework reveals intricate estimation issues that in turn motivate the
construction of new statistical AL algorithms. One new algorithm in particular
performs strongly in a large-scale experimental study, compared to standard AL
methods. This competitive performance suggests that practical efforts to
minimise estimation bias may be important for AL applications.
| Lewis P. G. Evans and Niall M. Adams and Christoforos Anagnostopoulos | null | 1502.01664 | null | null |
Use of Modality and Negation in Semantically-Informed Syntactic MT | cs.CL cs.LG stat.ML | This paper describes the resource- and system-building efforts of an
eight-week Johns Hopkins University Human Language Technology Center of
Excellence Summer Camp for Applied Language Exploration (SCALE-2009) on
Semantically-Informed Machine Translation (SIMT). We describe a new
modality/negation (MN) annotation scheme, the creation of a (publicly
available) MN lexicon, and two automated MN taggers that we built using the
annotation scheme and lexicon. Our annotation scheme isolates three components
of modality and negation: a trigger (a word that conveys modality or negation),
a target (an action associated with modality or negation) and a holder (an
experiencer of modality). We describe how our MN lexicon was semi-automatically
produced and we demonstrate that a structure-based MN tagger results in
precision around 86% (depending on genre) for tagging of a standard LDC data
set.
We apply our MN annotation scheme to statistical machine translation using a
syntactic framework that supports the inclusion of semantic annotations.
Syntactic tags enriched with semantic annotations are assigned to parse trees
in the target-language training texts through a process of tree grafting. While
the focus of our work is modality and negation, the tree grafting procedure is
general and supports other types of semantic information. We exploit this
capability by including named entities, produced by a pre-existing tagger, in
addition to the MN elements produced by the taggers described in this paper.
The resulting system significantly outperformed a linguistically naive baseline
model (Hiero), and reached the highest scores yet reported on the NIST 2009
Urdu-English test set. This finding supports the hypothesis that both syntactic
and semantic information can improve translation quality.
| Kathryn Baker, Michael Bloodgood, Bonnie J. Dorr, Chris
Callison-Burch, Nathaniel W. Filardo, Christine Piatko, Lori Levin and Scott
Miller | null | 1502.01682 | null | null |
A Confident Information First Principle for Parametric Reduction and
Model Selection of Boltzmann Machines | cs.LG stat.ML | Typical dimensionality reduction (DR) methods are often data-oriented,
focusing on directly reducing the number of random variables (features) while
retaining the maximal variations in the high-dimensional data. In unsupervised
situations, one of the main limitations of these methods lies in their
dependency on the scale of data features. This paper aims to address the
problem from a new perspective and considers model-oriented dimensionality
reduction in parameter spaces of binary multivariate distributions.
Specifically, we propose a general parameter reduction criterion, called
Confident-Information-First (CIF) principle, to maximally preserve confident
parameters and rule out less confident parameters. Formally, the confidence of
each parameter can be assessed by its contribution to the expected Fisher
information distance within the geometric manifold over the neighbourhood of
the underlying real distribution.
We then revisit Boltzmann machines (BM) from a model selection perspective
and theoretically show that both the fully visible BM (VBM) and the BM with
hidden units can be derived from the general binary multivariate distribution
using the CIF principle. This can help us uncover and formalize the essential
parts of the target density that BM aims to capture and the non-essential parts
that BM should discard. Guided by the theoretical analysis, we develop a
sample-specific CIF for model selection of BM that is adaptive to the observed
samples. The method is studied in a series of density estimation experiments
and has been shown effective in terms of the estimate accuracy.
| Xiaozhao Zhao, Yuexian Hou, Dawei Song, Wenjie Li | null | 1502.01705 | null | null |
Text Understanding from Scratch | cs.LG cs.CL | This article demontrates that we can apply deep learning to text
understanding from character-level inputs all the way up to abstract text
concepts, using temporal convolutional networks (ConvNets). We apply ConvNets
to various large-scale datasets, including ontology classification, sentiment
analysis, and text categorization. We show that temporal ConvNets can achieve
astonishing performance without the knowledge of words, phrases, sentences and
any other syntactic or semantic structures with regards to a human language.
Evidence shows that our models can work for both English and Chinese.
| Xiang Zhang, Yann LeCun | null | 1502.01710 | null | null |
Arrhythmia Detection using Mutual Information-Based Integration Method | cs.CE cs.LG | The aim of this paper is to propose an application of mutual
information-based ensemble methods to the analysis and classification of heart
beats associated with different types of Arrhythmia. Models of multilayer
perceptrons, support vector machines, and radial basis function neural networks
were trained and tested using the MIT-BIH arrhythmia database. This research
brings a focus to an ensemble method that, to our knowledge, is a novel
application in the area of ECG Arrhythmia detection. The proposed classifier
ensemble method showed improved performance, relative to either majority voting
classifier integration or to individual classifier performance. The overall
ensemble accuracy was 98.25%.
| Othman Soufan and Samer Arafat | null | 1502.01733 | null | null |
Monitoring Term Drift Based on Semantic Consistency in an Evolving
Vector Field | cs.CL cs.LG cs.NE stat.ML | Based on the Aristotelian concept of potentiality vs. actuality allowing for
the study of energy and dynamics in language, we propose a field approach to
lexical analysis. Falling back on the distributional hypothesis to
statistically model word meaning, we used evolving fields as a metaphor to
express time-dependent changes in a vector space model by a combination of
random indexing and evolving self-organizing maps (ESOM). To monitor semantic
drifts within the observation period, an experiment was carried out on the term
space of a collection of 12.8 million Amazon book reviews. For evaluation, the
semantic consistency of ESOM term clusters was compared with their respective
neighbourhoods in WordNet, and contrasted with distances among term vectors by
random indexing. We found that at 0.05 level of significance, the terms in the
clusters showed a high level of semantic consistency. Tracking the drift of
distributional patterns in the term space across time periods, we found that
consistency decreased, but not at a statistically significant level. Our method
is highly scalable, with interpretations in philosophy.
| Peter Wittek, S\'andor Dar\'anyi, Efstratios Kontopoulos, Theodoros
Moysiadis, Ioannis Kompatsiaris | 10.1109/IJCNN.2015.7280766 | 1502.01753 | null | null |
Learning Efficient Anomaly Detectors from $K$-NN Graphs | cs.LG stat.ML | We propose a non-parametric anomaly detection algorithm for high dimensional
data. We score each datapoint by its average $K$-NN distance, and rank them
accordingly. We then train limited complexity models to imitate these scores
based on the max-margin learning-to-rank framework. A test-point is declared as
an anomaly at $\alpha$-false alarm level if the predicted score is in the
$\alpha$-percentile. The resulting anomaly detector is shown to be
asymptotically optimal in that for any false alarm rate $\alpha$, its decision
region converges to the $\alpha$-percentile minimum volume level set of the
unknown underlying density. In addition, we test both the statistical
performance and computational efficiency of our algorithm on a number of
synthetic and real-data experiments. Our results demonstrate the superiority of
our algorithm over existing $K$-NN based anomaly detection algorithms, with
significant computational savings.
| Jing Qian, Jonathan Root, Venkatesh Saligrama | null | 1502.01783 | null | null |
Unsupervised Fusion Weight Learning in Multiple Classifier Systems | cs.LG cs.CV | In this paper we present an unsupervised method to learn the weights with
which the scores of multiple classifiers must be combined in classifier fusion
settings. We also introduce a novel metric for ranking instances based on an
index which depends upon the rank of weighted scores of test points among the
weighted scores of training points. We show that the optimized index can be
used for computing measures such as average precision. Unlike most classifier
fusion methods where a single weight is learned to weigh all examples our
method learns instance-specific weights. The problem is formulated as learning
the weight which maximizes a clarity index; subsequently the index itself and
the learned weights both are used separately to rank all the test points. Our
method gives an unsupervised method of optimizing performance on actual test
data, unlike the well known stacking-based methods where optimization is done
over a labeled training set. Moreover, we show that our method is tolerant to
noisy classifiers and can be used for selecting N-best classifiers.
| Anurag Kumar, Bhiksha Raj | null | 1502.01823 | null | null |
Hierarchical Maximum-Margin Clustering | cs.LG cs.CV | We present a hierarchical maximum-margin clustering method for unsupervised
data analysis. Our method extends beyond flat maximum-margin clustering, and
performs clustering recursively in a top-down manner. We propose an effective
greedy splitting criteria for selecting which cluster to split next, and employ
regularizers that enforce feature sharing/competition for capturing data
semantics. Experimental results obtained on four standard datasets show that
our method outperforms flat and hierarchical clustering baselines, while
forming clean and semantically meaningful cluster hierarchies.
| Guang-Tong Zhou, Sung Ju Hwang, Mark Schmidt, Leonid Sigal and Greg
Mori | null | 1502.01827 | null | null |
Delving Deep into Rectifiers: Surpassing Human-Level Performance on
ImageNet Classification | cs.CV cs.AI cs.LG | Rectified activation units (rectifiers) are essential for state-of-the-art
neural networks. In this work, we study rectifier neural networks for image
classification from two aspects. First, we propose a Parametric Rectified
Linear Unit (PReLU) that generalizes the traditional rectified unit. PReLU
improves model fitting with nearly zero extra computational cost and little
overfitting risk. Second, we derive a robust initialization method that
particularly considers the rectifier nonlinearities. This method enables us to
train extremely deep rectified models directly from scratch and to investigate
deeper or wider network architectures. Based on our PReLU networks
(PReLU-nets), we achieve 4.94% top-5 test error on the ImageNet 2012
classification dataset. This is a 26% relative improvement over the ILSVRC 2014
winner (GoogLeNet, 6.66%). To our knowledge, our result is the first to surpass
human-level performance (5.1%, Russakovsky et al.) on this visual recognition
challenge.
| Kaiming He, Xiangyu Zhang, Shaoqing Ren, Jian Sun | null | 1502.01852 | null | null |
Massively Multitask Networks for Drug Discovery | stat.ML cs.LG cs.NE | Massively multitask neural architectures provide a learning framework for
drug discovery that synthesizes information from many distinct biological
sources. To train these architectures at scale, we gather large amounts of data
from public sources to create a dataset of nearly 40 million measurements
across more than 200 biological targets. We investigate several aspects of the
multitask framework by performing a series of empirical studies and obtain some
interesting results: (1) massively multitask networks obtain predictive
accuracies significantly better than single-task methods, (2) the predictive
power of multitask networks improves as additional tasks and data are added,
(3) the total amount of data and the total number of tasks both contribute
significantly to multitask improvement, and (4) multitask networks afford
limited transferability to tasks not in the training set. Our results
underscore the need for greater data sharing and further algorithmic innovation
to accelerate the drug discovery process.
| Bharath Ramsundar, Steven Kearnes, Patrick Riley, Dale Webster, David
Konerding, Vijay Pande | null | 1502.02072 | null | null |
Quantum Energy Regression using Scattering Transforms | cs.LG cs.CV physics.chem-ph physics.comp-ph quant-ph | We present a novel approach to the regression of quantum mechanical energies
based on a scattering transform of an intermediate electron density
representation. A scattering transform is a deep convolution network computed
with a cascade of multiscale wavelet transforms. It possesses appropriate
invariant and stability properties for quantum energy regression. This new
framework removes fundamental limitations of Coulomb matrix based energy
regressions, and numerical experiments give state-of-the-art accuracy over
planar molecules.
| Matthew Hirn and Nicolas Poilvert and St\'ephane Mallat | null | 1502.02077 | null | null |
Contextual Online Learning for Multimedia Content Aggregation | cs.MM cs.LG cs.MA | The last decade has witnessed a tremendous growth in the volume as well as
the diversity of multimedia content generated by a multitude of sources (news
agencies, social media, etc.). Faced with a variety of content choices,
consumers are exhibiting diverse preferences for content; their preferences
often depend on the context in which they consume content as well as various
exogenous events. To satisfy the consumers' demand for such diverse content,
multimedia content aggregators (CAs) have emerged which gather content from
numerous multimedia sources. A key challenge for such systems is to accurately
predict what type of content each of its consumers prefers in a certain
context, and adapt these predictions to the evolving consumers' preferences,
contexts and content characteristics. We propose a novel, distributed, online
multimedia content aggregation framework, which gathers content generated by
multiple heterogeneous producers to fulfill its consumers' demand for content.
Since both the multimedia content characteristics and the consumers'
preferences and contexts are unknown, the optimal content aggregation strategy
is unknown a priori. Our proposed content aggregation algorithm is able to
learn online what content to gather and how to match content and users by
exploiting similarities between consumer types. We prove bounds for our
proposed learning algorithms that guarantee both the accuracy of the
predictions as well as the learning speed. Importantly, our algorithms operate
efficiently even when feedback from consumers is missing or content and
preferences evolve over time. Illustrative results highlight the merits of the
proposed content aggregation system in a variety of settings.
| Cem Tekin and Mihaela van der Schaar | null | 1502.02125 | null | null |
Hyperparameter Search in Machine Learning | cs.LG stat.ML | We introduce the hyperparameter search problem in the field of machine
learning and discuss its main challenges from an optimization perspective.
Machine learning methods attempt to build models that capture some element of
interest based on given data. Most common learning algorithms feature a set of
hyperparameters that must be determined before training commences. The choice
of hyperparameters can significantly affect the resulting model's performance,
but determining good values can be complex; hence a disciplined, theoretically
sound search strategy is essential.
| Marc Claesen and Bart De Moor | null | 1502.02127 | null | null |
Learning Parametric-Output HMMs with Two Aliased States | cs.LG | In various applications involving hidden Markov models (HMMs), some of the
hidden states are aliased, having identical output distributions. The
minimality, identifiability and learnability of such aliased HMMs have been
long standing problems, with only partial solutions provided thus far. In this
paper we focus on parametric-output HMMs, whose output distributions come from
a parametric family, and that have exactly two aliased states. For this class,
we present a complete characterization of their minimality and identifiability.
Furthermore, for a large family of parametric output distributions, we derive
computationally efficient and statistically consistent algorithms to detect the
presence of aliasing and learn the aliased HMM transition and emission
parameters. We illustrate our theoretical analysis by several simulations.
| Roi Weiss, Boaz Nadler | null | 1502.02158 | null | null |
Learning to Search Better Than Your Teacher | cs.LG stat.ML | Methods for learning to search for structured prediction typically imitate a
reference policy, with existing theoretical guarantees demonstrating low regret
compared to that reference. This is unsatisfactory in many applications where
the reference policy is suboptimal and the goal of learning is to improve upon
it. Can learning to search work even when the reference is poor?
We provide a new learning to search algorithm, LOLS, which does well relative
to the reference policy, but additionally guarantees low regret compared to
deviations from the learned policy: a local-optimality guarantee. Consequently,
LOLS can improve upon the reference policy, unlike previous algorithms. This
enables us to develop structured contextual bandits, a partial information
structured prediction setting with many potential applications.
| Kai-Wei Chang, Akshay Krishnamurthy, Alekh Agarwal, Hal Daum\'e III,
John Langford | null | 1502.02206 | null | null |
Real World Applications of Machine Learning Techniques over Large Mobile
Subscriber Datasets | cs.LG cs.CY cs.SE | Communication Service Providers (CSPs) are in a unique position to utilize
their vast transactional data assets generated from interactions of subscribers
with network elements as well as with other subscribers. CSPs could leverage
its data assets for a gamut of applications such as service personalization,
predictive offer management, loyalty management, revenue forecasting, network
capacity planning, product bundle optimization and churn management to gain
significant competitive advantage. However, due to the sheer data volume,
variety, velocity and veracity of mobile subscriber datasets, sophisticated
data analytics techniques and frameworks are necessary to derive actionable
insights in a useable timeframe. In this paper, we describe our journey from a
relational database management system (RDBMS) based campaign management
solution which allowed data scientists and marketers to use hand-written rules
for service personalization and targeted promotions to a distributed Big Data
Analytics platform, capable of performing large scale machine learning and data
mining to deliver real time service personalization, predictive modelling and
product optimization. Our work involves a careful blend of technology,
processes and best practices, which facilitate man-machine collaboration and
continuous experimentation to derive measurable economic value from data. Our
platform has a reach of more than 500 million mobile subscribers worldwide,
delivering over 1 billion personalized recommendations annually, processing a
total data volume of 64 Petabytes, corresponding to 8.5 trillion events.
| Jobin Wilson, Chitharanj Kachappilly, Rakesh Mohan, Prateek Kapadia,
Arun Soman, Santanu Chaudhury | null | 1502.02215 | null | null |
From Pixels to Torques: Policy Learning with Deep Dynamical Models | stat.ML cs.LG cs.RO cs.SY | Data-efficient learning in continuous state-action spaces using very
high-dimensional observations remains a key challenge in developing fully
autonomous systems. In this paper, we consider one instance of this challenge,
the pixels to torques problem, where an agent must learn a closed-loop control
policy from pixel information only. We introduce a data-efficient, model-based
reinforcement learning algorithm that learns such a closed-loop policy directly
from pixel information. The key ingredient is a deep dynamical model that uses
deep auto-encoders to learn a low-dimensional embedding of images jointly with
a predictive model in this low-dimensional feature space. Joint learning
ensures that not only static but also dynamic properties of the data are
accounted for. This is crucial for long-term predictions, which lie at the core
of the adaptive model predictive control strategy that we use for closed-loop
control. Compared to state-of-the-art reinforcement learning methods for
continuous states and actions, our approach learns quickly, scales to
high-dimensional state spaces and is an important step toward fully autonomous
learning from pixels to torques.
| Niklas Wahlstr\"om and Thomas B. Sch\"on and Marc Peter Deisenroth | null | 1502.02251 | null | null |
Contextual Markov Decision Processes | stat.ML cs.LG | We consider a planning problem where the dynamics and rewards of the
environment depend on a hidden static parameter referred to as the context. The
objective is to learn a strategy that maximizes the accumulated reward across
all contexts. The new model, called Contextual Markov Decision Process (CMDP),
can model a customer's behavior when interacting with a website (the learner).
The customer's behavior depends on gender, age, location, device, etc. Based on
that behavior, the website objective is to determine customer characteristics,
and to optimize the interaction between them. Our work focuses on one basic
scenario--finite horizon with a small known number of possible contexts. We
suggest a family of algorithms with provable guarantees that learn the
underlying models and the latent contexts, and optimize the CMDPs. Bounds are
obtained for specific naive implementations, and extensions of the framework
are discussed, laying the ground for future research.
| Assaf Hallak, Dotan Di Castro and Shie Mannor | null | 1502.02259 | null | null |
SDNA: Stochastic Dual Newton Ascent for Empirical Risk Minimization | cs.LG | We propose a new algorithm for minimizing regularized empirical loss:
Stochastic Dual Newton Ascent (SDNA). Our method is dual in nature: in each
iteration we update a random subset of the dual variables. However, unlike
existing methods such as stochastic dual coordinate ascent, SDNA is capable of
utilizing all curvature information contained in the examples, which leads to
striking improvements in both theory and practice - sometimes by orders of
magnitude. In the special case when an L2-regularizer is used in the primal,
the dual problem is a concave quadratic maximization problem plus a separable
term. In this regime, SDNA in each step solves a proximal subproblem involving
a random principal submatrix of the Hessian of the quadratic function; whence
the name of the method. If, in addition, the loss functions are quadratic, our
method can be interpreted as a novel variant of the recently introduced
Iterative Hessian Sketch.
| Zheng Qu and Peter Richt\'arik and Martin Tak\'a\v{c} and Olivier
Fercoq | null | 1502.02268 | null | null |
Rademacher Observations, Private Data, and Boosting | cs.LG | The minimization of the logistic loss is a popular approach to batch
supervised learning. Our paper starts from the surprising observation that,
when fitting linear (or kernelized) classifiers, the minimization of the
logistic loss is \textit{equivalent} to the minimization of an exponential
\textit{rado}-loss computed (i) over transformed data that we call Rademacher
observations (rados), and (ii) over the \textit{same} classifier as the one of
the logistic loss. Thus, a classifier learnt from rados can be
\textit{directly} used to classify \textit{observations}. We provide a learning
algorithm over rados with boosting-compliant convergence rates on the
\textit{logistic loss} (computed over examples). Experiments on domains with up
to millions of examples, backed up by theoretical arguments, display that
learning over a small set of random rados can challenge the state of the art
that learns over the \textit{complete} set of examples. We show that rados
comply with various privacy requirements that make them good candidates for
machine learning in a privacy framework. We give several algebraic, geometric
and computational hardness results on reconstructing examples from rados. We
also show how it is possible to craft, and efficiently learn from, rados in a
differential privacy framework. Tests reveal that learning from differentially
private rados can compete with learning from random rados, and hence with batch
learning from examples, achieving non-trivial privacy vs accuracy tradeoffs.
| Richard Nock and Giorgio Patrini and Arik Friedman | null | 1502.02322 | null | null |
Tensor Canonical Correlation Analysis for Multi-view Dimension Reduction | stat.ML cs.CV cs.LG | Canonical correlation analysis (CCA) has proven an effective tool for
two-view dimension reduction due to its profound theoretical foundation and
success in practical applications. In respect of multi-view learning, however,
it is limited by its capability of only handling data represented by two-view
features, while in many real-world applications, the number of views is
frequently many more. Although the ad hoc way of simultaneously exploring all
possible pairs of features can numerically deal with multi-view data, it
ignores the high order statistics (correlation information) which can only be
discovered by simultaneously exploring all features.
Therefore, in this work, we develop tensor CCA (TCCA) which straightforwardly
yet naturally generalizes CCA to handle the data of an arbitrary number of
views by analyzing the covariance tensor of the different views. TCCA aims to
directly maximize the canonical correlation of multiple (more than two) views.
Crucially, we prove that the multi-view canonical correlation maximization
problem is equivalent to finding the best rank-1 approximation of the data
covariance tensor, which can be solved efficiently using the well-known
alternating least squares (ALS) algorithm. As a consequence, the high order
correlation information contained in the different views is explored and thus a
more reliable common subspace shared by all features can be obtained. In
addition, a non-linear extension of TCCA is presented. Experiments on various
challenge tasks, including large scale biometric structure prediction, internet
advertisement classification and web image annotation, demonstrate the
effectiveness of the proposed method.
| Yong Luo, Dacheng Tao, Yonggang Wen, Kotagiri Ramamohanarao, Chao Xu | null | 1502.02330 | null | null |
Counterfactual Risk Minimization: Learning from Logged Bandit Feedback | cs.LG stat.ML | We develop a learning principle and an efficient algorithm for batch learning
from logged bandit feedback. This learning setting is ubiquitous in online
systems (e.g., ad placement, web search, recommendation), where an algorithm
makes a prediction (e.g., ad ranking) for a given input (e.g., query) and
observes bandit feedback (e.g., user clicks on presented ads). We first address
the counterfactual nature of the learning problem through propensity scoring.
Next, we prove generalization error bounds that account for the variance of the
propensity-weighted empirical risk estimator. These constructive bounds give
rise to the Counterfactual Risk Minimization (CRM) principle. We show how CRM
can be used to derive a new learning method -- called Policy Optimizer for
Exponential Models (POEM) -- for learning stochastic linear rules for
structured output prediction. We present a decomposition of the POEM objective
that enables efficient stochastic gradient optimization. POEM is evaluated on
several multi-label classification problems showing substantially improved
robustness and generalization performance compared to the state-of-the-art.
| Adith Swaminathan and Thorsten Joachims | null | 1502.02362 | null | null |
Gated Feedback Recurrent Neural Networks | cs.NE cs.LG stat.ML | In this work, we propose a novel recurrent neural network (RNN) architecture.
The proposed RNN, gated-feedback RNN (GF-RNN), extends the existing approach of
stacking multiple recurrent layers by allowing and controlling signals flowing
from upper recurrent layers to lower layers using a global gating unit for each
pair of layers. The recurrent signals exchanged between layers are gated
adaptively based on the previous hidden states and the current input. We
evaluated the proposed GF-RNN with different types of recurrent units, such as
tanh, long short-term memory and gated recurrent units, on the tasks of
character-level language modeling and Python program evaluation. Our empirical
evaluation of different RNN units, revealed that in both tasks, the GF-RNN
outperforms the conventional approaches to build deep stacked RNNs. We suggest
that the improvement arises because the GF-RNN can adaptively assign different
layers to different timescales and layer-to-layer interactions (including the
top-down ones which are not usually present in a stacked RNN) by learning to
gate these interactions.
| Junyoung Chung, Caglar Gulcehre, Kyunghyun Cho and Yoshua Bengio | null | 1502.02367 | null | null |
Sparse Coding with Earth Mover's Distance for Multi-Instance Histogram
Representation | cs.LG stat.ML | Sparse coding (Sc) has been studied very well as a powerful data
representation method. It attempts to represent the feature vector of a data
sample by reconstructing it as the sparse linear combination of some basic
elements, and a $L_2$ norm distance function is usually used as the loss
function for the reconstruction error. In this paper, we investigate using Sc
as the representation method within multi-instance learning framework, where a
sample is given as a bag of instances, and further represented as a histogram
of the quantized instances. We argue that for the data type of histogram, using
$L_2$ norm distance is not suitable, and propose to use the earth mover's
distance (EMD) instead of $L_2$ norm distance as a measure of the
reconstruction error. By minimizing the EMD between the histogram of a sample
and the its reconstruction from some basic histograms, a novel sparse coding
method is developed, which is refereed as SC-EMD. We evaluate its performances
as a histogram representation method in tow multi-instance learning problems
--- abnormal image detection in wireless capsule endoscopy videos, and protein
binding site retrieval. The encouraging results demonstrate the advantages of
the new method over the traditional method using $L_2$ norm distance.
| Mohua Zhang, Jianhua Peng, Xuejie Liu, Jim Jing-Yan Wang | 10.1007/s00521-016-2269-9 | 1502.02377 | null | null |
Out-of-sample generalizations for supervised manifold learning for
classification | cs.CV cs.LG | Supervised manifold learning methods for data classification map data samples
residing in a high-dimensional ambient space to a lower-dimensional domain in a
structure-preserving way, while enhancing the separation between different
classes in the learned embedding. Most nonlinear supervised manifold learning
methods compute the embedding of the manifolds only at the initially available
training points, while the generalization of the embedding to novel points,
known as the out-of-sample extension problem in manifold learning, becomes
especially important in classification applications. In this work, we propose a
semi-supervised method for building an interpolation function that provides an
out-of-sample extension for general supervised manifold learning algorithms
studied in the context of classification. The proposed algorithm computes a
radial basis function (RBF) interpolator that minimizes an objective function
consisting of the total embedding error of unlabeled test samples, defined as
their distance to the embeddings of the manifolds of their own class, as well
as a regularization term that controls the smoothness of the interpolation
function in a direction-dependent way. The class labels of test data and the
interpolation function parameters are estimated jointly with a progressive
procedure. Experimental results on face and object images demonstrate the
potential of the proposed out-of-sample extension algorithm for the
classification of manifold-modeled data sets.
| Elif Vural and Christine Guillemot | 10.1109/TIP.2016.2520368 | 1502.02410 | null | null |
Deep Neural Networks for Anatomical Brain Segmentation | cs.CV cs.LG stat.AP stat.ML | We present a novel approach to automatically segment magnetic resonance (MR)
images of the human brain into anatomical regions. Our methodology is based on
a deep artificial neural network that assigns each voxel in an MR image of the
brain to its corresponding anatomical region. The inputs of the network capture
information at different scales around the voxel of interest: 3D and orthogonal
2D intensity patches capture the local spatial context while large, compressed
2D orthogonal patches and distances to the regional centroids enforce global
spatial consistency. Contrary to commonly used segmentation methods, our
technique does not require any non-linear registration of the MR images. To
benchmark our model, we used the dataset provided for the MICCAI 2012 challenge
on multi-atlas labelling, which consists of 35 manually segmented MR images of
the brain. We obtained competitive results (mean dice coefficient 0.725, error
rate 0.163) showing the potential of our approach. To our knowledge, our
technique is the first to tackle the anatomical segmentation of the whole brain
using deep neural networks.
| Alexandre de Brebisson, Giovanni Montana | null | 1502.02445 | null | null |
An Infinite Restricted Boltzmann Machine | cs.LG | We present a mathematical construction for the restricted Boltzmann machine
(RBM) that doesn't require specifying the number of hidden units. In fact, the
hidden layer size is adaptive and can grow during training. This is obtained by
first extending the RBM to be sensitive to the ordering of its hidden units.
Then, thanks to a carefully chosen definition of the energy function, we show
that the limit of infinitely many hidden units is well defined. As with RBM,
approximate maximum likelihood training can be performed, resulting in an
algorithm that naturally and adaptively adds trained hidden units during
learning. We empirically study the behaviour of this infinite RBM, showing that
its performance is competitive to that of the RBM, while not requiring the
tuning of a hidden layer size.
| Marc-Alexandre C\^ot\'e, Hugo Larochelle | null | 1502.02476 | null | null |
Predicting Alzheimer's disease: a neuroimaging study with 3D
convolutional neural networks | cs.CV cs.LG stat.AP stat.ML | Pattern recognition methods using neuroimaging data for the diagnosis of
Alzheimer's disease have been the subject of extensive research in recent
years. In this paper, we use deep learning methods, and in particular sparse
autoencoders and 3D convolutional neural networks, to build an algorithm that
can predict the disease status of a patient, based on an MRI scan of the brain.
We report on experiments using the ADNI data set involving 2,265 historical
scans. We demonstrate that 3D convolutional neural networks outperform several
other classifiers reported in the literature and produce state-of-art results.
| Adrien Payan, Giovanni Montana | null | 1502.02506 | null | null |
The Adaptive Mean-Linkage Algorithm: A Bottom-Up Hierarchical Cluster
Technique | stat.ME cs.LG stat.AP | In this paper a variant of the classical hierarchical cluster analysis is
reported. This agglomerative (bottom-up) cluster technique is referred to as
the Adaptive Mean-Linkage Algorithm. It can be interpreted as a linkage
algorithm where the value of the threshold is conveniently up-dated at each
interaction. The superiority of the adaptive clustering with respect to the
average-linkage algorithm follows because it achieves a good compromise on
threshold values: Thresholds based on the cut-off distance are sufficiently
small to assure the homogeneity and also large enough to guarantee at least a
pair of merging sets. This approach is applied to a set of possible
substituents in a chemical series.
| H.M. de Oliveira | null | 1502.02512 | null | null |
Deep Learning with Limited Numerical Precision | cs.LG cs.NE stat.ML | Training of large-scale deep neural networks is often constrained by the
available computational resources. We study the effect of limited precision
data representation and computation on neural network training. Within the
context of low-precision fixed-point computations, we observe the rounding
scheme to play a crucial role in determining the network's behavior during
training. Our results show that deep networks can be trained using only 16-bit
wide fixed-point number representation when using stochastic rounding, and
incur little to no degradation in the classification accuracy. We also
demonstrate an energy-efficient hardware accelerator that implements
low-precision fixed-point arithmetic with stochastic rounding.
| Suyog Gupta, Ankur Agrawal, Kailash Gopalakrishnan, Pritish Narayanan | null | 1502.02551 | null | null |
K2-ABC: Approximate Bayesian Computation with Kernel Embeddings | stat.ML cs.LG | Complicated generative models often result in a situation where computing the
likelihood of observed data is intractable, while simulating from the
conditional density given a parameter value is relatively easy. Approximate
Bayesian Computation (ABC) is a paradigm that enables simulation-based
posterior inference in such cases by measuring the similarity between simulated
and observed data in terms of a chosen set of summary statistics. However,
there is no general rule to construct sufficient summary statistics for complex
models. Insufficient summary statistics will "leak" information, which leads to
ABC algorithms yielding samples from an incorrect (partial) posterior. In this
paper, we propose a fully nonparametric ABC paradigm which circumvents the need
for manually selecting summary statistics. Our approach, K2-ABC, uses maximum
mean discrepancy (MMD) as a dissimilarity measure between the distributions
over observed and simulated data. MMD is easily estimated as the squared
difference between their empirical kernel embeddings. Experiments on a
simulated scenario and a real-world biological problem illustrate the
effectiveness of the proposed algorithm.
| Mijung Park and Wittawat Jitkrittum and Dino Sejdinovic | null | 1502.02558 | null | null |
Analysis of classifiers' robustness to adversarial perturbations | cs.LG cs.CV stat.ML | The goal of this paper is to analyze an intriguing phenomenon recently
discovered in deep networks, namely their instability to adversarial
perturbations (Szegedy et. al., 2014). We provide a theoretical framework for
analyzing the robustness of classifiers to adversarial perturbations, and show
fundamental upper bounds on the robustness of classifiers. Specifically, we
establish a general upper bound on the robustness of classifiers to adversarial
perturbations, and then illustrate the obtained upper bound on the families of
linear and quadratic classifiers. In both cases, our upper bound depends on a
distinguishability measure that captures the notion of difficulty of the
classification task. Our results for both classes imply that in tasks involving
small distinguishability, no classifier in the considered set will be robust to
adversarial perturbations, even if a good accuracy is achieved. Our theoretical
framework moreover suggests that the phenomenon of adversarial instability is
due to the low flexibility of classifiers, compared to the difficulty of the
classification task (captured by the distinguishability). Moreover, we show the
existence of a clear distinction between the robustness of a classifier to
random noise and its robustness to adversarial perturbations. Specifically, the
former is shown to be larger than the latter by a factor that is proportional
to \sqrt{d} (with d being the signal dimension) for linear classifiers. This
result gives a theoretical explanation for the discrepancy between the two
robustness properties in high dimensional problems, which was empirically
observed in the context of neural networks. To the best of our knowledge, our
results provide the first theoretical work that addresses the phenomenon of
adversarial instability recently observed for deep networks. Our analysis is
complemented by experimental results on controlled and real-world data.
| Alhussein Fawzi, Omar Fawzi, Pascal Frossard | null | 1502.02590 | null | null |
Adaptive Random SubSpace Learning (RSSL) Algorithm for Prediction | cs.LG | We present a novel adaptive random subspace learning algorithm (RSSL) for
prediction purpose. This new framework is flexible where it can be adapted with
any learning technique. In this paper, we tested the algorithm for regression
and classification problems. In addition, we provide a variety of weighting
schemes to increase the robustness of the developed algorithm. These different
wighting flavors were evaluated on simulated as well as on real-world data sets
considering the cases where the ratio between features (attributes) and
instances (samples) is large and vice versa. The framework of the new algorithm
consists of many stages: first, calculate the weights of all features on the
data set using the correlation coefficient and F-statistic statistical
measurements. Second, randomly draw n samples with replacement from the data
set. Third, perform regular bootstrap sampling (bagging). Fourth, draw without
replacement the indices of the chosen variables. The decision was taken based
on the heuristic subspacing scheme. Fifth, call base learners and build the
model. Sixth, use the model for prediction purpose on test set of the data. The
results show the advancement of the adaptive RSSL algorithm in most of the
cases compared with the synonym (conventional) machine learning algorithms.
| Mohamed Elshrif, Ernest Fokoue | null | 1502.02599 | null | null |
The Power of Randomization: Distributed Submodular Maximization on
Massive Datasets | cs.LG cs.AI cs.DC | A wide variety of problems in machine learning, including exemplar
clustering, document summarization, and sensor placement, can be cast as
constrained submodular maximization problems. Unfortunately, the resulting
submodular optimization problems are often too large to be solved on a single
machine. We develop a simple distributed algorithm that is embarrassingly
parallel and it achieves provable, constant factor, worst-case approximation
guarantees. In our experiments, we demonstrate its efficiency in large problems
with different kinds of constraints with objective values always close to what
is achievable in the centralized setting.
| Rafael da Ponte Barbosa and Alina Ene and Huy L. Nguyen and Justin
Ward | null | 1502.02606 | null | null |
Efficient model-based reinforcement learning for approximate online
optimal | cs.SY cs.LG math.OC | In this paper the infinite horizon optimal regulation problem is solved
online for a deterministic control-affine nonlinear dynamical system using the
state following (StaF) kernel method to approximate the value function. Unlike
traditional methods that aim to approximate a function over a large compact
set, the StaF kernel method aims to approximate a function in a small
neighborhood of a state that travels within a compact set. Simulation results
demonstrate that stability and approximate optimality of the control system can
be achieved with significantly fewer basis functions than may be required for
global approximation methods.
| Rushikesh Kamalapurkar, Joel A. Rosenfeld, Warren E. Dixon | 10.1016/j.automatica.2016.08.004 | 1502.02609 | null | null |
Random Coordinate Descent Methods for Minimizing Decomposable Submodular
Functions | cs.LG cs.AI | Submodular function minimization is a fundamental optimization problem that
arises in several applications in machine learning and computer vision. The
problem is known to be solvable in polynomial time, but general purpose
algorithms have high running times and are unsuitable for large-scale problems.
Recent work have used convex optimization techniques to obtain very practical
algorithms for minimizing functions that are sums of ``simple" functions. In
this paper, we use random coordinate descent methods to obtain algorithms with
faster linear convergence rates and cheaper iteration costs. Compared to
alternating projection methods, our algorithms do not rely on full-dimensional
vector operations and they converge in significantly fewer iterations.
| Alina Ene and Huy L. Nguyen | null | 1502.02643 | null | null |
Optimal and Adaptive Algorithms for Online Boosting | cs.LG | We study online boosting, the task of converting any weak online learner into
a strong online learner. Based on a novel and natural definition of weak online
learnability, we develop two online boosting algorithms. The first algorithm is
an online version of boost-by-majority. By proving a matching lower bound, we
show that this algorithm is essentially optimal in terms of the number of weak
learners and the sample complexity needed to achieve a specified accuracy. This
optimal algorithm is not adaptive however. Using tools from online loss
minimization, we derive an adaptive online boosting algorithm that is also
parameter-free, but not optimal. Both algorithms work with base learners that
can handle example importance weights directly, as well as by rejection
sampling examples with probability defined by the booster. Results are
complemented with an extensive experimental study.
| Alina Beygelzimer, Satyen Kale, and Haipeng Luo | null | 1502.02651 | null | null |
Learning Reductions that Really Work | cs.LG | We provide a summary of the mathematical and computational techniques that
have enabled learning reductions to effectively address a wide class of
problems, and show that this approach to solving machine learning problems can
be broadly useful.
| Alina Beygelzimer, Hal Daum\'e III, John Langford, Paul Mineiro | null | 1502.02704 | null | null |
Scalable Multilabel Prediction via Randomized Methods | cs.LG | Modeling the dependence between outputs is a fundamental challenge in
multilabel classification. In this work we show that a generic regularized
nonlinearity mapping independent predictions to joint predictions is sufficient
to achieve state-of-the-art performance on a variety of benchmark problems.
Crucially, we compute the joint predictions without ever obtaining any
independent predictions, while incorporating low-rank and smoothness
regularization. We achieve this by leveraging randomized algorithms for matrix
decomposition and kernel approximation. Furthermore, our techniques are
applicable to the multiclass setting. We apply our method to a variety of
multiclass and multilabel data sets, obtaining state-of-the-art results.
| Nikos Karampatziakis, Paul Mineiro | null | 1502.02710 | null | null |
Generative Moment Matching Networks | cs.LG cs.AI stat.ML | We consider the problem of learning deep generative models from data. We
formulate a method that generates an independent sample via a single
feedforward pass through a multilayer perceptron, as in the recently proposed
generative adversarial networks (Goodfellow et al., 2014). Training a
generative adversarial network, however, requires careful optimization of a
difficult minimax program. Instead, we utilize a technique from statistical
hypothesis testing known as maximum mean discrepancy (MMD), which leads to a
simple objective that can be interpreted as matching all orders of statistics
between a dataset and samples from the model, and can be trained by
backpropagation. We further boost the performance of this approach by combining
our generative network with an auto-encoder network, using MMD to learn to
generate codes that can then be decoded to produce samples. We show that the
combination of these techniques yields excellent generative models compared to
baseline approaches as measured on MNIST and the Toronto Face Database.
| Yujia Li, Kevin Swersky and Richard Zemel | null | 1502.02761 | null | null |
Cascading Bandits: Learning to Rank in the Cascade Model | cs.LG stat.ML | A search engine usually outputs a list of $K$ web pages. The user examines
this list, from the first web page to the last, and chooses the first
attractive page. This model of user behavior is known as the cascade model. In
this paper, we propose cascading bandits, a learning variant of the cascade
model where the objective is to identify $K$ most attractive items. We
formulate our problem as a stochastic combinatorial partial monitoring problem.
We propose two algorithms for solving it, CascadeUCB1 and CascadeKL-UCB. We
also prove gap-dependent upper bounds on the regret of these algorithms and
derive a lower bound on the regret in cascading bandits. The lower bound
matches the upper bound of CascadeKL-UCB up to a logarithmic factor. We
experiment with our algorithms on several problems. The algorithms perform
surprisingly well even when our modeling assumptions are violated.
| Branislav Kveton, Csaba Szepesvari, Zheng Wen, and Azin Ashkan | null | 1502.02763 | null | null |
Learning Transferable Features with Deep Adaptation Networks | cs.LG | Recent studies reveal that a deep neural network can learn transferable
features which generalize well to novel tasks for domain adaptation. However,
as deep features eventually transition from general to specific along the
network, the feature transferability drops significantly in higher layers with
increasing domain discrepancy. Hence, it is important to formally reduce the
dataset bias and enhance the transferability in task-specific layers. In this
paper, we propose a new Deep Adaptation Network (DAN) architecture, which
generalizes deep convolutional neural network to the domain adaptation
scenario. In DAN, hidden representations of all task-specific layers are
embedded in a reproducing kernel Hilbert space where the mean embeddings of
different domain distributions can be explicitly matched. The domain
discrepancy is further reduced using an optimal multi-kernel selection method
for mean embedding matching. DAN can learn transferable features with
statistical guarantees, and can scale linearly by unbiased estimate of kernel
embedding. Extensive empirical evidence shows that the proposed architecture
yields state-of-the-art image classification error rates on standard domain
adaptation benchmarks.
| Mingsheng Long, Yue Cao, Jianmin Wang, Michael I. Jordan | null | 1502.02791 | null | null |
Probabilistic Line Searches for Stochastic Optimization | cs.LG math.OC stat.ML | In deterministic optimization, line searches are a standard tool ensuring
stability and efficiency. Where only stochastic gradients are available, no
direct equivalent has so far been formulated, because uncertain gradients do
not allow for a strict sequence of decisions collapsing the search space. We
construct a probabilistic line search by combining the structure of existing
deterministic methods with notions from Bayesian optimization. Our method
retains a Gaussian process surrogate of the univariate optimization objective,
and uses a probabilistic belief over the Wolfe conditions to monitor the
descent. The algorithm has very low computational cost, and no user-controlled
parameters. Experiments show that it effectively removes the need to define a
learning rate for stochastic gradient descent.
| Maren Mahsereci and Philipp Hennig | null | 1502.02846 | null | null |
Gaussian Processes for Data-Efficient Learning in Robotics and Control | stat.ML cs.LG cs.RO cs.SY | Autonomous learning has been a promising direction in control and robotics
for more than a decade since data-driven learning allows to reduce the amount
of engineering knowledge, which is otherwise required. However, autonomous
reinforcement learning (RL) approaches typically require many interactions with
the system to learn controllers, which is a practical limitation in real
systems, such as robots, where many interactions can be impractical and time
consuming. To address this problem, current learning approaches typically
require task-specific knowledge in form of expert demonstrations, realistic
simulators, pre-shaped policies, or specific knowledge about the underlying
dynamics. In this article, we follow a different approach and speed up learning
by extracting more information from data. In particular, we learn a
probabilistic, non-parametric Gaussian process transition model of the system.
By explicitly incorporating model uncertainty into long-term planning and
controller learning our approach reduces the effects of model errors, a key
problem in model-based learning. Compared to state-of-the art RL our
model-based policy search method achieves an unprecedented speed of learning.
We demonstrate its applicability to autonomous learning in real robot and
control tasks.
| Marc Peter Deisenroth, Dieter Fox and Carl Edward Rasmussen | 10.1109/TPAMI.2013.218 | 1502.02860 | null | null |
Show, Attend and Tell: Neural Image Caption Generation with Visual
Attention | cs.LG cs.CV | Inspired by recent work in machine translation and object detection, we
introduce an attention based model that automatically learns to describe the
content of images. We describe how we can train this model in a deterministic
manner using standard backpropagation techniques and stochastically by
maximizing a variational lower bound. We also show through visualization how
the model is able to automatically learn to fix its gaze on salient objects
while generating the corresponding words in the output sequence. We validate
the use of attention with state-of-the-art performance on three benchmark
datasets: Flickr8k, Flickr30k and MS COCO.
| Kelvin Xu and Jimmy Ba and Ryan Kiros and Kyunghyun Cho and Aaron
Courville and Ruslan Salakhutdinov and Richard Zemel and Yoshua Bengio | null | 1502.03044 | null | null |
Kernel Task-Driven Dictionary Learning for Hyperspectral Image
Classification | stat.ML cs.CV cs.LG | Dictionary learning algorithms have been successfully used in both
reconstructive and discriminative tasks, where the input signal is represented
by a linear combination of a few dictionary atoms. While these methods are
usually developed under $\ell_1$ sparsity constrain (prior) in the input
domain, recent studies have demonstrated the advantages of sparse
representation using structured sparsity priors in the kernel domain. In this
paper, we propose a supervised dictionary learning algorithm in the kernel
domain for hyperspectral image classification. In the proposed formulation, the
dictionary and classifier are obtained jointly for optimal classification
performance. The supervised formulation is task-driven and provides learned
features from the hyperspectral data that are well suited for the
classification task. Moreover, the proposed algorithm uses a joint
($\ell_{12}$) sparsity prior to enforce collaboration among the neighboring
pixels. The simulation results illustrate the efficiency of the proposed
dictionary learning algorithm.
| Soheil Bahrampour and Nasser M. Nasrabadi and Asok Ray and Kenneth W.
Jenkins | null | 1502.03126 | null | null |
Gaussian Process Models for HRTF based Sound-Source Localization and
Active-Learning | cs.SD cs.LG stat.ML | From a machine learning perspective, the human ability localize sounds can be
modeled as a non-parametric and non-linear regression problem between binaural
spectral features of sound received at the ears (input) and their sound-source
directions (output). The input features can be summarized in terms of the
individual's head-related transfer functions (HRTFs) which measure the spectral
response between the listener's eardrum and an external point in $3$D. Based on
these viewpoints, two related problems are considered: how can one achieve an
optimal sampling of measurements for training sound-source localization (SSL)
models, and how can SSL models be used to infer the subject's HRTFs in
listening tests. First, we develop a class of binaural SSL models based on
Gaussian process regression and solve a \emph{forward selection} problem that
finds a subset of input-output samples that best generalize to all SSL
directions. Second, we use an \emph{active-learning} approach that updates an
online SSL model for inferring the subject's SSL errors via headphones and a
graphical user interface. Experiments show that only a small fraction of HRTFs
are required for $5^{\circ}$ localization accuracy and that the learned HRTFs
are localized closer to their intended directions than non-individualized
HRTFs.
| Yuancheng Luo, Dmitry N. Zotkin, Ramani Duraiswami | null | 1502.03163 | null | null |
Batch Normalization: Accelerating Deep Network Training by Reducing
Internal Covariate Shift | cs.LG | Training Deep Neural Networks is complicated by the fact that the
distribution of each layer's inputs changes during training, as the parameters
of the previous layers change. This slows down the training by requiring lower
learning rates and careful parameter initialization, and makes it notoriously
hard to train models with saturating nonlinearities. We refer to this
phenomenon as internal covariate shift, and address the problem by normalizing
layer inputs. Our method draws its strength from making normalization a part of
the model architecture and performing the normalization for each training
mini-batch. Batch Normalization allows us to use much higher learning rates and
be less careful about initialization. It also acts as a regularizer, in some
cases eliminating the need for Dropout. Applied to a state-of-the-art image
classification model, Batch Normalization achieves the same accuracy with 14
times fewer training steps, and beats the original model by a significant
margin. Using an ensemble of batch-normalized networks, we improve upon the
best published result on ImageNet classification: reaching 4.9% top-5
validation error (and 4.8% test error), exceeding the accuracy of human raters.
| Sergey Ioffe, Christian Szegedy | null | 1502.03167 | null | null |
Proximal Algorithms in Statistics and Machine Learning | stat.ML cs.LG stat.ME | In this paper we develop proximal methods for statistical learning. Proximal
point algorithms are useful in statistics and machine learning for obtaining
optimization solutions for composite functions. Our approach exploits
closed-form solutions of proximal operators and envelope representations based
on the Moreau, Forward-Backward, Douglas-Rachford and Half-Quadratic envelopes.
Envelope representations lead to novel proximal algorithms for statistical
optimisation of composite objective functions which include both non-smooth and
non-convex objectives. We illustrate our methodology with regularized Logistic
and Poisson regression and non-convex bridge penalties with a fused lasso norm.
We provide a discussion of convergence of non-descent algorithms with
acceleration and for non-convex functions. Finally, we provide directions for
future research.
| Nicholas G. Polson, James G. Scott and Brandon T. Willard | null | 1502.03175 | null | null |
Off-policy evaluation for MDPs with unknown structure | stat.ML cs.LG | Off-policy learning in dynamic decision problems is essential for providing
strong evidence that a new policy is better than the one in use. But how can we
prove superiority without testing the new policy? To answer this question, we
introduce the G-SCOPE algorithm that evaluates a new policy based on data
generated by the existing policy. Our algorithm is both computationally and
sample efficient because it greedily learns to exploit factored structure in
the dynamics of the environment. We present a finite sample analysis of our
approach and show through experiments that the algorithm scales well on
high-dimensional problems with few samples.
| Assaf Hallak and Fran\c{c}ois Schnitzler and Timothy Mann and Shie
Mannor | null | 1502.03255 | null | null |
Statistical laws in linguistics | physics.soc-ph cs.LG physics.data-an | Zipf's law is just one out of many universal laws proposed to describe
statistical regularities in language. Here we review and critically discuss how
these laws can be statistically interpreted, fitted, and tested (falsified).
The modern availability of large databases of written text allows for tests
with an unprecedent statistical accuracy and also a characterization of the
fluctuations around the typical behavior. We find that fluctuations are usually
much larger than expected based on simplifying statistical assumptions (e.g.,
independence and lack of correlations between observations).These
simplifications appear also in usual statistical tests so that the large
fluctuations can be erroneously interpreted as a falsification of the law.
Instead, here we argue that linguistic laws are only meaningful (falsifiable)
if accompanied by a model for which the fluctuations can be computed (e.g., a
generative model of the text). The large fluctuations we report show that the
constraints imposed by linguistic laws on the creativity process of text
generation are not as tight as one could expect.
| Eduardo G. Altmann and Martin Gerlach | 10.1007/978-3-319-24403-7_2 | 1502.03296 | null | null |
Using Distance Estimation and Deep Learning to Simplify Calibration in
Food Calorie Measurement | cs.CY cs.HC cs.LG | High calorie intake in the human body on the one hand, has proved harmful in
numerous occasions leading to several diseases and on the other hand, a
standard amount of calorie intake has been deemed essential by dieticians to
maintain the right balance of calorie content in human body. As such,
researchers have proposed a variety of automatic tools and systems to assist
users measure their calorie in-take. In this paper, we consider the category of
those tools that use image processing to recognize the food, and we propose a
method for fully automatic and user-friendly calibration of the dimension of
the food portion sizes, which is needed in order to measure food portion weight
and its ensuing amount of calories. Experimental results show that our method,
which uses deep learning, mobile cloud computing, distance estimation and size
calibration inside a mobile device, leads to an accuracy improvement to 95% on
average compared to previous work
| Pallavi Kuhad, Abdulsalam Yassine, Shervin Shirmohammadi | null | 1502.03302 | null | null |
Large-Scale Deep Learning on the YFCC100M Dataset | cs.LG cs.CV | We present a work-in-progress snapshot of learning with a 15 billion
parameter deep learning network on HPC architectures applied to the largest
publicly available natural image and video dataset released to-date. Recent
advancements in unsupervised deep neural networks suggest that scaling up such
networks in both model and training dataset size can yield significant
improvements in the learning of concepts at the highest layers. We train our
three-layer deep neural network on the Yahoo! Flickr Creative Commons 100M
dataset. The dataset comprises approximately 99.2 million images and 800,000
user-created videos from Yahoo's Flickr image and video sharing platform.
Training of our network takes eight days on 98 GPU nodes at the High
Performance Computing Center at Lawrence Livermore National Laboratory.
Encouraging preliminary results and future research directions are presented
and discussed.
| Karl Ni, Roger Pearce, Kofi Boakye, Brian Van Essen, Damian Borth,
Barry Chen, Eric Wang | null | 1502.03409 | null | null |
Collaborative Filtering Bandits | cs.LG cs.AI stat.ML | Classical collaborative filtering, and content-based filtering methods try to
learn a static recommendation model given training data. These approaches are
far from ideal in highly dynamic recommendation domains such as news
recommendation and computational advertisement, where the set of items and
users is very fluid. In this work, we investigate an adaptive clustering
technique for content recommendation based on exploration-exploitation
strategies in contextual multi-armed bandit settings. Our algorithm takes into
account the collaborative effects that arise due to the interaction of the
users with the items, by dynamically grouping users based on the items under
consideration and, at the same time, grouping items based on the similarity of
the clusterings induced over the users. The resulting algorithm thus takes
advantage of preference patterns in the data in a way akin to collaborative
filtering methods. We provide an empirical analysis on medium-size real-world
datasets, showing scalability and increased prediction performance (as measured
by click-through rate) over state-of-the-art methods for clustering bandits. We
also provide a regret analysis within a standard linear stochastic noise
setting.
| Shuai Li and Alexandros Karatzoglou and Claudio Gentile | null | 1502.03473 | null | null |
Combinatorial Bandits Revisited | cs.LG math.OC stat.ML | This paper investigates stochastic and adversarial combinatorial multi-armed
bandit problems. In the stochastic setting under semi-bandit feedback, we
derive a problem-specific regret lower bound, and discuss its scaling with the
dimension of the decision space. We propose ESCB, an algorithm that efficiently
exploits the structure of the problem and provide a finite-time analysis of its
regret. ESCB has better performance guarantees than existing algorithms, and
significantly outperforms these algorithms in practice. In the adversarial
setting under bandit feedback, we propose \textsc{CombEXP}, an algorithm with
the same regret scaling as state-of-the-art algorithms, but with lower
computational complexity for some combinatorial problems.
| Richard Combes and M. Sadegh Talebi and Alexandre Proutiere and Marc
Lelarge | null | 1502.03475 | null | null |
How to show a probabilistic model is better | stat.ML cs.LG | We present a simple theoretical framework, and corresponding practical
procedures, for comparing probabilistic models on real data in a traditional
machine learning setting. This framework is based on the theory of proper
scoring rules, but requires only basic algebra and probability theory to
understand and verify. The theoretical concepts presented are well-studied,
primarily in the statistics literature. The goal of this paper is to advocate
their wider adoption for performance evaluation in empirical machine learning.
| Mithun Chakraborty, Sanmay Das, Allen Lavoie | null | 1502.03491 | null | null |
Gradient-based Hyperparameter Optimization through Reversible Learning | stat.ML cs.LG | Tuning hyperparameters of learning algorithms is hard because gradients are
usually unavailable. We compute exact gradients of cross-validation performance
with respect to all hyperparameters by chaining derivatives backwards through
the entire training procedure. These gradients allow us to optimize thousands
of hyperparameters, including step-size and momentum schedules, weight
initialization distributions, richly parameterized regularization schemes, and
neural network architectures. We compute hyperparameter gradients by exactly
reversing the dynamics of stochastic gradient descent with momentum.
| Dougal Maclaurin, David Duvenaud, Ryan P. Adams | null | 1502.03492 | null | null |
Spectral Sparsification of Random-Walk Matrix Polynomials | cs.DS cs.DM cs.LG cs.SI stat.ML | We consider a fundamental algorithmic question in spectral graph theory:
Compute a spectral sparsifier of random-walk matrix-polynomial
$$L_\alpha(G)=D-\sum_{r=1}^d\alpha_rD(D^{-1}A)^r$$ where $A$ is the adjacency
matrix of a weighted, undirected graph, $D$ is the diagonal matrix of weighted
degrees, and $\alpha=(\alpha_1...\alpha_d)$ are nonnegative coefficients with
$\sum_{r=1}^d\alpha_r=1$. Recall that $D^{-1}A$ is the transition matrix of
random walks on the graph. The sparsification of $L_\alpha(G)$ appears to be
algorithmically challenging as the matrix power $(D^{-1}A)^r$ is defined by all
paths of length $r$, whose precise calculation would be prohibitively
expensive.
In this paper, we develop the first nearly linear time algorithm for this
sparsification problem: For any $G$ with $n$ vertices and $m$ edges, $d$
coefficients $\alpha$, and $\epsilon > 0$, our algorithm runs in time
$O(d^2m\log^2n/\epsilon^{2})$ to construct a Laplacian matrix
$\tilde{L}=D-\tilde{A}$ with $O(n\log n/\epsilon^{2})$ non-zeros such that
$\tilde{L}\approx_{\epsilon}L_\alpha(G)$.
Matrix polynomials arise in mathematical analysis of matrix functions as well
as numerical solutions of matrix equations. Our work is particularly motivated
by the algorithmic problems for speeding up the classic Newton's method in
applications such as computing the inverse square-root of the precision matrix
of a Gaussian random field, as well as computing the $q$th-root transition (for
$q\geq1$) in a time-reversible Markov model. The key algorithmic step for both
applications is the construction of a spectral sparsifier of a constant degree
random-walk matrix-polynomials introduced by Newton's method. Our algorithm can
also be used to build efficient data structures for effective resistances for
multi-step time-reversible Markov models, and we anticipate that it could be
useful for other tasks in network analysis.
| Dehua Cheng, Yu Cheng, Yan Liu, Richard Peng, Shang-Hua Teng | null | 1502.03496 | null | null |
Supervised LogEuclidean Metric Learning for Symmetric Positive Definite
Matrices | cs.LG | Metric learning has been shown to be highly effective to improve the
performance of nearest neighbor classification. In this paper, we address the
problem of metric learning for Symmetric Positive Definite (SPD) matrices such
as covariance matrices, which arise in many real-world applications. Naively
using standard Mahalanobis metric learning methods under the Euclidean geometry
for SPD matrices is not appropriate, because the difference of SPD matrices can
be a non-SPD matrix and thus the obtained solution can be uninterpretable. To
cope with this problem, we propose to use a properly parameterized LogEuclidean
distance and optimize the metric with respect to kernel-target alignment, which
is a supervised criterion for kernel learning. Then the resulting non-trivial
optimization problem is solved by utilizing the Riemannian geometry. Finally,
we experimentally demonstrate the usefulness of our LogEuclidean metric
learning algorithm on real-world classification tasks for EEG signals and
texture patches.
| Florian Yger and Masashi Sugiyama | null | 1502.03505 | null | null |
Adding vs. Averaging in Distributed Primal-Dual Optimization | cs.LG | Distributed optimization methods for large-scale machine learning suffer from
a communication bottleneck. It is difficult to reduce this bottleneck while
still efficiently and accurately aggregating partial work from different
machines. In this paper, we present a novel generalization of the recent
communication-efficient primal-dual framework (CoCoA) for distributed
optimization. Our framework, CoCoA+, allows for additive combination of local
updates to the global parameters at each iteration, whereas previous schemes
with convergence guarantees only allow conservative averaging. We give stronger
(primal-dual) convergence rate guarantees for both CoCoA as well as our new
variants, and generalize the theory for both methods to cover non-smooth convex
loss functions. We provide an extensive experimental comparison that shows the
markedly improved performance of CoCoA+ on several real-world distributed
datasets, especially when scaling up the number of machines.
| Chenxin Ma, Virginia Smith, Martin Jaggi, Michael I. Jordan, Peter
Richt\'arik and Martin Tak\'a\v{c} | null | 1502.03508 | null | null |
MADE: Masked Autoencoder for Distribution Estimation | cs.LG cs.NE stat.ML | There has been a lot of recent interest in designing neural network models to
estimate a distribution from a set of examples. We introduce a simple
modification for autoencoder neural networks that yields powerful generative
models. Our method masks the autoencoder's parameters to respect autoregressive
constraints: each input is reconstructed only from previous inputs in a given
ordering. Constrained this way, the autoencoder outputs can be interpreted as a
set of conditional probabilities, and their product, the full joint
probability. We can also train a single network that can decompose the joint
probability in multiple different orderings. Our simple framework can be
applied to multiple architectures, including deep ones. Vectorized
implementations, such as on GPUs, are simple and fast. Experiments demonstrate
that this approach is competitive with state-of-the-art tractable distribution
estimators. At test time, the method is significantly faster and scales better
than other autoregressive estimators.
| Mathieu Germain, Karol Gregor, Iain Murray, Hugo Larochelle | null | 1502.03509 | null | null |
A Latent Variable Model Approach to PMI-based Word Embeddings | cs.LG cs.CL stat.ML | Semantic word embeddings represent the meaning of a word via a vector, and
are created by diverse methods. Many use nonlinear operations on co-occurrence
statistics, and have hand-tuned hyperparameters and reweighting methods.
This paper proposes a new generative model, a dynamic version of the
log-linear topic model of~\citet{mnih2007three}. The methodological novelty is
to use the prior to compute closed form expressions for word statistics. This
provides a theoretical justification for nonlinear models like PMI, word2vec,
and GloVe, as well as some hyperparameter choices. It also helps explain why
low-dimensional semantic embeddings contain linear algebraic structure that
allows solution of word analogies, as shown by~\citet{mikolov2013efficient} and
many subsequent papers.
Experimental support is provided for the generative model assumptions, the
most important of which is that latent word vectors are fairly uniformly
dispersed in space.
| Sanjeev Arora, Yuanzhi Li, Yingyu Liang, Tengyu Ma, Andrej Risteski | null | 1502.03520 | null | null |
Scalable Stochastic Alternating Direction Method of Multipliers | cs.LG | Stochastic alternating direction method of multipliers (ADMM), which visits
only one sample or a mini-batch of samples each time, has recently been proved
to achieve better performance than batch ADMM. However, most stochastic methods
can only achieve a convergence rate $O(1/\sqrt T)$ on general convex
problems,where T is the number of iterations. Hence, these methods are not
scalable with respect to convergence rate (computation cost). There exists only
one stochastic method, called SA-ADMM, which can achieve convergence rate
$O(1/T)$ on general convex problems. However, an extra memory is needed for
SA-ADMM to store the historic gradients on all samples, and thus it is not
scalable with respect to storage cost. In this paper, we propose a novel
method, called scalable stochastic ADMM(SCAS-ADMM), for large-scale
optimization and learning problems. Without the need to store the historic
gradients, SCAS-ADMM can achieve the same convergence rate $O(1/T)$ as the best
stochastic method SA-ADMM and batch ADMM on general convex problems.
Experiments on graph-guided fused lasso show that SCAS-ADMM can achieve
state-of-the-art performance in real applications
| Shen-Yi Zhao, Wu-Jun Li, Zhi-Hua Zhou | null | 1502.03529 | null | null |
Convergence of gradient based pre-training in Denoising autoencoders | cs.LG cs.CV math.OC | The success of deep architectures is at least in part attributed to the
layer-by-layer unsupervised pre-training that initializes the network. Various
papers have reported extensive empirical analysis focusing on the design and
implementation of good pre-training procedures. However, an understanding
pertaining to the consistency of parameter estimates, the convergence of
learning procedures and the sample size estimates is still unavailable in the
literature. In this work, we study pre-training in classical and distributed
denoising autoencoders with these goals in mind. We show that the gradient
converges at the rate of $\frac{1}{\sqrt{N}}$ and has a sub-linear dependence
on the size of the autoencoder network. In a distributed setting where disjoint
sections of the whole network are pre-trained synchronously, we show that the
convergence improves by at least $\tau^{3/4}$, where $\tau$ corresponds to the
size of the sections. We provide a broad set of experiments to empirically
evaluate the suggested behavior.
| Vamsi K Ithapu, Sathya Ravi, Vikas Singh | null | 1502.03537 | null | null |
Web spam classification using supervised artificial neural network
algorithms | cs.NE cs.LG | Due to the rapid growth in technology employed by the spammers, there is a
need of classifiers that are more efficient, generic and highly adaptive.
Neural Network based technologies have high ability of adaption as well as
generalization. As per our knowledge, very little work has been done in this
field using neural network. We present this paper to fill this gap. This paper
evaluates performance of three supervised learning algorithms of artificial
neural network by creating classifiers for the complex problem of latest web
spam pattern classification. These algorithms are Conjugate Gradient algorithm,
Resilient Backpropagation learning, and Levenberg-Marquardt algorithm.
| Ashish Chandra, Mohammad Suaib, and Dr. Rizwan Beg | null | 1502.03581 | null | null |
A Predictive System for detection of Bankruptcy using Machine Learning
techniques | cs.LG | Bankruptcy is a legal procedure that claims a person or organization as a
debtor. It is essential to ascertain the risk of bankruptcy at initial stages
to prevent financial losses. In this perspective, different soft computing
techniques can be employed to ascertain bankruptcy. This study proposes a
bankruptcy prediction system to categorize the companies based on extent of
risk. The prediction system acts as a decision support tool for detection of
bankruptcy
Keywords: Bankruptcy, soft computing, decision support tool
| Kalyan Nagaraj, Amulyashree Sridhar | 10.5121/ijdkp.2015.5103 | 1502.03601 | null | null |
Ordering-sensitive and Semantic-aware Topic Modeling | cs.LG cs.CL cs.IR | Topic modeling of textual corpora is an important and challenging problem. In
most previous work, the "bag-of-words" assumption is usually made which ignores
the ordering of words. This assumption simplifies the computation, but it
unrealistically loses the ordering information and the semantic of words in the
context. In this paper, we present a Gaussian Mixture Neural Topic Model
(GMNTM) which incorporates both the ordering of words and the semantic meaning
of sentences into topic modeling. Specifically, we represent each topic as a
cluster of multi-dimensional vectors and embed the corpus into a collection of
vectors generated by the Gaussian mixture model. Each word is affected not only
by its topic, but also by the embedding vector of its surrounding words and the
context. The Gaussian mixture components and the topic of documents, sentences
and words can be learnt jointly. Extensive experiments show that our model can
learn better topics and more accurate word distributions for each topic.
Quantitatively, comparing to state-of-the-art topic modeling approaches, GMNTM
obtains significantly better performance in terms of perplexity, retrieval
accuracy and classification accuracy.
| Min Yang, Tianyi Cui, Wenting Tu | null | 1502.03630 | null | null |
Over-Sampling in a Deep Neural Network | cs.LG cs.NE | Deep neural networks (DNN) are the state of the art on many engineering
problems such as computer vision and audition. A key factor in the success of
the DNN is scalability - bigger networks work better. However, the reason for
this scalability is not yet well understood. Here, we interpret the DNN as a
discrete system, of linear filters followed by nonlinear activations, that is
subject to the laws of sampling theory. In this context, we demonstrate that
over-sampled networks are more selective, learn faster and learn more robustly.
Our findings may ultimately generalize to the human brain.
| Andrew J.R. Simpson | null | 1502.03648 | null | null |
Applying deep learning techniques on medical corpora from the World Wide
Web: a prototypical system and evaluation | cs.CL cs.IR cs.LG cs.NE | BACKGROUND: The amount of biomedical literature is rapidly growing and it is
becoming increasingly difficult to keep manually curated knowledge bases and
ontologies up-to-date. In this study we applied the word2vec deep learning
toolkit to medical corpora to test its potential for identifying relationships
from unstructured text. We evaluated the efficiency of word2vec in identifying
properties of pharmaceuticals based on mid-sized, unstructured medical text
corpora available on the web. Properties included relationships to diseases
('may treat') or physiological processes ('has physiological effect'). We
compared the relationships identified by word2vec with manually curated
information from the National Drug File - Reference Terminology (NDF-RT)
ontology as a gold standard. RESULTS: Our results revealed a maximum accuracy
of 49.28% which suggests a limited ability of word2vec to capture linguistic
regularities on the collected medical corpora compared with other published
results. We were able to document the influence of different parameter settings
on result accuracy and found and unexpected trade-off between ranking quality
and accuracy. Pre-processing corpora to reduce syntactic variability proved to
be a good strategy for increasing the utility of the trained vector models.
CONCLUSIONS: Word2vec is a very efficient implementation for computing vector
representations and for its ability to identify relationships in textual data
without any prior domain knowledge. We found that the ranking and retrieved
results generated by word2vec were not of sufficient quality for automatic
population of knowledge bases and ontologies, but could serve as a starting
point for further manual curation.
| Jose Antonio Mi\~narro-Gim\'enez, Oscar Mar\'in-Alonso, Matthias
Samwald | null | 1502.03682 | null | null |
Semi-supervised Data Representation via Affinity Graph Learning | cs.LG cs.CV | We consider the general problem of utilizing both labeled and unlabeled data
to improve data representation performance. A new semi-supervised learning
framework is proposed by combing manifold regularization and data
representation methods such as Non negative matrix factorization and sparse
coding. We adopt unsupervised data representation methods as the learning
machines because they do not depend on the labeled data, which can improve
machine's generation ability as much as possible. The proposed framework forms
the Laplacian regularizer through learning the affinity graph. We incorporate
the new Laplacian regularizer into the unsupervised data representation to
smooth the low dimensional representation of data and make use of label
information. Experimental results on several real benchmark datasets indicate
that our semi-supervised learning framework achieves encouraging results
compared with state-of-art methods.
| Weiya Ren | null | 1502.03879 | null | null |
Policy Gradient for Coherent Risk Measures | cs.AI cs.LG stat.ML | Several authors have recently developed risk-sensitive policy gradient
methods that augment the standard expected cost minimization problem with a
measure of variability in cost. These studies have focused on specific
risk-measures, such as the variance or conditional value at risk (CVaR). In
this work, we extend the policy gradient method to the whole class of coherent
risk measures, which is widely accepted in finance and operations research,
among other fields. We consider both static and time-consistent dynamic risk
measures. For static risk measures, our approach is in the spirit of policy
gradient algorithms and combines a standard sampling approach with convex
programming. For dynamic risk measures, our approach is actor-critic style and
involves explicit approximation of value function. Most importantly, our
contribution presents a unified approach to risk-sensitive reinforcement
learning that generalizes and extends previous results.
| Aviv Tamar, Yinlam Chow, Mohammad Ghavamzadeh, Shie Mannor | null | 1502.03919 | null | null |
The Responsibility Weighted Mahalanobis Kernel for Semi-Supervised
Training of Support Vector Machines for Classification | cs.LG stat.ML | Kernel functions in support vector machines (SVM) are needed to assess the
similarity of input samples in order to classify these samples, for instance.
Besides standard kernels such as Gaussian (i.e., radial basis function, RBF) or
polynomial kernels, there are also specific kernels tailored to consider
structure in the data for similarity assessment. In this article, we will
capture structure in data by means of probabilistic mixture density models, for
example Gaussian mixtures in the case of real-valued input spaces. From the
distance measures that are inherently contained in these models, e.g.,
Mahalanobis distances in the case of Gaussian mixtures, we derive a new kernel,
the responsibility weighted Mahalanobis (RWM) kernel. Basically, this kernel
emphasizes the influence of model components from which any two samples that
are compared are assumed to originate (that is, the "responsible" model
components). We will see that this kernel outperforms the RBF kernel and other
kernels capturing structure in data (such as the LAP kernel in Laplacian SVM)
in many applications where partially labeled data are available, i.e., for
semi-supervised training of SVM. Other key advantages are that the RWM kernel
can easily be used with standard SVM implementations and training algorithms
such as sequential minimal optimization, and heuristics known for the
parametrization of RBF kernels in a C-SVM can easily be transferred to this new
kernel. Properties of the RWM kernel are demonstrated with 20 benchmark data
sets and an increasing percentage of labeled samples in the training data.
| Tobias Reitmaier and Bernhard Sick | 10.1016/j.ins.2015.06.027 | 1502.04033 | null | null |
Abstract Learning via Demodulation in a Deep Neural Network | cs.LG cs.NE | Inspired by the brain, deep neural networks (DNN) are thought to learn
abstract representations through their hierarchical architecture. However, at
present, how this happens is not well understood. Here, we demonstrate that DNN
learn abstract representations by a process of demodulation. We introduce a
biased sigmoid activation function and use it to show that DNN learn and
perform better when optimized for demodulation. Our findings constitute the
first unambiguous evidence that DNN perform abstract learning in practical use.
Our findings may also explain abstract learning in the human brain.
| Andrew J.R. Simpson | null | 1502.04042 | null | null |
A Linear Dynamical System Model for Text | stat.ML cs.CL cs.LG | Low dimensional representations of words allow accurate NLP models to be
trained on limited annotated data. While most representations ignore words'
local context, a natural way to induce context-dependent representations is to
perform inference in a probabilistic latent-variable sequence model. Given the
recent success of continuous vector space word representations, we provide such
an inference procedure for continuous states, where words' representations are
given by the posterior mean of a linear dynamical system. Here, efficient
inference can be performed using Kalman filtering. Our learning algorithm is
extremely scalable, operating on simple cooccurrence counts for both parameter
initialization using the method of moments and subsequent iterations of EM. In
our experiments, we employ our inferred word embeddings as features in standard
tagging tasks, obtaining significant accuracy improvements. Finally, the Kalman
filter updates can be seen as a linear recurrent neural network. We demonstrate
that using the parameters of our model to initialize a non-linear recurrent
neural network language model reduces its training time by a day and yields
lower perplexity.
| David Belanger and Sham Kakade | null | 1502.04081 | null | null |
Non-Adaptive Learning a Hidden Hipergraph | cs.LG | We give a new deterministic algorithm that non-adaptively learns a hidden
hypergraph from edge-detecting queries. All previous non-adaptive algorithms
either run in exponential time or have non-optimal query complexity. We give
the first polynomial time non-adaptive learning algorithm for learning
hypergraph that asks almost optimal number of queries.
| Hasan Abasi and Nader H. Bshouty and Hanna Mazzawi | null | 1502.04137 | null | null |
A Pseudo-Euclidean Iteration for Optimal Recovery in Noisy ICA | cs.LG stat.ML | Independent Component Analysis (ICA) is a popular model for blind signal
separation. The ICA model assumes that a number of independent source signals
are linearly mixed to form the observed signals. We propose a new algorithm,
PEGI (for pseudo-Euclidean Gradient Iteration), for provable model recovery for
ICA with Gaussian noise. The main technical innovation of the algorithm is to
use a fixed point iteration in a pseudo-Euclidean (indefinite "inner product")
space. The use of this indefinite "inner product" resolves technical issues
common to several existing algorithms for noisy ICA. This leads to an algorithm
which is conceptually simple, efficient and accurate in testing.
Our second contribution is combining PEGI with the analysis of objectives for
optimal recovery in the noisy ICA model. It has been observed that the direct
approach of demixing with the inverse of the mixing matrix is suboptimal for
signal recovery in terms of the natural Signal to Interference plus Noise Ratio
(SINR) criterion. There have been several partial solutions proposed in the ICA
literature. It turns out that any solution to the mixing matrix reconstruction
problem can be used to construct an SINR-optimal ICA demixing, despite the fact
that SINR itself cannot be computed from data. That allows us to obtain a
practical and provably SINR-optimal recovery method for ICA with arbitrary
Gaussian noise.
| James Voss, Mikhail Belkin, and Luis Rademacher | null | 1502.04148 | null | null |
Joint Optimization of Masks and Deep Recurrent Neural Networks for
Monaural Source Separation | cs.SD cs.AI cs.LG cs.MM | Monaural source separation is important for many real world applications. It
is challenging because, with only a single channel of information available,
without any constraints, an infinite number of solutions are possible. In this
paper, we explore joint optimization of masking functions and deep recurrent
neural networks for monaural source separation tasks, including monaural speech
separation, monaural singing voice separation, and speech denoising. The joint
optimization of the deep recurrent neural networks with an extra masking layer
enforces a reconstruction constraint. Moreover, we explore a discriminative
criterion for training neural networks to further enhance the separation
performance. We evaluate the proposed system on the TSP, MIR-1K, and TIMIT
datasets for speech separation, singing voice separation, and speech denoising
tasks, respectively. Our approaches achieve 2.30--4.98 dB SDR gain compared to
NMF models in the speech separation task, 2.30--2.48 dB GNSDR gain and
4.32--5.42 dB GSIR gain compared to existing models in the singing voice
separation task, and outperform NMF and DNN baselines in the speech denoising
task.
| Po-Sen Huang, Minje Kim, Mark Hasegawa-Johnson, Paris Smaragdis | 10.1109/TASLP.2015.2468583 | 1502.04149 | null | null |
Towards Biologically Plausible Deep Learning | cs.LG | Neuroscientists have long criticised deep learning algorithms as incompatible
with current knowledge of neurobiology. We explore more biologically plausible
versions of deep representation learning, focusing here mostly on unsupervised
learning but developing a learning mechanism that could account for supervised,
unsupervised and reinforcement learning. The starting point is that the basic
learning rule believed to govern synaptic weight updates
(Spike-Timing-Dependent Plasticity) arises out of a simple update rule that
makes a lot of sense from a machine learning point of view and can be
interpreted as gradient descent on some objective function so long as the
neuronal dynamics push firing rates towards better values of the objective
function (be it supervised, unsupervised, or reward-driven). The second main
idea is that this corresponds to a form of the variational EM algorithm, i.e.,
with approximate rather than exact posteriors, implemented by neural dynamics.
Another contribution of this paper is that the gradients required for updating
the hidden states in the above variational interpretation can be estimated
using an approximation that only requires propagating activations forward and
backward, with pairs of layers learning to form a denoising auto-encoder.
Finally, we extend the theory about the probabilistic interpretation of
auto-encoders to justify improved sampling schemes based on the generative
interpretation of denoising auto-encoders, and we validate all these ideas on
generative learning tasks.
| Yoshua Bengio, Dong-Hyun Lee, Jorg Bornschein, Thomas Mesnard and
Zhouhan Lin | null | 1502.04156 | null | null |
Nonparametric regression using needlet kernels for spherical data | cs.LG stat.ML | Needlets have been recognized as state-of-the-art tools to tackle spherical
data, due to their excellent localization properties in both spacial and
frequency domains.
This paper considers developing kernel methods associated with the needlet
kernel for nonparametric regression problems whose predictor variables are
defined on a sphere. Due to the localization property in the frequency domain,
we prove that the regularization parameter of the kernel ridge regression
associated with the needlet kernel can decrease arbitrarily fast. A natural
consequence is that the regularization term for the kernel ridge regression is
not necessary in the sense of rate optimality. Based on the excellent
localization property in the spacial domain further, we also prove that all the
$l^{q}$ $(01\leq q < \infty)$ kernel regularization estimates associated with
the needlet kernel, including the kernel lasso estimate and the kernel bridge
estimate, possess almost the same generalization capability for a large range
of regularization parameters in the sense of rate optimality.
This finding tentatively reveals that, if the needlet kernel is utilized,
then the choice of $q$ might not have a strong impact in terms of the
generalization capability in some modeling contexts. From this perspective, $q$
can be arbitrarily specified, or specified merely by other no generalization
criteria like smoothness, computational complexity, sparsity, etc..
| Shaobo Lin | null | 1502.04168 | null | null |
Application of Deep Neural Network in Estimation of the Weld Bead
Parameters | cs.LG | We present a deep learning approach to estimation of the bead parameters in
welding tasks. Our model is based on a four-hidden-layer neural network
architecture. More specifically, the first three hidden layers of this
architecture utilize Sigmoid function to produce their respective intermediate
outputs. On the other hand, the last hidden layer uses a linear transformation
to generate the final output of this architecture. This transforms our deep
network architecture from a classifier to a non-linear regression model. We
compare the performance of our deep network with a selected number of results
in the literature to show a considerable improvement in reducing the errors in
estimation of these values. Furthermore, we show its scalability on estimating
the weld bead parameters with same level of accuracy on combination of datasets
that pertain to different welding techniques. This is a nontrivial result that
is counter-intuitive to the general belief in this field of research.
| Soheil Keshmiri, Xin Zheng, Chee Meng Chew, Chee Khiang Pang | null | 1502.04187 | null | null |
Asymptotic Justification of Bandlimited Interpolation of Graph signals
for Semi-Supervised Learning | cs.LG cs.IT math.IT | Graph-based methods play an important role in unsupervised and
semi-supervised learning tasks by taking into account the underlying geometry
of the data set. In this paper, we consider a statistical setting for
semi-supervised learning and provide a formal justification of the recently
introduced framework of bandlimited interpolation of graph signals. Our
analysis leads to the interpretation that, given enough labeled data, this
method is very closely related to a constrained low density separation problem
as the number of data points tends to infinity. We demonstrate the practical
utility of our results through simple experiments.
| Aamir Anis, Aly El Gamal, A. Salman Avestimehr, Antonio Ortega | null | 1502.04248 | null | null |
Supersparse Linear Integer Models for Optimized Medical Scoring Systems | stat.ML cs.DM cs.LG stat.AP stat.ME | Scoring systems are linear classification models that only require users to
add, subtract and multiply a few small numbers in order to make a prediction.
These models are in widespread use by the medical community, but are difficult
to learn from data because they need to be accurate and sparse, have coprime
integer coefficients, and satisfy multiple operational constraints. We present
a new method for creating data-driven scoring systems called a Supersparse
Linear Integer Model (SLIM). SLIM scoring systems are built by solving an
integer program that directly encodes measures of accuracy (the 0-1 loss) and
sparsity (the $\ell_0$-seminorm) while restricting coefficients to coprime
integers. SLIM can seamlessly incorporate a wide range of operational
constraints related to accuracy and sparsity, and can produce highly tailored
models without parameter tuning. We provide bounds on the testing and training
accuracy of SLIM scoring systems, and present a new data reduction technique
that can improve scalability by eliminating a portion of the training data
beforehand. Our paper includes results from a collaboration with the
Massachusetts General Hospital Sleep Laboratory, where SLIM was used to create
a highly tailored scoring system for sleep apnea screening
| Berk Ustun and Cynthia Rudin | 10.1007/s10994-015-5528-6 | 1502.04269 | null | null |
Equilibrated adaptive learning rates for non-convex optimization | cs.LG cs.NA | Parameter-specific adaptive learning rate methods are computationally
efficient ways to reduce the ill-conditioning problems encountered when
training large deep networks. Following recent work that strongly suggests that
most of the critical points encountered when training such networks are saddle
points, we find how considering the presence of negative eigenvalues of the
Hessian could help us design better suited adaptive learning rate schemes. We
show that the popular Jacobi preconditioner has undesirable behavior in the
presence of both positive and negative curvature, and present theoretical and
empirical evidence that the so-called equilibration preconditioner is
comparatively better suited to non-convex problems. We introduce a novel
adaptive learning rate scheme, called ESGD, based on the equilibration
preconditioner. Our experiments show that ESGD performs as well or better than
RMSProp in terms of convergence speed, always clearly improving over plain
stochastic gradient descent.
| Yann N. Dauphin, Harm de Vries, Yoshua Bengio | null | 1502.04390 | null | null |
Invariant backpropagation: how to train a transformation-invariant
neural network | stat.ML cs.LG cs.NE | In many classification problems a classifier should be robust to small
variations in the input vector. This is a desired property not only for
particular transformations, such as translation and rotation in image
classification problems, but also for all others for which the change is small
enough to retain the object perceptually indistinguishable. We propose two
extensions of the backpropagation algorithm that train a neural network to be
robust to variations in the feature vector. While the first of them enforces
robustness of the loss function to all variations, the second method trains the
predictions to be robust to a particular variation which changes the loss
function the most. The second methods demonstrates better results, but is
slightly slower. We analytically compare the proposed algorithm with two the
most similar approaches (Tangent BP and Adversarial Training), and propose
their fast versions. In the experimental part we perform comparison of all
algorithms in terms of classification accuracy and robustness to noise on MNIST
and CIFAR-10 datasets. Additionally we analyze how the performance of the
proposed algorithm depends on the dataset size and data augmentation.
| Sergey Demyanov, James Bailey, Ramamohanarao Kotagiri, Christopher
Leckie | null | 1502.04434 | null | null |
Classification and its applications for drug-target interaction
identification | cs.LG q-bio.MN q-bio.QM | Classification is one of the most popular and widely used supervised learning
tasks, which categorizes objects into predefined classes based on known
knowledge. Classification has been an important research topic in machine
learning and data mining. Different classification methods have been proposed
and applied to deal with various real-world problems. Unlike unsupervised
learning such as clustering, a classifier is typically trained with labeled
data before being used to make prediction, and usually achieves higher accuracy
than unsupervised one.
In this paper, we first define classification and then review several
representative methods. After that, we study in details the application of
classification to a critical problem in drug discovery, i.e., drug-target
prediction, due to the challenges in predicting possible interactions between
drugs and targets.
| Jian-Ping Mei, Chee-Keong Kwoh, Peng Yang and Xiao-Li Li | null | 1502.04469 | null | null |
Towards Building Deep Networks with Bayesian Factor Graphs | cs.CV cs.LG | We propose a Multi-Layer Network based on the Bayesian framework of the
Factor Graphs in Reduced Normal Form (FGrn) applied to a two-dimensional
lattice. The Latent Variable Model (LVM) is the basic building block of a
quadtree hierarchy built on top of a bottom layer of random variables that
represent pixels of an image, a feature map, or more generally a collection of
spatially distributed discrete variables. The multi-layer architecture
implements a hierarchical data representation that, via belief propagation, can
be used for learning and inference. Typical uses are pattern completion,
correction and classification. The FGrn paradigm provides great flexibility and
modularity and appears as a promising candidate for building deep networks: the
system can be easily extended by introducing new and different (in cardinality
and in type) variables. Prior knowledge, or supervised information, can be
introduced at different scales. The FGrn paradigm provides a handy way for
building all kinds of architectures by interconnecting only three types of
units: Single Input Single Output (SISO) blocks, Sources and Replicators. The
network is designed like a circuit diagram and the belief messages flow
bidirectionally in the whole system. The learning algorithms operate only
locally within each block. The framework is demonstrated in this paper in a
three-layer structure applied to images extracted from a standard data set.
| Amedeo Buonanno and Francesco A.N. Palmieri | null | 1502.04492 | null | null |
Clustering by Descending to the Nearest Neighbor in the Delaunay Graph
Space | stat.ML cs.CV cs.LG | In our previous works, we proposed a physically-inspired rule to organize the
data points into an in-tree (IT) structure, in which some undesired edges are
allowed to occur. By removing those undesired or redundant edges, this IT
structure is divided into several separate parts, each representing one
cluster. In this work, we seek to prevent the undesired edges from arising at
the source. Before using the physically-inspired rule, data points are at first
organized into a proximity graph which restricts each point to select the
optimal directed neighbor just among its neighbors. Consequently, separated
in-trees or clusters automatically arise, without redundant edges requiring to
be removed.
| Teng Qiu, Yongjie Li | null | 1502.04502 | null | null |
The Ladder: A Reliable Leaderboard for Machine Learning Competitions | cs.LG | The organizer of a machine learning competition faces the problem of
maintaining an accurate leaderboard that faithfully represents the quality of
the best submission of each competing team. What makes this estimation problem
particularly challenging is its sequential and adaptive nature. As participants
are allowed to repeatedly evaluate their submissions on the leaderboard, they
may begin to overfit to the holdout data that supports the leaderboard. Few
theoretical results give actionable advice on how to design a reliable
leaderboard. Existing approaches therefore often resort to poorly understood
heuristics such as limiting the bit precision of answers and the rate of
re-submission.
In this work, we introduce a notion of "leaderboard accuracy" tailored to the
format of a competition. We introduce a natural algorithm called "the Ladder"
and demonstrate that it simultaneously supports strong theoretical guarantees
in a fully adaptive model of estimation, withstands practical adversarial
attacks, and achieves high utility on real submission files from an actual
competition hosted by Kaggle.
Notably, we are able to sidestep a powerful recent hardness result for
adaptive risk estimation that rules out algorithms such as ours under a
seemingly very similar notion of accuracy. On a practical note, we provide a
completely parameter-free variant of our algorithm that can be deployed in a
real competition with no tuning required whatsoever.
| Avrim Blum and Moritz Hardt | null | 1502.04585 | null | null |
Deep Transform: Error Correction via Probabilistic Re-Synthesis | cs.LG | Errors in data are usually unwelcome and so some means to correct them is
useful. However, it is difficult to define, detect or correct errors in an
unsupervised way. Here, we train a deep neural network to re-synthesize its
inputs at its output layer for a given class of data. We then exploit the fact
that this abstract transformation, which we call a deep transform (DT),
inherently rejects information (errors) existing outside of the abstract
feature space. Using the DT to perform probabilistic re-synthesis, we
demonstrate the recovery of data that has been subject to extreme degradation.
| Andrew J.R. Simpson | null | 1502.04617 | null | null |
Particle Gibbs for Bayesian Additive Regression Trees | stat.ML cs.LG stat.CO | Additive regression trees are flexible non-parametric models and popular
off-the-shelf tools for real-world non-linear regression. In application
domains, such as bioinformatics, where there is also demand for probabilistic
predictions with measures of uncertainty, the Bayesian additive regression
trees (BART) model, introduced by Chipman et al. (2010), is increasingly
popular. As data sets have grown in size, however, the standard
Metropolis-Hastings algorithms used to perform inference in BART are proving
inadequate. In particular, these Markov chains make local changes to the trees
and suffer from slow mixing when the data are high-dimensional or the best
fitting trees are more than a few layers deep. We present a novel sampler for
BART based on the Particle Gibbs (PG) algorithm (Andrieu et al., 2010) and a
top-down particle filtering algorithm for Bayesian decision trees
(Lakshminarayanan et al., 2013). Rather than making local changes to individual
trees, the PG sampler proposes a complete tree to fit the residual. Experiments
show that the PG sampler outperforms existing samplers in many settings.
| Balaji Lakshminarayanan, Daniel M. Roy and Yee Whye Teh | null | 1502.04622 | null | null |
DRAW: A Recurrent Neural Network For Image Generation | cs.CV cs.LG cs.NE | This paper introduces the Deep Recurrent Attentive Writer (DRAW) neural
network architecture for image generation. DRAW networks combine a novel
spatial attention mechanism that mimics the foveation of the human eye, with a
sequential variational auto-encoding framework that allows for the iterative
construction of complex images. The system substantially improves on the state
of the art for generative models on MNIST, and, when trained on the Street View
House Numbers dataset, it generates images that cannot be distinguished from
real data with the naked eye.
| Karol Gregor, Ivo Danihelka, Alex Graves, Danilo Jimenez Rezende, Daan
Wierstra | null | 1502.04623 | null | null |
Parameter estimation in softmax decision-making models with linear
objective functions | math.OC cs.LG stat.ML | With an eye towards human-centered automation, we contribute to the
development of a systematic means to infer features of human decision-making
from behavioral data. Motivated by the common use of softmax selection in
models of human decision-making, we study the maximum likelihood parameter
estimation problem for softmax decision-making models with linear objective
functions. We present conditions under which the likelihood function is convex.
These allow us to provide sufficient conditions for convergence of the
resulting maximum likelihood estimator and to construct its asymptotic
distribution. In the case of models with nonlinear objective functions, we show
how the estimator can be applied by linearizing about a nominal parameter
value. We apply the estimator to fit the stochastic UCL (Upper Credible Limit)
model of human decision-making to human subject data. We show statistically
significant differences in behavior across related, but distinct, tasks.
| Paul Reverdy and Naomi E. Leonard | null | 1502.04635 | null | null |
Unsupervised Learning of Video Representations using LSTMs | cs.LG cs.CV cs.NE | We use multilayer Long Short Term Memory (LSTM) networks to learn
representations of video sequences. Our model uses an encoder LSTM to map an
input sequence into a fixed length representation. This representation is
decoded using single or multiple decoder LSTMs to perform different tasks, such
as reconstructing the input sequence, or predicting the future sequence. We
experiment with two kinds of input sequences - patches of image pixels and
high-level representations ("percepts") of video frames extracted using a
pretrained convolutional net. We explore different design choices such as
whether the decoder LSTMs should condition on the generated output. We analyze
the outputs of the model qualitatively to see how well the model can
extrapolate the learned video representation into the future and into the past.
We try to visualize and interpret the learned features. We stress test the
model by running it on longer time scales and on out-of-domain data. We further
evaluate the representations by finetuning them for a supervised learning
problem - human action recognition on the UCF-101 and HMDB-51 datasets. We show
that the representations help improve classification accuracy, especially when
there are only a few training examples. Even models pretrained on unrelated
datasets (300 hours of YouTube videos) can help action recognition performance.
| Nitish Srivastava, Elman Mansimov and Ruslan Salakhutdinov | null | 1502.04681 | null | null |
Exact tensor completion using t-SVD | cs.LG cs.NA stat.ML | In this paper we focus on the problem of completion of multidimensional
arrays (also referred to as tensors) from limited sampling. Our approach is
based on a recently proposed tensor-Singular Value Decomposition (t-SVD) [1].
Using this factorization one can derive notion of tensor rank, referred to as
the tensor tubal rank, which has optimality properties similar to that of
matrix rank derived from SVD. As shown in [2] some multidimensional data, such
as panning video sequences exhibit low tensor tubal rank and we look at the
problem of completing such data under random sampling of the data cube. We show
that by solving a convex optimization problem, which minimizes the tensor
nuclear norm obtained as the convex relaxation of tensor tubal rank, one can
guarantee recovery with overwhelming probability as long as samples in
proportion to the degrees of freedom in t-SVD are observed. In this sense our
results are order-wise optimal. The conditions under which this result holds
are very similar to the incoherency conditions for the matrix completion,
albeit we define incoherency under the algebraic set-up of t-SVD. We show the
performance of the algorithm on some real data sets and compare it with other
existing approaches based on tensor flattening and Tucker decomposition.
| Zemin Zhang, Shuchin Aeron | null | 1502.04689 | null | null |
Nonparametric Nearest Neighbor Descent Clustering based on Delaunay
Triangulation | stat.ML cs.CV cs.LG | In our physically inspired in-tree (IT) based clustering algorithm and the
series after it, there is only one free parameter involved in computing the
potential value of each point. In this work, based on the Delaunay
Triangulation or its dual Voronoi tessellation, we propose a nonparametric
process to compute potential values by the local information. This computation,
though nonparametric, is relatively very rough, and consequently, many local
extreme points will be generated. However, unlike those gradient-based methods,
our IT-based methods are generally insensitive to those local extremes. This
positively demonstrates the superiority of these parametric (previous) and
nonparametric (in this work) IT-based methods.
| Teng Qiu, Yongjie Li | null | 1502.04837 | null | null |
Generalized Gradient Learning on Time Series under Elastic
Transformations | cs.LG | The majority of machine learning algorithms assumes that objects are
represented as vectors. But often the objects we want to learn on are more
naturally represented by other data structures such as sequences and time
series. For these representations many standard learning algorithms are
unavailable. We generalize gradient-based learning algorithms to time series
under dynamic time warping. To this end, we introduce elastic functions, which
extend functions on time series to matrix spaces. Necessary conditions are
presented under which generalized gradient learning on time series is
consistent. We indicate how results carry over to arbitrary elastic distance
functions and to sequences consisting of symbolic elements. Specifically, four
linear classifiers are extended to time series under dynamic time warping and
applied to benchmark datasets. Results indicate that generalized gradient
learning via elastic functions have the potential to complement the
state-of-the-art in statistical pattern recognition on time series.
| Brijnesh Jain | null | 1502.04843 | null | null |
Proper Complex Gaussian Processes for Regression | cs.LG stat.ML | Complex-valued signals are used in the modeling of many systems in
engineering and science, hence being of fundamental interest. Often, random
complex-valued signals are considered to be proper. A proper complex random
variable or process is uncorrelated with its complex conjugate. This assumption
is a good model of the underlying physics in many problems, and simplifies the
computations. While linear processing and neural networks have been widely
studied for these signals, the development of complex-valued nonlinear kernel
approaches remains an open problem. In this paper we propose Gaussian processes
for regression as a framework to develop 1) a solution for proper
complex-valued kernel regression and 2) the design of the reproducing kernel
for complex-valued inputs, using the convolutional approach for
cross-covariances. In this design we pay attention to preserve, in the complex
domain, the measure of similarity between near inputs. The hyperparameters of
the kernel are learned maximizing the marginal likelihood using Wirtinger
derivatives. Besides, the approach is connected to the multiple output learning
scenario. In the experiments included, we first solve a proper complex Gaussian
process where the cross-covariance does not cancel, a challenging scenario when
dealing with proper complex signals. Then we successfully use these novel
results to solve some problems previously proposed in the literature as
benchmarks, reporting a remarkable improvement in the estimation error.
| Rafael Boloix-Tortosa, F. Javier Pay\'an-Somet, Eva Arias-de-Reyna and
Juan Jos\'e Murillo-Fuentes | null | 1502.04868 | null | null |
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