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On the Computational Complexity of High-Dimensional Bayesian Variable
Selection | math.ST cs.LG stat.CO stat.ME stat.ML stat.TH | We study the computational complexity of Markov chain Monte Carlo (MCMC)
methods for high-dimensional Bayesian linear regression under sparsity
constraints. We first show that a Bayesian approach can achieve
variable-selection consistency under relatively mild conditions on the design
matrix. We then demonstrate that the statistical criterion of posterior
concentration need not imply the computational desideratum of rapid mixing of
the MCMC algorithm. By introducing a truncated sparsity prior for variable
selection, we provide a set of conditions that guarantee both
variable-selection consistency and rapid mixing of a particular
Metropolis-Hastings algorithm. The mixing time is linear in the number of
covariates up to a logarithmic factor. Our proof controls the spectral gap of
the Markov chain by constructing a canonical path ensemble that is inspired by
the steps taken by greedy algorithms for variable selection.
| Yun Yang, Martin J. Wainwright, Michael I. Jordan | null | 1505.07925 | null | null |
Transition-Based Dependency Parsing with Stack Long Short-Term Memory | cs.CL cs.LG cs.NE | We propose a technique for learning representations of parser states in
transition-based dependency parsers. Our primary innovation is a new control
structure for sequence-to-sequence neural networks---the stack LSTM. Like the
conventional stack data structures used in transition-based parsing, elements
can be pushed to or popped from the top of the stack in constant time, but, in
addition, an LSTM maintains a continuous space embedding of the stack contents.
This lets us formulate an efficient parsing model that captures three facets of
a parser's state: (i) unbounded look-ahead into the buffer of incoming words,
(ii) the complete history of actions taken by the parser, and (iii) the
complete contents of the stack of partially built tree fragments, including
their internal structures. Standard backpropagation techniques are used for
training and yield state-of-the-art parsing performance.
| Chris Dyer, Miguel Ballesteros, Wang Ling, Austin Matthews, Noah A.
Smith | null | 1505.08075 | null | null |
CURL: Co-trained Unsupervised Representation Learning for Image
Classification | cs.LG cs.CV stat.ML | In this paper we propose a strategy for semi-supervised image classification
that leverages unsupervised representation learning and co-training. The
strategy, that is called CURL from Co-trained Unsupervised Representation
Learning, iteratively builds two classifiers on two different views of the
data. The two views correspond to different representations learned from both
labeled and unlabeled data and differ in the fusion scheme used to combine the
image features. To assess the performance of our proposal, we conducted several
experiments on widely used data sets for scene and object recognition. We
considered three scenarios (inductive, transductive and self-taught learning)
that differ in the strategy followed to exploit the unlabeled data. As image
features we considered a combination of GIST, PHOG, and LBP as well as features
extracted from a Convolutional Neural Network. Moreover, two embodiments of
CURL are investigated: one using Ensemble Projection as unsupervised
representation learning coupled with Logistic Regression, and one based on
LapSVM. The results show that CURL clearly outperforms other supervised and
semi-supervised learning methods in the state of the art.
| Simone Bianco, Gianluigi Ciocca, Claudio Cusano | null | 1505.08098 | null | null |
A Critical Review of Recurrent Neural Networks for Sequence Learning | cs.LG cs.NE | Countless learning tasks require dealing with sequential data. Image
captioning, speech synthesis, and music generation all require that a model
produce outputs that are sequences. In other domains, such as time series
prediction, video analysis, and musical information retrieval, a model must
learn from inputs that are sequences. Interactive tasks, such as translating
natural language, engaging in dialogue, and controlling a robot, often demand
both capabilities. Recurrent neural networks (RNNs) are connectionist models
that capture the dynamics of sequences via cycles in the network of nodes.
Unlike standard feedforward neural networks, recurrent networks retain a state
that can represent information from an arbitrarily long context window.
Although recurrent neural networks have traditionally been difficult to train,
and often contain millions of parameters, recent advances in network
architectures, optimization techniques, and parallel computation have enabled
successful large-scale learning with them. In recent years, systems based on
long short-term memory (LSTM) and bidirectional (BRNN) architectures have
demonstrated ground-breaking performance on tasks as varied as image
captioning, language translation, and handwriting recognition. In this survey,
we review and synthesize the research that over the past three decades first
yielded and then made practical these powerful learning models. When
appropriate, we reconcile conflicting notation and nomenclature. Our goal is to
provide a self-contained explication of the state of the art together with a
historical perspective and references to primary research.
| Zachary C. Lipton, John Berkowitz, Charles Elkan | null | 1506.00019 | null | null |
Efficient combination of pairswise feature networks | stat.ML cs.LG | This paper presents a novel method for the reconstruction of a neural network
connectivity using calcium fluorescence data. We introduce a fast unsupervised
method to integrate different networks that reconstructs structural
connectivity from neuron activity. Our method improves the state-of-the-art
reconstruction method General Transfer Entropy (GTE). We are able to better
eliminate indirect links, improving therefore the quality of the network via a
normalization and ensemble process of GTE and three new informative features.
The approach is based on a simple combination of networks, which is remarkably
fast. The performance of our approach is benchmarked on simulated time series
provided at the connectomics challenge and also submitted at the public
competition.
| Pau Bellot, Patrick E. Meyer | null | 1506.00102 | null | null |
Labeled compression schemes for extremal classes | cs.LG cs.DM math.CO | It is a long-standing open problem whether there always exists a compression
scheme whose size is of the order of the Vapnik-Chervonienkis (VC) dimension
$d$. Recently compression schemes of size exponential in $d$ have been found
for any concept class of VC dimension $d$. Previously, compression schemes of
size $d$ have been given for maximum classes, which are special concept classes
whose size equals an upper bound due to Sauer-Shelah. We consider a
generalization of maximum classes called extremal classes. Their definition is
based on a powerful generalization of the Sauer-Shelah bound called the
Sandwich Theorem, which has been studied in several areas of combinatorics and
computer science. The key result of the paper is a construction of a sample
compression scheme for extremal classes of size equal to their VC dimension. We
also give a number of open problems concerning the combinatorial structure of
extremal classes and the existence of unlabeled compression schemes for them.
| Shay Moran and Manfred K. Warmuth | null | 1506.00165 | null | null |
Recurrent Neural Networks with External Memory for Language
Understanding | cs.CL cs.AI cs.LG cs.NE | Recurrent Neural Networks (RNNs) have become increasingly popular for the
task of language understanding. In this task, a semantic tagger is deployed to
associate a semantic label to each word in an input sequence. The success of
RNN may be attributed to its ability to memorize long-term dependence that
relates the current-time semantic label prediction to the observations many
time instances away. However, the memory capacity of simple RNNs is limited
because of the gradient vanishing and exploding problem. We propose to use an
external memory to improve memorization capability of RNNs. We conducted
experiments on the ATIS dataset, and observed that the proposed model was able
to achieve the state-of-the-art results. We compare our proposed model with
alternative models and report analysis results that may provide insights for
future research.
| Baolin Peng and Kaisheng Yao | null | 1506.00195 | null | null |
Parallel Spectral Clustering Algorithm Based on Hadoop | cs.DC cs.DS cs.LG | Spectral clustering and cloud computing is emerging branch of computer
science or related discipline. It overcome the shortcomings of some traditional
clustering algorithm and guarantee the convergence to the optimal solution,
thus have to the widespread attention. This article first introduced the
parallel spectral clustering algorithm research background and significance,
and then to Hadoop the cloud computing Framework has carried on the detailed
introduction, then has carried on the related to spectral clustering is
introduced, then introduces the spectral clustering arithmetic Method of
parallel and relevant steps, finally made the related experiments, and the
experiment are summarized.
| Yajun Cui, Yang Zhao, Kafei Xiao, Chenglong Zhang, Lei Wang | null | 1506.00227 | null | null |
Copeland Dueling Bandits | cs.LG | A version of the dueling bandit problem is addressed in which a Condorcet
winner may not exist. Two algorithms are proposed that instead seek to minimize
regret with respect to the Copeland winner, which, unlike the Condorcet winner,
is guaranteed to exist. The first, Copeland Confidence Bound (CCB), is designed
for small numbers of arms, while the second, Scalable Copeland Bandits (SCB),
works better for large-scale problems. We provide theoretical results bounding
the regret accumulated by CCB and SCB, both substantially improving existing
results. Such existing results either offer bounds of the form $O(K \log T)$
but require restrictive assumptions, or offer bounds of the form $O(K^2 \log
T)$ without requiring such assumptions. Our results offer the best of both
worlds: $O(K \log T)$ bounds without restrictive assumptions.
| Masrour Zoghi, Zohar Karnin, Shimon Whiteson and Maarten de Rijke | null | 1506.00312 | null | null |
Robust PCA: Optimization of the Robust Reconstruction Error over the
Stiefel Manifold | stat.ML cs.LG | It is well known that Principal Component Analysis (PCA) is strongly affected
by outliers and a lot of effort has been put into robustification of PCA. In
this paper we present a new algorithm for robust PCA minimizing the trimmed
reconstruction error. By directly minimizing over the Stiefel manifold, we
avoid deflation as often used by projection pursuit methods. In distinction to
other methods for robust PCA, our method has no free parameter and is
computationally very efficient. We illustrate the performance on various
datasets including an application to background modeling and subtraction. Our
method performs better or similar to current state-of-the-art methods while
being faster.
| Anastasia Podosinnikova, Simon Setzer, and Matthias Hein | null | 1506.00323 | null | null |
Imaging Time-Series to Improve Classification and Imputation | cs.LG cs.NE stat.ML | Inspired by recent successes of deep learning in computer vision, we propose
a novel framework for encoding time series as different types of images,
namely, Gramian Angular Summation/Difference Fields (GASF/GADF) and Markov
Transition Fields (MTF). This enables the use of techniques from computer
vision for time series classification and imputation. We used Tiled
Convolutional Neural Networks (tiled CNNs) on 20 standard datasets to learn
high-level features from the individual and compound GASF-GADF-MTF images. Our
approaches achieve highly competitive results when compared to nine of the
current best time series classification approaches. Inspired by the bijection
property of GASF on 0/1 rescaled data, we train Denoised Auto-encoders (DA) on
the GASF images of four standard and one synthesized compound dataset. The
imputation MSE on test data is reduced by 12.18%-48.02% when compared to using
the raw data. An analysis of the features and weights learned via tiled CNNs
and DAs explains why the approaches work.
| Zhiguang Wang and Tim Oates | null | 1506.00327 | null | null |
Learning to Answer Questions From Image Using Convolutional Neural
Network | cs.CL cs.CV cs.LG cs.NE | In this paper, we propose to employ the convolutional neural network (CNN)
for the image question answering (QA). Our proposed CNN provides an end-to-end
framework with convolutional architectures for learning not only the image and
question representations, but also their inter-modal interactions to produce
the answer. More specifically, our model consists of three CNNs: one image CNN
to encode the image content, one sentence CNN to compose the words of the
question, and one multimodal convolution layer to learn their joint
representation for the classification in the space of candidate answer words.
We demonstrate the efficacy of our proposed model on the DAQUAR and COCO-QA
datasets, which are two benchmark datasets for the image QA, with the
performances significantly outperforming the state-of-the-art.
| Lin Ma, Zhengdong Lu, Hang Li | null | 1506.00333 | null | null |
Learning with hidden variables | q-bio.NC cond-mat.dis-nn cs.LG cs.NE stat.ML | Learning and inferring features that generate sensory input is a task
continuously performed by cortex. In recent years, novel algorithms and
learning rules have been proposed that allow neural network models to learn
such features from natural images, written text, audio signals, etc. These
networks usually involve deep architectures with many layers of hidden neurons.
Here we review recent advancements in this area emphasizing, amongst other
things, the processing of dynamical inputs by networks with hidden nodes and
the role of single neuron models. These points and the questions they arise can
provide conceptual advancements in understanding of learning in the cortex and
the relationship between machine learning approaches to learning with hidden
nodes and those in cortical circuits.
| Yasser Roudi and Graham Taylor | 10.1016/j.conb.2015.07.006 | 1506.00354 | null | null |
Network Topology Identification using PCA and its Graph Theoretic
Interpretations | cs.LG cs.DM cs.SY stat.ME | We solve the problem of identifying (reconstructing) network topology from
steady state network measurements. Concretely, given only a data matrix
$\mathbf{X}$ where the $X_{ij}$ entry corresponds to flow in edge $i$ in
configuration (steady-state) $j$, we wish to find a network structure for which
flow conservation is obeyed at all the nodes. This models many network problems
involving conserved quantities like water, power, and metabolic networks. We
show that identification is equivalent to learning a model $\mathbf{A_n}$ which
captures the approximate linear relationships between the different variables
comprising $\mathbf{X}$ (i.e. of the form $\mathbf{A_n X \approx 0}$) such that
$\mathbf{A_n}$ is full rank (highest possible) and consistent with a network
node-edge incidence structure. The problem is solved through a sequence of
steps like estimating approximate linear relationships using Principal
Component Analysis, obtaining f-cut-sets from these approximate relationships,
and graph realization from f-cut-sets (or equivalently f-circuits). Each step
and the overall process is polynomial time. The method is illustrated by
identifying topology of a water distribution network. We also study the extent
of identifiability from steady-state data.
| Aravind Rajeswaran and Shankar Narasimhan | null | 1506.00438 | null | null |
Classifying Tweet Level Judgements of Rumours in Social Media | cs.SI cs.CL cs.LG | Social media is a rich source of rumours and corresponding community
reactions. Rumours reflect different characteristics, some shared and some
individual. We formulate the problem of classifying tweet level judgements of
rumours as a supervised learning task. Both supervised and unsupervised domain
adaptation are considered, in which tweets from a rumour are classified on the
basis of other annotated rumours. We demonstrate how multi-task learning helps
achieve good results on rumours from the 2011 England riots.
| Michal Lukasik and Trevor Cohn and Kalina Bontcheva | null | 1506.00468 | null | null |
Predicting Deep Zero-Shot Convolutional Neural Networks using Textual
Descriptions | cs.LG cs.CV cs.NE | One of the main challenges in Zero-Shot Learning of visual categories is
gathering semantic attributes to accompany images. Recent work has shown that
learning from textual descriptions, such as Wikipedia articles, avoids the
problem of having to explicitly define these attributes. We present a new model
that can classify unseen categories from their textual description.
Specifically, we use text features to predict the output weights of both the
convolutional and the fully connected layers in a deep convolutional neural
network (CNN). We take advantage of the architecture of CNNs and learn features
at different layers, rather than just learning an embedding space for both
modalities, as is common with existing approaches. The proposed model also
allows us to automatically generate a list of pseudo- attributes for each
visual category consisting of words from Wikipedia articles. We train our
models end-to-end us- ing the Caltech-UCSD bird and flower datasets and
evaluate both ROC and Precision-Recall curves. Our empirical results show that
the proposed model significantly outperforms previous methods.
| Jimmy Ba, Kevin Swersky, Sanja Fidler and Ruslan Salakhutdinov | null | 1506.00511 | null | null |
Coordinate Descent Converges Faster with the Gauss-Southwell Rule Than
Random Selection | math.OC cs.LG stat.CO stat.ML | There has been significant recent work on the theory and application of
randomized coordinate descent algorithms, beginning with the work of Nesterov
[SIAM J. Optim., 22(2), 2012], who showed that a random-coordinate selection
rule achieves the same convergence rate as the Gauss-Southwell selection rule.
This result suggests that we should never use the Gauss-Southwell rule, as it
is typically much more expensive than random selection. However, the empirical
behaviours of these algorithms contradict this theoretical result: in
applications where the computational costs of the selection rules are
comparable, the Gauss-Southwell selection rule tends to perform substantially
better than random coordinate selection. We give a simple analysis of the
Gauss-Southwell rule showing that---except in extreme cases---its convergence
rate is faster than choosing random coordinates. Further, in this work we (i)
show that exact coordinate optimization improves the convergence rate for
certain sparse problems, (ii) propose a Gauss-Southwell-Lipschitz rule that
gives an even faster convergence rate given knowledge of the Lipschitz
constants of the partial derivatives, (iii) analyze the effect of approximate
Gauss-Southwell rules, and (iv) analyze proximal-gradient variants of the
Gauss-Southwell rule.
| Julie Nutini, Mark Schmidt, Issam H. Laradji, Michael Friedlander,
Hoyt Koepke | null | 1506.00552 | null | null |
Blocks and Fuel: Frameworks for deep learning | cs.LG cs.NE stat.ML | We introduce two Python frameworks to train neural networks on large
datasets: Blocks and Fuel. Blocks is based on Theano, a linear algebra compiler
with CUDA-support. It facilitates the training of complex neural network models
by providing parametrized Theano operations, attaching metadata to Theano's
symbolic computational graph, and providing an extensive set of utilities to
assist training the networks, e.g. training algorithms, logging, monitoring,
visualization, and serialization. Fuel provides a standard format for machine
learning datasets. It allows the user to easily iterate over large datasets,
performing many types of pre-processing on the fly.
| Bart van Merri\"enboer, Dzmitry Bahdanau, Vincent Dumoulin, Dmitriy
Serdyuk, David Warde-Farley, Jan Chorowski, Yoshua Bengio | null | 1506.00619 | null | null |
Sample-Optimal Density Estimation in Nearly-Linear Time | cs.DS cs.IT cs.LG math.IT math.ST stat.TH | We design a new, fast algorithm for agnostically learning univariate
probability distributions whose densities are well approximated by piecewise
polynomial functions. Let $f$ be the density function of an arbitrary
univariate distribution, and suppose that $f$ is $\mathrm{OPT}$-close in
$L_1$-distance to an unknown piecewise polynomial function with $t$ interval
pieces and degree $d$. Our algorithm draws $n = O(t(d+1)/\epsilon^2)$ samples
from $f$, runs in time $\tilde{O}(n \cdot \mathrm{poly}(d))$, and with
probability at least $9/10$ outputs an $O(t)$-piecewise degree-$d$ hypothesis
$h$ that is $4 \cdot \mathrm{OPT} +\epsilon$ close to $f$.
Our general algorithm yields (nearly) sample-optimal and nearly-linear time
estimators for a wide range of structured distribution families over both
continuous and discrete domains in a unified way. For most of our applications,
these are the first sample-optimal and nearly-linear time estimators in the
literature. As a consequence, our work resolves the sample and computational
complexities of a broad class of inference tasks via a single "meta-algorithm".
Moreover, we experimentally demonstrate that our algorithm performs very well
in practice.
Our algorithm consists of three "levels": (i) At the top level, we employ an
iterative greedy algorithm for finding a good partition of the real line into
the pieces of a piecewise polynomial. (ii) For each piece, we show that the
sub-problem of finding a good polynomial fit on the current interval can be
solved efficiently with a separation oracle method. (iii) We reduce the task of
finding a separating hyperplane to a combinatorial problem and give an
efficient algorithm for this problem. Combining these three procedures gives a
density estimation algorithm with the claimed guarantees.
| Jayadev Acharya, Ilias Diakonikolas, Jerry Li, Ludwig Schmidt | null | 1506.00671 | null | null |
An objective prior that unifies objective Bayes and information-based
inference | stat.ML cs.LG physics.data-an | There are three principle paradigms of statistical inference: (i) Bayesian,
(ii) information-based and (iii) frequentist inference. We describe an
objective prior (the weighting or $w$-prior) which unifies objective Bayes and
information-based inference. The $w$-prior is chosen to make the marginal
probability an unbiased estimator of the predictive performance of the model.
This definition has several other natural interpretations. From the perspective
of the information content of the prior, the $w$-prior is both uniformly and
maximally uninformative. The $w$-prior can also be understood to result in a
uniform density of distinguishable models in parameter space. Finally we
demonstrate the the $w$-prior is equivalent to the Akaike Information Criterion
(AIC) for regular models in the asymptotic limit. The $w$-prior appears to be
generically applicable to statistical inference and is free of {\it ad hoc}
regularization. The mechanism for suppressing complexity is analogous to AIC:
model complexity reduces model predictivity. We expect this new objective-Bayes
approach to inference to be widely-applicable to machine-learning problems
including singular models.
| Colin H. LaMont and Paul A. Wiggins | null | 1506.00745 | null | null |
Optimal Regret Analysis of Thompson Sampling in Stochastic Multi-armed
Bandit Problem with Multiple Plays | stat.ML cs.LG | We discuss a multiple-play multi-armed bandit (MAB) problem in which several
arms are selected at each round. Recently, Thompson sampling (TS), a randomized
algorithm with a Bayesian spirit, has attracted much attention for its
empirically excellent performance, and it is revealed to have an optimal regret
bound in the standard single-play MAB problem. In this paper, we propose the
multiple-play Thompson sampling (MP-TS) algorithm, an extension of TS to the
multiple-play MAB problem, and discuss its regret analysis. We prove that MP-TS
for binary rewards has the optimal regret upper bound that matches the regret
lower bound provided by Anantharam et al. (1987). Therefore, MP-TS is the first
computationally efficient algorithm with optimal regret. A set of computer
simulations was also conducted, which compared MP-TS with state-of-the-art
algorithms. We also propose a modification of MP-TS, which is shown to have
better empirical performance.
| Junpei Komiyama, Junya Honda, Hiroshi Nakagawa | null | 1506.00779 | null | null |
Learning Speech Rate in Speech Recognition | cs.CL cs.LG | A significant performance reduction is often observed in speech recognition
when the rate of speech (ROS) is too low or too high. Most of present
approaches to addressing the ROS variation focus on the change of speech
signals in dynamic properties caused by ROS, and accordingly modify the dynamic
model, e.g., the transition probabilities of the hidden Markov model (HMM).
However, an abnormal ROS changes not only the dynamic but also the static
property of speech signals, and thus can not be compensated for purely by
modifying the dynamic model. This paper proposes an ROS learning approach based
on deep neural networks (DNN), which involves an ROS feature as the input of
the DNN model and so the spectrum distortion caused by ROS can be learned and
compensated for. The experimental results show that this approach can deliver
better performance for too slow and too fast utterances, demonstrating our
conjecture that ROS impacts both the dynamic and the static property of speech.
In addition, the proposed approach can be combined with the conventional HMM
transition adaptation method, offering additional performance gains.
| Xiangyu Zeng and Shi Yin and Dong Wang | null | 1506.00799 | null | null |
A Generalized Labeled Multi-Bernoulli Filter Implementation using Gibbs
Sampling | stat.CO cs.LG | This paper proposes an efficient implementation of the generalized labeled
multi-Bernoulli (GLMB) filter by combining the prediction and update into a
single step. In contrast to the original approach which involves separate
truncations in the prediction and update steps, the proposed implementation
requires only one single truncation for each iteration, which can be performed
using a standard ranked optimal assignment algorithm. Furthermore, we propose a
new truncation technique based on Markov Chain Monte Carlo methods such as
Gibbs sampling, which drastically reduces the complexity of the filter. The
superior performance of the proposed approach is demonstrated through extensive
numerical studies.
| Hung Gia Hoang and Ba-Tuong Vo and Ba-Ngu Vo | null | 1506.00821 | null | null |
Peer Grading in a Course on Algorithms and Data Structures: Machine
Learning Algorithms do not Improve over Simple Baselines | cs.LG stat.ML | Peer grading is the process of students reviewing each others' work, such as
homework submissions, and has lately become a popular mechanism used in massive
open online courses (MOOCs). Intrigued by this idea, we used it in a course on
algorithms and data structures at the University of Hamburg. Throughout the
whole semester, students repeatedly handed in submissions to exercises, which
were then evaluated both by teaching assistants and by a peer grading
mechanism, yielding a large dataset of teacher and peer grades. We applied
different statistical and machine learning methods to aggregate the peer grades
in order to come up with accurate final grades for the submissions (supervised
and unsupervised, methods based on numeric scores and ordinal rankings).
Surprisingly, none of them improves over the baseline of using the mean peer
grade as the final grade. We discuss a number of possible explanations for
these results and present a thorough analysis of the generated dataset.
| Mehdi S. M. Sajjadi, Morteza Alamgir, Ulrike von Luxburg | null | 1506.00852 | null | null |
Discovering Valuable Items from Massive Data | cs.LG cs.AI cs.IT math.IT | Suppose there is a large collection of items, each with an associated cost
and an inherent utility that is revealed only once we commit to selecting it.
Given a budget on the cumulative cost of the selected items, how can we pick a
subset of maximal value? This task generalizes several important problems such
as multi-arm bandits, active search and the knapsack problem. We present an
algorithm, GP-Select, which utilizes prior knowledge about similarity be- tween
items, expressed as a kernel function. GP-Select uses Gaussian process
prediction to balance exploration (estimating the unknown value of items) and
exploitation (selecting items of high value). We extend GP-Select to be able to
discover sets that simultaneously have high utility and are diverse. Our
preference for diversity can be specified as an arbitrary monotone submodular
function that quantifies the diminishing returns obtained when selecting
similar items. Furthermore, we exploit the structure of the model updates to
achieve an order of magnitude (up to 40X) speedup in our experiments without
resorting to approximations. We provide strong guarantees on the performance of
GP-Select and apply it to three real-world case studies of industrial
relevance: (1) Refreshing a repository of prices in a Global Distribution
System for the travel industry, (2) Identifying diverse, binding-affine
peptides in a vaccine de- sign task and (3) Maximizing clicks in a web-scale
recommender system by recommending items to users.
| Hastagiri P. Vanchinathan, Andreas Marfurt, Charles-Antoine Robelin,
Donald Kossmann, Andreas Krause | null | 1506.00935 | null | null |
Toward a generic representation of random variables for machine learning | cs.LG stat.ML | This paper presents a pre-processing and a distance which improve the
performance of machine learning algorithms working on independent and
identically distributed stochastic processes. We introduce a novel
non-parametric approach to represent random variables which splits apart
dependency and distribution without losing any information. We also propound an
associated metric leveraging this representation and its statistical estimate.
Besides experiments on synthetic datasets, the benefits of our contribution is
illustrated through the example of clustering financial time series, for
instance prices from the credit default swaps market. Results are available on
the website www.datagrapple.com and an IPython Notebook tutorial is available
at www.datagrapple.com/Tech for reproducible research.
| Gautier Marti, Philippe Very and Philippe Donnat | null | 1506.00976 | null | null |
Unsupervised Learning on Neural Network Outputs: with Application in
Zero-shot Learning | cs.LG | The outputs of a trained neural network contain much richer information than
just an one-hot classifier. For example, a neural network might give an image
of a dog the probability of one in a million of being a cat but it is still
much larger than the probability of being a car. To reveal the hidden structure
in them, we apply two unsupervised learning algorithms, PCA and ICA, to the
outputs of a deep Convolutional Neural Network trained on the ImageNet of 1000
classes. The PCA/ICA embedding of the object classes reveals their visual
similarity and the PCA/ICA components can be interpreted as common visual
features shared by similar object classes. For an application, we proposed a
new zero-shot learning method, in which the visual features learned by PCA/ICA
are employed. Our zero-shot learning method achieves the state-of-the-art
results on the ImageNet of over 20000 classes.
| Yao Lu | null | 1506.00990 | null | null |
Combining Two And Three-Way Embeddings Models for Link Prediction in
Knowledge Bases | cs.AI cs.CL cs.LG | This paper tackles the problem of endogenous link prediction for Knowledge
Base completion. Knowledge Bases can be represented as directed graphs whose
nodes correspond to entities and edges to relationships. Previous attempts
either consist of powerful systems with high capacity to model complex
connectivity patterns, which unfortunately usually end up overfitting on rare
relationships, or in approaches that trade capacity for simplicity in order to
fairly model all relationships, frequent or not. In this paper, we propose
Tatec a happy medium obtained by complementing a high-capacity model with a
simpler one, both pre-trained separately and then combined. We present several
variants of this model with different kinds of regularization and combination
strategies and show that this approach outperforms existing methods on
different types of relationships by achieving state-of-the-art results on four
benchmarks of the literature.
| Alberto Garcia-Duran, Antoine Bordes, Nicolas Usunier, Yves Grandvalet | null | 1506.00999 | null | null |
Global and Local Structure Preserving Sparse Subspace Learning: An
Iterative Approach to Unsupervised Feature Selection | cs.LG | As we aim at alleviating the curse of high-dimensionality, subspace learning
is becoming more popular. Existing approaches use either information about
global or local structure of the data, and few studies simultaneously focus on
global and local structures as the both of them contain important information.
In this paper, we propose a global and local structure preserving sparse
subspace learning (GLoSS) model for unsupervised feature selection. The model
can simultaneously realize feature selection and subspace learning. In
addition, we develop a greedy algorithm to establish a generic combinatorial
model, and an iterative strategy based on an accelerated block coordinate
descent is used to solve the GLoSS problem. We also provide whole iterate
sequence convergence analysis of the proposed iterative algorithm. Extensive
experiments are conducted on real-world datasets to show the superiority of the
proposed approach over several state-of-the-art unsupervised feature selection
approaches.
| Nan Zhou, Yangyang Xu, Hong Cheng, Jun Fang, Witold Pedrycz | null | 1506.01060 | null | null |
On bicluster aggregation and its benefits for enumerative solutions | cs.LG | Biclustering involves the simultaneous clustering of objects and their
attributes, thus defining local two-way clustering models. Recently, efficient
algorithms were conceived to enumerate all biclusters in real-valued datasets.
In this case, the solution composes a complete set of maximal and non-redundant
biclusters. However, the ability to enumerate biclusters revealed a challenging
scenario: in noisy datasets, each true bicluster may become highly fragmented
and with a high degree of overlapping. It prevents a direct analysis of the
obtained results. To revert the fragmentation, we propose here two approaches
for properly aggregating the whole set of enumerated biclusters: one based on
single linkage and the other directly exploring the rate of overlapping. Both
proposals were compared with each other and with the actual state-of-the-art in
several experiments, and they not only significantly reduced the number of
biclusters but also consistently increased the quality of the solution.
| Saullo Haniell Galv\~ao de Oliveira, Rosana Veroneze, Fernando Jos\'e
Von Zuben | null | 1506.01077 | null | null |
Multi-View Factorization Machines | cs.LG stat.ML | For a learning task, data can usually be collected from different sources or
be represented from multiple views. For example, laboratory results from
different medical examinations are available for disease diagnosis, and each of
them can only reflect the health state of a person from a particular
aspect/view. Therefore, different views provide complementary information for
learning tasks. An effective integration of the multi-view information is
expected to facilitate the learning performance. In this paper, we propose a
general predictor, named multi-view machines (MVMs), that can effectively
include all the possible interactions between features from multiple views. A
joint factorization is embedded for the full-order interaction parameters which
allows parameter estimation under sparsity. Moreover, MVMs can work in
conjunction with different loss functions for a variety of machine learning
tasks. A stochastic gradient descent method is presented to learn the MVM
model. We further illustrate the advantages of MVMs through comparison with
other methods for multi-view classification, including support vector machines
(SVMs), support tensor machines (STMs) and factorization machines (FMs).
| Bokai Cao, Hucheng Zhou, Guoqiang Li and Philip S. Yu | 10.1145/2835776.2835777 | 1506.01110 | null | null |
Multi-Objective Optimization for Self-Adjusting Weighted Gradient in
Machine Learning Tasks | stat.ML cs.LG | Much of the focus in machine learning research is placed in creating new
architectures and optimization methods, but the overall loss function is seldom
questioned. This paper interprets machine learning from a multi-objective
optimization perspective, showing the limitations of the default linear
combination of loss functions over a data set and introducing the hypervolume
indicator as an alternative. It is shown that the gradient of the hypervolume
is defined by a self-adjusting weighted mean of the individual loss gradients,
making it similar to the gradient of a weighted mean loss but without requiring
the weights to be defined a priori. This enables an inner boosting-like
behavior, where the current model is used to automatically place higher weights
on samples with higher losses but without requiring the use of multiple models.
Results on a denoising autoencoder show that the new formulation is able to
achieve better mean loss than the direct optimization of the mean loss,
providing evidence to the conjecture that self-adjusting the weights creates a
smoother loss surface.
| Conrado Silva Miranda, Fernando Jos\'e Von Zuben | null | 1506.01113 | null | null |
Towards Structured Deep Neural Network for Automatic Speech Recognition | cs.LG | In this paper we propose the Structured Deep Neural Network (Structured DNN)
as a structured and deep learning algorithm, learning to find the best
structured object (such as a label sequence) given a structured input (such as
a vector sequence) by globally considering the mapping relationships between
the structure rather than item by item.
When automatic speech recognition is viewed as a special case of such a
structured learning problem, where we have the acoustic vector sequence as the
input and the phoneme label sequence as the output, it becomes possible to
comprehensively learned utterance by utterance as a whole, rather than frame by
frame.
Structured Support Vector Machine (structured SVM) was proposed to perform
ASR with structured learning previously, but limited by the linear nature of
SVM. Here we propose structured DNN to use nonlinear transformations in
multi-layers as a structured and deep learning algorithm. It was shown to beat
structured SVM in preliminary experiments on TIMIT.
| Yi-Hsiu Liao, Hung-Yi Lee, Lin-shan Lee | null | 1506.01163 | null | null |
Cyclical Learning Rates for Training Neural Networks | cs.CV cs.LG cs.NE | It is known that the learning rate is the most important hyper-parameter to
tune for training deep neural networks. This paper describes a new method for
setting the learning rate, named cyclical learning rates, which practically
eliminates the need to experimentally find the best values and schedule for the
global learning rates. Instead of monotonically decreasing the learning rate,
this method lets the learning rate cyclically vary between reasonable boundary
values. Training with cyclical learning rates instead of fixed values achieves
improved classification accuracy without a need to tune and often in fewer
iterations. This paper also describes a simple way to estimate "reasonable
bounds" -- linearly increasing the learning rate of the network for a few
epochs. In addition, cyclical learning rates are demonstrated on the CIFAR-10
and CIFAR-100 datasets with ResNets, Stochastic Depth networks, and DenseNets,
and the ImageNet dataset with the AlexNet and GoogLeNet architectures. These
are practical tools for everyone who trains neural networks.
| Leslie N. Smith | null | 1506.01186 | null | null |
Personalizing Universal Recurrent Neural Network Language Model with
User Characteristic Features by Social Network Crowdsouring | cs.CL cs.LG | With the popularity of mobile devices, personalized speech recognizer becomes
more realizable today and highly attractive. Each mobile device is primarily
used by a single user, so it's possible to have a personalized recognizer well
matching to the characteristics of individual user. Although acoustic model
personalization has been investigated for decades, much less work have been
reported on personalizing language model, probably because of the difficulties
in collecting enough personalized corpora. Previous work used the corpora
collected from social networks to solve the problem, but constructing a
personalized model for each user is troublesome. In this paper, we propose a
universal recurrent neural network language model with user characteristic
features, so all users share the same model, except each with different user
characteristic features. These user characteristic features can be obtained by
crowdsouring over social networks, which include huge quantity of texts posted
by users with known friend relationships, who may share some subject topics and
wording patterns. The preliminary experiments on Facebook corpus showed that
this proposed approach not only drastically reduced the model perplexity, but
offered very good improvement in recognition accuracy in n-best rescoring
tests. This approach also mitigated the data sparseness problem for
personalized language models.
| Bo-Hsiang Tseng, Hung-Yi Lee, and Lin-Shan Lee | 10.1109/ASRU.2015.7404778 | 1506.01192 | null | null |
Implementation of Training Convolutional Neural Networks | cs.CV cs.LG cs.NE | Deep learning refers to the shining branch of machine learning that is based
on learning levels of representations. Convolutional Neural Networks (CNN) is
one kind of deep neural network. It can study concurrently. In this article, we
gave a detailed analysis of the process of CNN algorithm both the forward
process and back propagation. Then we applied the particular convolutional
neural network to implement the typical face recognition problem by java. Then,
a parallel strategy was proposed in section4. In addition, by measuring the
actual time of forward and backward computing, we analysed the maximal speed up
and parallel efficiency theoretically.
| Tianyi Liu, Shuangsang Fang, Yuehui Zhao, Peng Wang, Jun Zhang | null | 1506.01195 | null | null |
Probabilistic Numerics and Uncertainty in Computations | math.NA cs.AI cs.LG stat.CO stat.ML | We deliver a call to arms for probabilistic numerical methods: algorithms for
numerical tasks, including linear algebra, integration, optimization and
solving differential equations, that return uncertainties in their
calculations. Such uncertainties, arising from the loss of precision induced by
numerical calculation with limited time or hardware, are important for much
contemporary science and industry. Within applications such as climate science
and astrophysics, the need to make decisions on the basis of computations with
large and complex data has led to a renewed focus on the management of
numerical uncertainty. We describe how several seminal classic numerical
methods can be interpreted naturally as probabilistic inference. We then show
that the probabilistic view suggests new algorithms that can flexibly be
adapted to suit application specifics, while delivering improved empirical
performance. We provide concrete illustrations of the benefits of probabilistic
numeric algorithms on real scientific problems from astrometry and astronomical
imaging, while highlighting open problems with these new algorithms. Finally,
we describe how probabilistic numerical methods provide a coherent framework
for identifying the uncertainty in calculations performed with a combination of
numerical algorithms (e.g. both numerical optimisers and differential equation
solvers), potentially allowing the diagnosis (and control) of error sources in
computations.
| Philipp Hennig and Michael A Osborne and Mark Girolami | 10.1098/rspa.2015.0142 | 1506.01326 | null | null |
Unsupervised Feature Analysis with Class Margin Optimization | cs.LG | Unsupervised feature selection has been always attracting research attention
in the communities of machine learning and data mining for decades. In this
paper, we propose an unsupervised feature selection method seeking a feature
coefficient matrix to select the most distinctive features. Specifically, our
proposed algorithm integrates the Maximum Margin Criterion with a
sparsity-based model into a joint framework, where the class margin and feature
correlation are taken into account at the same time. To maximize the total data
separability while preserving minimized within-class scatter simultaneously, we
propose to embed Kmeans into the framework generating pseudo class label
information in a scenario of unsupervised feature selection. Meanwhile, a
sparsity-based model, ` 2 ,p-norm, is imposed to the regularization term to
effectively discover the sparse structures of the feature coefficient matrix.
In this way, noisy and irrelevant features are removed by ruling out those
features whose corresponding coefficients are zeros. To alleviate the local
optimum problem that is caused by random initializations of K-means, a
convergence guaranteed algorithm with an updating strategy for the clustering
indicator matrix, is proposed to iteractively chase the optimal solution.
Performance evaluation is extensively conducted over six benchmark data sets.
From plenty of experimental results, it is demonstrated that our method has
superior performance against all other compared approaches.
| Sen Wang, Feiping Nie, Xiaojun Chang, Lina Yao, Xue Li, Quan Z. Sheng | null | 1506.01330 | null | null |
Optimal change point detection in Gaussian processes | math.ST cs.IT cs.LG math.IT stat.ML stat.TH | We study the problem of detecting a change in the mean of one-dimensional
Gaussian process data. This problem is investigated in the setting of
increasing domain (customarily employed in time series analysis) and in the
setting of fixed domain (typically arising in spatial data analysis). We
propose a detection method based on the generalized likelihood ratio test
(GLRT), and show that our method achieves nearly asymptotically optimal rate in
the minimax sense, in both settings. The salient feature of the proposed method
is that it exploits in an efficient way the data dependence captured by the
Gaussian process covariance structure. When the covariance is not known, we
propose the plug-in GLRT method and derive conditions under which the method
remains asymptotically near optimal. By contrast, the standard CUSUM method,
which does not account for the covariance structure, is shown to be
asymptotically optimal only in the increasing domain. Our algorithms and
accompanying theory are applicable to a wide variety of covariance structures,
including the Matern class, the powered exponential class, and others. The
plug-in GLRT method is shown to perform well for maximum likelihood estimators
with a dense covariance matrix.
| Hossein Keshavarz, Clayton Scott, XuanLong Nguyen | null | 1506.01338 | null | null |
Exploiting an Oracle that Reports AUC Scores in Machine Learning
Contests | cs.LG | In machine learning contests such as the ImageNet Large Scale Visual
Recognition Challenge and the KDD Cup, contestants can submit candidate
solutions and receive from an oracle (typically the organizers of the
competition) the accuracy of their guesses compared to the ground-truth labels.
One of the most commonly used accuracy metrics for binary classification tasks
is the Area Under the Receiver Operating Characteristics Curve (AUC). In this
paper we provide proofs-of-concept of how knowledge of the AUC of a set of
guesses can be used, in two different kinds of attacks, to improve the accuracy
of those guesses. On the other hand, we also demonstrate the intractability of
one kind of AUC exploit by proving that the number of possible binary labelings
of $n$ examples for which a candidate solution obtains a AUC score of $c$ grows
exponentially in $n$, for every $c\in (0,1)$.
| Jacob Whitehill | null | 1506.01339 | null | null |
A Nearly Optimal and Agnostic Algorithm for Properly Learning a Mixture
of k Gaussians, for any Constant k | cs.DS cs.IT cs.LG math.IT math.ST stat.TH | Learning a Gaussian mixture model (GMM) is a fundamental problem in machine
learning, learning theory, and statistics. One notion of learning a GMM is
proper learning: here, the goal is to find a mixture of $k$ Gaussians
$\mathcal{M}$ that is close to the density $f$ of the unknown distribution from
which we draw samples. The distance between $\mathcal{M}$ and $f$ is typically
measured in the total variation or $L_1$-norm.
We give an algorithm for learning a mixture of $k$ univariate Gaussians that
is nearly optimal for any fixed $k$. The sample complexity of our algorithm is
$\tilde{O}(\frac{k}{\epsilon^2})$ and the running time is $(k \cdot
\log\frac{1}{\epsilon})^{O(k^4)} + \tilde{O}(\frac{k}{\epsilon^2})$. It is
well-known that this sample complexity is optimal (up to logarithmic factors),
and it was already achieved by prior work. However, the best known time
complexity for proper learning a $k$-GMM was
$\tilde{O}(\frac{1}{\epsilon^{3k-1}})$. In particular, the dependence between
$\frac{1}{\epsilon}$ and $k$ was exponential. We significantly improve this
dependence by replacing the $\frac{1}{\epsilon}$ term with a $\log
\frac{1}{\epsilon}$ while only increasing the exponent moderately. Hence, for
any fixed $k$, the $\tilde{O} (\frac{k}{\epsilon^2})$ term dominates our
running time, and thus our algorithm runs in time which is nearly-linear in the
number of samples drawn. Achieving a running time of $\textrm{poly}(k,
\frac{1}{\epsilon})$ for proper learning of $k$-GMMs has recently been stated
as an open problem by multiple researchers, and we make progress on this
question.
Moreover, our approach offers an agnostic learning guarantee: our algorithm
returns a good GMM even if the distribution we are sampling from is not a
mixture of Gaussians. To the best of our knowledge, our algorithm is the first
agnostic proper learning algorithm for GMMs.
| Jerry Li, Ludwig Schmidt | null | 1506.01367 | null | null |
Rivalry of Two Families of Algorithms for Memory-Restricted Streaming
PCA | stat.ML cs.LG | We study the problem of recovering the subspace spanned by the first $k$
principal components of $d$-dimensional data under the streaming setting, with
a memory bound of $O(kd)$. Two families of algorithms are known for this
problem. The first family is based on the framework of stochastic gradient
descent. Nevertheless, the convergence rate of the family can be seriously
affected by the learning rate of the descent steps and deserves more serious
study. The second family is based on the power method over blocks of data, but
setting the block size for its existing algorithms is not an easy task. In this
paper, we analyze the convergence rate of a representative algorithm with
decayed learning rate (Oja and Karhunen, 1985) in the first family for the
general $k>1$ case. Moreover, we propose a novel algorithm for the second
family that sets the block sizes automatically and dynamically with faster
convergence rate. We then conduct empirical studies that fairly compare the two
families on real-world data. The studies reveal the advantages and
disadvantages of these two families.
| Chun-Liang Li, Hsuan-Tien Lin, Chi-Jen Lu | null | 1506.01490 | null | null |
An Average Classification Algorithm | stat.ML cs.LG | Many classification algorithms produce a classifier that is a weighted
average of kernel evaluations. When working with a high or infinite dimensional
kernel, it is imperative for speed of evaluation and storage issues that as few
training samples as possible are used in the kernel expansion. Popular existing
approaches focus on altering standard learning algorithms, such as the Support
Vector Machine, to induce sparsity, as well as post-hoc procedures for sparse
approximations. Here we adopt the latter approach. We begin with a very simple
classifier, given by the kernel mean $$ f(x) = \frac{1}{n}
\sum\limits_{i=i}^{n} y_i K(x_i,x) $$ We then find a sparse approximation to
this kernel mean via herding. The result is an accurate, easily parallelized
algorithm for learning classifiers.
| Brendan van Rooyen, Aditya Krishna Menon, Robert C. Williamson | null | 1506.01520 | null | null |
The Preference Learning Toolbox | stat.ML cs.IR cs.LG | Preference learning (PL) is a core area of machine learning that handles
datasets with ordinal relations. As the number of generated data of ordinal
nature is increasing, the importance and role of the PL field becomes central
within machine learning research and practice. This paper introduces an open
source, scalable, efficient and accessible preference learning toolbox that
supports the key phases of the data training process incorporating various
popular data preprocessing, feature selection and preference learning methods.
| Vincent E. Farrugia, H\'ector P. Mart\'inez, Georgios N. Yannakakis | null | 1506.01709 | null | null |
Spectral Learning of Large Structured HMMs for Comparative Epigenomics | stat.ML cs.LG math.ST q-bio.GN stat.TH | We develop a latent variable model and an efficient spectral algorithm
motivated by the recent emergence of very large data sets of chromatin marks
from multiple human cell types. A natural model for chromatin data in one cell
type is a Hidden Markov Model (HMM); we model the relationship between multiple
cell types by connecting their hidden states by a fixed tree of known
structure. The main challenge with learning parameters of such models is that
iterative methods such as EM are very slow, while naive spectral methods result
in time and space complexity exponential in the number of cell types. We
exploit properties of the tree structure of the hidden states to provide
spectral algorithms that are more computationally efficient for current
biological datasets. We provide sample complexity bounds for our algorithm and
evaluate it experimentally on biological data from nine human cell types.
Finally, we show that beyond our specific model, some of our algorithmic ideas
can be applied to other graphical models.
| Chicheng Zhang, Jimin Song, Kevin C Chen, Kamalika Chaudhuri | null | 1506.01744 | null | null |
Semidefinite and Spectral Relaxations for Multi-Label Classification | cs.LG | In this paper, we address the problem of multi-label classification. We
consider linear classifiers and propose to learn a prior over the space of
labels to directly leverage the performance of such methods. This prior takes
the form of a quadratic function of the labels and permits to encode both
attractive and repulsive relations between labels. We cast this problem as a
structured prediction one aiming at optimizing either the accuracies of the
predictors or the F 1-score. This leads to an optimization problem closely
related to the max-cut problem, which naturally leads to semidefinite and
spectral relaxations. We show on standard datasets how such a general prior can
improve the performances of multi-label techniques.
| R\'emi Lajugie (SIERRA, DI-ENS), Piotr Bojanowski (WILLOW, DI-ENS),
Sylvain Arlot (SIERRA, DI-ENS), Francis Bach (SIERRA, DI-ENS) | null | 1506.01829 | null | null |
Communication Complexity of Distributed Convex Learning and Optimization | cs.LG math.OC stat.ML | We study the fundamental limits to communication-efficient distributed
methods for convex learning and optimization, under different assumptions on
the information available to individual machines, and the types of functions
considered. We identify cases where existing algorithms are already worst-case
optimal, as well as cases where room for further improvement is still possible.
Among other things, our results indicate that without similarity between the
local objective functions (due to statistical data similarity or otherwise)
many communication rounds may be required, even if the machines have unbounded
computational power.
| Yossi Arjevani and Ohad Shamir | null | 1506.01900 | null | null |
Beyond Temporal Pooling: Recurrence and Temporal Convolutions for
Gesture Recognition in Video | cs.CV cs.AI cs.LG cs.NE stat.ML | Recent studies have demonstrated the power of recurrent neural networks for
machine translation, image captioning and speech recognition. For the task of
capturing temporal structure in video, however, there still remain numerous
open research questions. Current research suggests using a simple temporal
feature pooling strategy to take into account the temporal aspect of video. We
demonstrate that this method is not sufficient for gesture recognition, where
temporal information is more discriminative compared to general video
classification tasks. We explore deep architectures for gesture recognition in
video and propose a new end-to-end trainable neural network architecture
incorporating temporal convolutions and bidirectional recurrence. Our main
contributions are twofold; first, we show that recurrence is crucial for this
task; second, we show that adding temporal convolutions leads to significant
improvements. We evaluate the different approaches on the Montalbano gesture
recognition dataset, where we achieve state-of-the-art results.
| Lionel Pigou, A\"aron van den Oord, Sander Dieleman, Mieke Van
Herreweghe, Joni Dambre | null | 1506.01911 | null | null |
Improved SVRG for Non-Strongly-Convex or Sum-of-Non-Convex Objectives | cs.LG cs.DS math.OC stat.ML | Many classical algorithms are found until several years later to outlive the
confines in which they were conceived, and continue to be relevant in
unforeseen settings. In this paper, we show that SVRG is one such method: being
originally designed for strongly convex objectives, it is also very robust in
non-strongly convex or sum-of-non-convex settings.
More precisely, we provide new analysis to improve the state-of-the-art
running times in both settings by either applying SVRG or its novel variant.
Since non-strongly convex objectives include important examples such as Lasso
or logistic regression, and sum-of-non-convex objectives include famous
examples such as stochastic PCA and is even believed to be related to training
deep neural nets, our results also imply better performances in these
applications.
| Zeyuan Allen-Zhu, Yang Yuan | null | 1506.01972 | null | null |
Large-scale Simple Question Answering with Memory Networks | cs.LG cs.CL | Training large-scale question answering systems is complicated because
training sources usually cover a small portion of the range of possible
questions. This paper studies the impact of multitask and transfer learning for
simple question answering; a setting for which the reasoning required to answer
is quite easy, as long as one can retrieve the correct evidence given a
question, which can be difficult in large-scale conditions. To this end, we
introduce a new dataset of 100k questions that we use in conjunction with
existing benchmarks. We conduct our study within the framework of Memory
Networks (Weston et al., 2015) because this perspective allows us to eventually
scale up to more complex reasoning, and show that Memory Networks can be
successfully trained to achieve excellent performance.
| Antoine Bordes, Nicolas Usunier, Sumit Chopra, Jason Weston | null | 1506.02075 | null | null |
Visualizing and Understanding Recurrent Networks | cs.LG cs.CL cs.NE | Recurrent Neural Networks (RNNs), and specifically a variant with Long
Short-Term Memory (LSTM), are enjoying renewed interest as a result of
successful applications in a wide range of machine learning problems that
involve sequential data. However, while LSTMs provide exceptional results in
practice, the source of their performance and their limitations remain rather
poorly understood. Using character-level language models as an interpretable
testbed, we aim to bridge this gap by providing an analysis of their
representations, predictions and error types. In particular, our experiments
reveal the existence of interpretable cells that keep track of long-range
dependencies such as line lengths, quotes and brackets. Moreover, our
comparative analysis with finite horizon n-gram models traces the source of the
LSTM improvements to long-range structural dependencies. Finally, we provide
analysis of the remaining errors and suggests areas for further study.
| Andrej Karpathy, Justin Johnson, Li Fei-Fei | null | 1506.02078 | null | null |
Local Nonstationarity for Efficient Bayesian Optimization | cs.LG stat.ML | Bayesian optimization has shown to be a fundamental global optimization
algorithm in many applications: ranging from automatic machine learning,
robotics, reinforcement learning, experimental design, simulations, etc. The
most popular and effective Bayesian optimization relies on a surrogate model in
the form of a Gaussian process due to its flexibility to represent a prior over
function. However, many algorithms and setups relies on the stationarity
assumption of the Gaussian process. In this paper, we present a novel
nonstationary strategy for Bayesian optimization that is able to outperform the
state of the art in Bayesian optimization both in stationary and nonstationary
problems.
| Ruben Martinez-Cantin | null | 1506.02080 | null | null |
Gene selection for cancer classification using a hybrid of univariate
and multivariate feature selection methods | q-bio.QM cs.CE cs.LG stat.ML | Various approaches to gene selection for cancer classification based on
microarray data can be found in the literature and they may be grouped into two
categories: univariate methods and multivariate methods. Univariate methods
look at each gene in the data in isolation from others. They measure the
contribution of a particular gene to the classification without considering the
presence of the other genes. In contrast, multivariate methods measure the
relative contribution of a gene to the classification by taking the other genes
in the data into consideration. Multivariate methods select fewer genes in
general. However, the selection process of multivariate methods may be
sensitive to the presence of irrelevant genes, noises in the expression and
outliers in the training data. At the same time, the computational cost of
multivariate methods is high. To overcome the disadvantages of the two types of
approaches, we propose a hybrid method to obtain gene sets that are small and
highly discriminative.
We devise our hybrid method from the univariate Maximum Likelihood method
(LIK) and the multivariate Recursive Feature Elimination method (RFE). We
analyze the properties of these methods and systematically test the
effectiveness of our proposed method on two cancer microarray datasets. Our
experiments on a leukemia dataset and a small, round blue cell tumors dataset
demonstrate the effectiveness of our hybrid method. It is able to discover sets
consisting of fewer genes than those reported in the literature and at the same
time achieve the same or better prediction accuracy.
| Min Xu, Rudy Setiono | null | 1506.02085 | null | null |
Global Gene Expression Analysis Using Machine Learning Methods | q-bio.QM cs.CE cs.LG stat.ML | Microarray is a technology to quantitatively monitor the expression of large
number of genes in parallel. It has become one of the main tools for global
gene expression analysis in molecular biology research in recent years. The
large amount of expression data generated by this technology makes the study of
certain complex biological problems possible and machine learning methods are
playing a crucial role in the analysis process. At present, many machine
learning methods have been or have the potential to be applied to major areas
of gene expression analysis. These areas include clustering, classification,
dynamic modeling and reverse engineering.
In this thesis, we focus our work on using machine learning methods to solve
the classification problems arising from microarray data. We first identify the
major types of the classification problems; then apply several machine learning
methods to solve the problems and perform systematic tests on real and
artificial datasets. We propose improvement to existing methods. Specifically,
we develop a multivariate and a hybrid feature selection method to obtain high
classification performance for high dimension classification problems. Using
the hybrid feature selection method, we are able to identify small sets of
features that give predictive accuracy that is as good as that from other
methods which require many more features.
| Min Xu | null | 1506.02087 | null | null |
Data-Driven Learning of the Number of States in Multi-State
Autoregressive Models | stat.ML cs.LG | In this work, we consider the class of multi-state autoregressive processes
that can be used to model non-stationary time-series of interest. In order to
capture different autoregressive (AR) states underlying an observed time
series, it is crucial to select the appropriate number of states. We propose a
new model selection technique based on the Gap statistics, which uses a null
reference distribution on the stable AR filters to check whether adding a new
AR state significantly improves the performance of the model. To that end, we
define a new distance measure between AR filters based on mean squared
prediction error (MSPE), and propose an efficient method to generate random
stable filters that are uniformly distributed in the coefficient space.
Numerical results are provided to evaluate the performance of the proposed
approach.
| Jie Ding, Mohammad Noshad, and Vahid Tarokh | null | 1506.02107 | null | null |
Deeply Learning the Messages in Message Passing Inference | cs.CV cs.LG stat.ML | Deep structured output learning shows great promise in tasks like semantic
image segmentation. We proffer a new, efficient deep structured model learning
scheme, in which we show how deep Convolutional Neural Networks (CNNs) can be
used to estimate the messages in message passing inference for structured
prediction with Conditional Random Fields (CRFs). With such CNN message
estimators, we obviate the need to learn or evaluate potential functions for
message calculation. This confers significant efficiency for learning, since
otherwise when performing structured learning for a CRF with CNN potentials it
is necessary to undertake expensive inference for every stochastic gradient
iteration. The network output dimension for message estimation is the same as
the number of classes, in contrast to the network output for general CNN
potential functions in CRFs, which is exponential in the order of the
potentials. Hence CNN message learning has fewer network parameters and is more
scalable for cases that a large number of classes are involved. We apply our
method to semantic image segmentation on the PASCAL VOC 2012 dataset. We
achieve an intersection-over-union score of 73.4 on its test set, which is the
best reported result for methods using the VOC training images alone. This
impressive performance demonstrates the effectiveness and usefulness of our CNN
message learning method.
| Guosheng Lin, Chunhua Shen, Ian Reid, Anton van den Hengel | null | 1506.02108 | null | null |
Selective Greedy Equivalence Search: Finding Optimal Bayesian Networks
Using a Polynomial Number of Score Evaluations | cs.LG cs.AI | We introduce Selective Greedy Equivalence Search (SGES), a restricted version
of Greedy Equivalence Search (GES). SGES retains the asymptotic correctness of
GES but, unlike GES, has polynomial performance guarantees. In particular, we
show that when data are sampled independently from a distribution that is
perfect with respect to a DAG ${\cal G}$ defined over the observable variables
then, in the limit of large data, SGES will identify ${\cal G}$'s equivalence
class after a number of score evaluations that is (1) polynomial in the number
of nodes and (2) exponential in various complexity measures including
maximum-number-of-parents, maximum-clique-size, and a new measure called {\em
v-width} that is at least as small as---and potentially much smaller than---the
other two. More generally, we show that for any hereditary and
equivalence-invariant property $\Pi$ known to hold in ${\cal G}$, we retain the
large-sample optimality guarantees of GES even if we ignore any GES deletion
operator during the backward phase that results in a state for which $\Pi$ does
not hold in the common-descendants subgraph.
| David Maxwell Chickering and Christopher Meek | null | 1506.02113 | null | null |
Learning Multiple Tasks with Multilinear Relationship Networks | cs.LG | Deep networks trained on large-scale data can learn transferable features to
promote learning multiple tasks. Since deep features eventually transition from
general to specific along deep networks, a fundamental problem of multi-task
learning is how to exploit the task relatedness underlying parameter tensors
and improve feature transferability in the multiple task-specific layers. This
paper presents Multilinear Relationship Networks (MRN) that discover the task
relationships based on novel tensor normal priors over parameter tensors of
multiple task-specific layers in deep convolutional networks. By jointly
learning transferable features and multilinear relationships of tasks and
features, MRN is able to alleviate the dilemma of negative-transfer in the
feature layers and under-transfer in the classifier layer. Experiments show
that MRN yields state-of-the-art results on three multi-task learning datasets.
| Mingsheng Long, Zhangjie Cao, Jianmin Wang, Philip S. Yu | null | 1506.02117 | null | null |
Dropout as a Bayesian Approximation: Representing Model Uncertainty in
Deep Learning | stat.ML cs.LG | Deep learning tools have gained tremendous attention in applied machine
learning. However such tools for regression and classification do not capture
model uncertainty. In comparison, Bayesian models offer a mathematically
grounded framework to reason about model uncertainty, but usually come with a
prohibitive computational cost. In this paper we develop a new theoretical
framework casting dropout training in deep neural networks (NNs) as approximate
Bayesian inference in deep Gaussian processes. A direct result of this theory
gives us tools to model uncertainty with dropout NNs -- extracting information
from existing models that has been thrown away so far. This mitigates the
problem of representing uncertainty in deep learning without sacrificing either
computational complexity or test accuracy. We perform an extensive study of the
properties of dropout's uncertainty. Various network architectures and
non-linearities are assessed on tasks of regression and classification, using
MNIST as an example. We show a considerable improvement in predictive
log-likelihood and RMSE compared to existing state-of-the-art methods, and
finish by using dropout's uncertainty in deep reinforcement learning.
| Yarin Gal, Zoubin Ghahramani | null | 1506.02142 | null | null |
Optimal Rates for Random Fourier Features | math.ST cs.LG math.FA stat.ML stat.TH | Kernel methods represent one of the most powerful tools in machine learning
to tackle problems expressed in terms of function values and derivatives due to
their capability to represent and model complex relations. While these methods
show good versatility, they are computationally intensive and have poor
scalability to large data as they require operations on Gram matrices. In order
to mitigate this serious computational limitation, recently randomized
constructions have been proposed in the literature, which allow the application
of fast linear algorithms. Random Fourier features (RFF) are among the most
popular and widely applied constructions: they provide an easily computable,
low-dimensional feature representation for shift-invariant kernels. Despite the
popularity of RFFs, very little is understood theoretically about their
approximation quality. In this paper, we provide a detailed finite-sample
theoretical analysis about the approximation quality of RFFs by (i)
establishing optimal (in terms of the RFF dimension, and growing set size)
performance guarantees in uniform norm, and (ii) presenting guarantees in $L^r$
($1\le r<\infty$) norms. We also propose an RFF approximation to derivatives of
a kernel with a theoretical study on its approximation quality.
| Bharath K. Sriperumbudur and Zoltan Szabo | null | 1506.02155 | null | null |
Bayesian Convolutional Neural Networks with Bernoulli Approximate
Variational Inference | stat.ML cs.LG | Convolutional neural networks (CNNs) work well on large datasets. But
labelled data is hard to collect, and in some applications larger amounts of
data are not available. The problem then is how to use CNNs with small data --
as CNNs overfit quickly. We present an efficient Bayesian CNN, offering better
robustness to over-fitting on small data than traditional approaches. This is
by placing a probability distribution over the CNN's kernels. We approximate
our model's intractable posterior with Bernoulli variational distributions,
requiring no additional model parameters.
On the theoretical side, we cast dropout network training as approximate
inference in Bayesian neural networks. This allows us to implement our model
using existing tools in deep learning with no increase in time complexity,
while highlighting a negative result in the field. We show a considerable
improvement in classification accuracy compared to standard techniques and
improve on published state-of-the-art results for CIFAR-10.
| Yarin Gal, Zoubin Ghahramani | null | 1506.02158 | null | null |
Riemannian preconditioning for tensor completion | cs.NA cs.LG math.OC | We propose a novel Riemannian preconditioning approach for the tensor
completion problem with rank constraint. A Riemannian metric or inner product
is proposed that exploits the least-squares structure of the cost function and
takes into account the structured symmetry in Tucker decomposition. The
specific metric allows to use the versatile framework of Riemannian
optimization on quotient manifolds to develop a preconditioned nonlinear
conjugate gradient algorithm for the problem. To this end, concrete matrix
representations of various optimization-related ingredients are listed.
Numerical comparisons suggest that our proposed algorithm robustly outperforms
state-of-the-art algorithms across different problem instances encompassing
various synthetic and real-world datasets.
| Hiroyuki Kasai and Bamdev Mishra | null | 1506.02159 | null | null |
Learning from Rational Behavior: Predicting Solutions to Unknown Linear
Programs | cs.DS cs.GT cs.LG | We define and study the problem of predicting the solution to a linear
program (LP) given only partial information about its objective and
constraints. This generalizes the problem of learning to predict the purchasing
behavior of a rational agent who has an unknown objective function, that has
been studied under the name "Learning from Revealed Preferences". We give
mistake bound learning algorithms in two settings: in the first, the objective
of the LP is known to the learner but there is an arbitrary, fixed set of
constraints which are unknown. Each example is defined by an additional known
constraint and the goal of the learner is to predict the optimal solution of
the LP given the union of the known and unknown constraints. This models the
problem of predicting the behavior of a rational agent whose goals are known,
but whose resources are unknown. In the second setting, the objective of the LP
is unknown, and changing in a controlled way. The constraints of the LP may
also change every day, but are known. An example is given by a set of
constraints and partial information about the objective, and the task of the
learner is again to predict the optimal solution of the partially known LP.
| Shahin Jabbari, Ryan Rogers, Aaron Roth, Zhiwei Steven Wu | null | 1506.02162 | null | null |
Thresholding for Top-k Recommendation with Temporal Dynamics | cs.IR cs.LG | This work focuses on top-k recommendation in domains where underlying data
distribution shifts overtime. We propose to learn a time-dependent bias for
each item over whatever existing recommendation engine. Such a bias learning
process alleviates data sparsity in constructing the engine, and at the same
time captures recent trend shift observed in data. We present an alternating
optimization framework to resolve the bias learning problem, and develop
methods to handle a variety of commonly used recommendation evaluation
criteria, as well as large number of items and users in practice. The proposed
algorithm is examined, both offline and online, using real world data sets
collected from the largest retailer worldwide. Empirical results demonstrate
that the bias learning can almost always boost recommendation performance. We
encourage other practitioners to adopt it as a standard component in
recommender systems where temporal dynamics is a norm.
| Lei Tang | null | 1506.02190 | null | null |
A Recurrent Latent Variable Model for Sequential Data | cs.LG | In this paper, we explore the inclusion of latent random variables into the
dynamic hidden state of a recurrent neural network (RNN) by combining elements
of the variational autoencoder. We argue that through the use of high-level
latent random variables, the variational RNN (VRNN)1 can model the kind of
variability observed in highly structured sequential data such as natural
speech. We empirically evaluate the proposed model against related sequential
models on four speech datasets and one handwriting dataset. Our results show
the important roles that latent random variables can play in the RNN dynamic
hidden state.
| Junyoung Chung, Kyle Kastner, Laurent Dinh, Kratarth Goel, Aaron
Courville, Yoshua Bengio | null | 1506.02216 | null | null |
No penalty no tears: Least squares in high-dimensional linear models | stat.ME cs.LG math.ST stat.ML stat.TH | Ordinary least squares (OLS) is the default method for fitting linear models,
but is not applicable for problems with dimensionality larger than the sample
size. For these problems, we advocate the use of a generalized version of OLS
motivated by ridge regression, and propose two novel three-step algorithms
involving least squares fitting and hard thresholding. The algorithms are
methodologically simple to understand intuitively, computationally easy to
implement efficiently, and theoretically appealing for choosing models
consistently. Numerical exercises comparing our methods with penalization-based
approaches in simulations and data analyses illustrate the great potential of
the proposed algorithms.
| Xiangyu Wang, David Dunson and Chenlei Leng | null | 1506.02222 | null | null |
Primal Method for ERM with Flexible Mini-batching Schemes and Non-convex
Losses | math.OC cs.DS cs.LG stat.ML | In this work we develop a new algorithm for regularized empirical risk
minimization. Our method extends recent techniques of Shalev-Shwartz [02/2015],
which enable a dual-free analysis of SDCA, to arbitrary mini-batching schemes.
Moreover, our method is able to better utilize the information in the data
defining the ERM problem. For convex loss functions, our complexity results
match those of QUARTZ, which is a primal-dual method also allowing for
arbitrary mini-batching schemes. The advantage of a dual-free analysis comes
from the fact that it guarantees convergence even for non-convex loss
functions, as long as the average loss is convex. We illustrate through
experiments the utility of being able to design arbitrary mini-batching
schemes.
| Dominik Csiba and Peter Richt\'arik | null | 1506.02227 | null | null |
Knowledge Transfer Pre-training | cs.LG cs.NE stat.ML | Pre-training is crucial for learning deep neural networks. Most of existing
pre-training methods train simple models (e.g., restricted Boltzmann machines)
and then stack them layer by layer to form the deep structure. This layer-wise
pre-training has found strong theoretical foundation and broad empirical
support. However, it is not easy to employ such method to pre-train models
without a clear multi-layer structure,e.g., recurrent neural networks (RNNs).
This paper presents a new pre-training approach based on knowledge transfer
learning. In contrast to the layer-wise approach which trains model components
incrementally, the new approach trains the entire model as a whole but with an
easier objective function. This is achieved by utilizing soft targets produced
by a prior trained model (teacher model). Compared to the conventional
layer-wise methods, this new method does not care about the model structure, so
can be used to pre-train very complex models. Experiments on a speech
recognition task demonstrated that with this approach, complex RNNs can be well
trained with a weaker deep neural network (DNN) model. Furthermore, the new
method can be combined with conventional layer-wise pre-training to deliver
additional gains.
| Zhiyuan Tang, Dong Wang, Yiqiao Pan, Zhiyong Zhang | null | 1506.02256 | null | null |
Visual Learning of Arithmetic Operations | cs.LG cs.AI cs.CV | A simple Neural Network model is presented for end-to-end visual learning of
arithmetic operations from pictures of numbers. The input consists of two
pictures, each showing a 7-digit number. The output, also a picture, displays
the number showing the result of an arithmetic operation (e.g., addition or
subtraction) on the two input numbers. The concepts of a number, or of an
operator, are not explicitly introduced. This indicates that addition is a
simple cognitive task, which can be learned visually using a very small number
of neurons.
Other operations, e.g., multiplication, were not learnable using this
architecture. Some tasks were not learnable end-to-end (e.g., addition with
Roman numerals), but were easily learnable once broken into two separate
sub-tasks: a perceptual \textit{Character Recognition} and cognitive
\textit{Arithmetic} sub-tasks. This indicates that while some tasks may be
easily learnable end-to-end, other may need to be broken into sub-tasks.
| Yedid Hoshen, Shmuel Peleg | null | 1506.02264 | null | null |
A Framework for Constrained and Adaptive Behavior-Based Agents | cs.AI cs.LG cs.RO cs.SY | Behavior Trees are commonly used to model agents for robotics and games,
where constrained behaviors must be designed by human experts in order to
guarantee that these agents will execute a specific chain of actions given a
specific set of perceptions. In such application areas, learning is a desirable
feature to provide agents with the ability to adapt and improve interactions
with humans and environment, but often discarded due to its unreliability. In
this paper, we propose a framework that uses Reinforcement Learning nodes as
part of Behavior Trees to address the problem of adding learning capabilities
in constrained agents. We show how this framework relates to Options in
Hierarchical Reinforcement Learning, ensuring convergence of nested learning
nodes, and we empirically show that the learning nodes do not affect the
execution of other nodes in the tree.
| Renato de Pontes Pereira and Paulo Martins Engel | null | 1506.02312 | null | null |
A Multi-layered Acoustic Tokenizing Deep Neural Network (MAT-DNN) for
Unsupervised Discovery of Linguistic Units and Generation of High Quality
Features | cs.CL cs.LG cs.NE | This paper summarizes the work done by the authors for the Zero Resource
Speech Challenge organized in the technical program of Interspeech 2015. The
goal of the challenge is to discover linguistic units directly from unlabeled
speech data. The Multi-layered Acoustic Tokenizer (MAT) proposed in this work
automatically discovers multiple sets of acoustic tokens from the given corpus.
Each acoustic token set is specified by a set of hyperparameters that describe
the model configuration. These sets of acoustic tokens carry different
characteristics of the given corpus and the language behind thus can be
mutually reinforced. The multiple sets of token labels are then used as the
targets of a Multi-target DNN (MDNN) trained on low-level acoustic features.
Bottleneck features extracted from the MDNN are used as feedback for the MAT
and the MDNN itself. We call this iterative system the Multi-layered Acoustic
Tokenizing Deep Neural Network (MAT-DNN) which generates high quality features
for track 1 of the challenge and acoustic tokens for track 2 of the challenge.
| Cheng-Tao Chung, Cheng-Yu Tsai, Hsiang-Hung Lu, Yuan-ming Liou,
Yen-Chen Wu, Yen-Ju Lu, Hung-yi Lee and Lin-shan Lee | null | 1506.02327 | null | null |
Stay on path: PCA along graph paths | stat.ML cs.IT cs.LG math.IT math.OC | We introduce a variant of (sparse) PCA in which the set of feasible support
sets is determined by a graph. In particular, we consider the following
setting: given a directed acyclic graph $G$ on $p$ vertices corresponding to
variables, the non-zero entries of the extracted principal component must
coincide with vertices lying along a path in $G$.
From a statistical perspective, information on the underlying network may
potentially reduce the number of observations required to recover the
population principal component. We consider the canonical estimator which
optimally exploits the prior knowledge by solving a non-convex quadratic
maximization on the empirical covariance. We introduce a simple network and
analyze the estimator under the spiked covariance model. We show that side
information potentially improves the statistical complexity.
We propose two algorithms to approximate the solution of the constrained
quadratic maximization, and recover a component with the desired properties. We
empirically evaluate our schemes on synthetic and real datasets.
| Megasthenis Asteris, Anastasios Kyrillidis, Alexandros G. Dimakis,
Han-Gyol Yi and, Bharath Chandrasekaran | null | 1506.02344 | null | null |
Convergence Rates of Active Learning for Maximum Likelihood Estimation | cs.LG stat.ML | An active learner is given a class of models, a large set of unlabeled
examples, and the ability to interactively query labels of a subset of these
examples; the goal of the learner is to learn a model in the class that fits
the data well.
Previous theoretical work has rigorously characterized label complexity of
active learning, but most of this work has focused on the PAC or the agnostic
PAC model. In this paper, we shift our attention to a more general setting --
maximum likelihood estimation. Provided certain conditions hold on the model
class, we provide a two-stage active learning algorithm for this problem. The
conditions we require are fairly general, and cover the widely popular class of
Generalized Linear Models, which in turn, include models for binary and
multi-class classification, regression, and conditional random fields.
We provide an upper bound on the label requirement of our algorithm, and a
lower bound that matches it up to lower order terms. Our analysis shows that
unlike binary classification in the realizable case, just a single extra round
of interaction is sufficient to achieve near-optimal performance in maximum
likelihood estimation. On the empirical side, the recent work in
~\cite{Zhang12} and~\cite{Zhang14} (on active linear and logistic regression)
shows the promise of this approach.
| Kamalika Chaudhuri and Sham Kakade and Praneeth Netrapalli and Sujay
Sanghavi | null | 1506.02348 | null | null |
Stacked What-Where Auto-encoders | stat.ML cs.LG cs.NE | We present a novel architecture, the "stacked what-where auto-encoders"
(SWWAE), which integrates discriminative and generative pathways and provides a
unified approach to supervised, semi-supervised and unsupervised learning
without relying on sampling during training. An instantiation of SWWAE uses a
convolutional net (Convnet) (LeCun et al. (1998)) to encode the input, and
employs a deconvolutional net (Deconvnet) (Zeiler et al. (2010)) to produce the
reconstruction. The objective function includes reconstruction terms that
induce the hidden states in the Deconvnet to be similar to those of the
Convnet. Each pooling layer produces two sets of variables: the "what" which
are fed to the next layer, and its complementary variable "where" that are fed
to the corresponding layer in the generative decoder.
| Junbo Zhao, Michael Mathieu, Ross Goroshin, Yann LeCun | null | 1506.02351 | null | null |
Robust Regression via Hard Thresholding | cs.LG stat.ML | We study the problem of Robust Least Squares Regression (RLSR) where several
response variables can be adversarially corrupted. More specifically, for a
data matrix X \in R^{p x n} and an underlying model w*, the response vector is
generated as y = X'w* + b where b \in R^n is the corruption vector supported
over at most C.n coordinates. Existing exact recovery results for RLSR focus
solely on L1-penalty based convex formulations and impose relatively strict
model assumptions such as requiring the corruptions b to be selected
independently of X.
In this work, we study a simple hard-thresholding algorithm called TORRENT
which, under mild conditions on X, can recover w* exactly even if b corrupts
the response variables in an adversarial manner, i.e. both the support and
entries of b are selected adversarially after observing X and w*. Our results
hold under deterministic assumptions which are satisfied if X is sampled from
any sub-Gaussian distribution. Finally unlike existing results that apply only
to a fixed w*, generated independently of X, our results are universal and hold
for any w* \in R^p.
Next, we propose gradient descent-based extensions of TORRENT that can scale
efficiently to large scale problems, such as high dimensional sparse recovery
and prove similar recovery guarantees for these extensions. Empirically we find
TORRENT, and more so its extensions, offering significantly faster recovery
than the state-of-the-art L1 solvers. For instance, even on moderate-sized
datasets (with p = 50K) with around 40% corrupted responses, a variant of our
proposed method called TORRENT-HYB is more than 20x faster than the best L1
solver.
| Kush Bhatia and Prateek Jain and Purushottam Kar | null | 1506.02428 | null | null |
High-Dimensional Continuous Control Using Generalized Advantage
Estimation | cs.LG cs.RO cs.SY | Policy gradient methods are an appealing approach in reinforcement learning
because they directly optimize the cumulative reward and can straightforwardly
be used with nonlinear function approximators such as neural networks. The two
main challenges are the large number of samples typically required, and the
difficulty of obtaining stable and steady improvement despite the
nonstationarity of the incoming data. We address the first challenge by using
value functions to substantially reduce the variance of policy gradient
estimates at the cost of some bias, with an exponentially-weighted estimator of
the advantage function that is analogous to TD(lambda). We address the second
challenge by using trust region optimization procedure for both the policy and
the value function, which are represented by neural networks.
Our approach yields strong empirical results on highly challenging 3D
locomotion tasks, learning running gaits for bipedal and quadrupedal simulated
robots, and learning a policy for getting the biped to stand up from starting
out lying on the ground. In contrast to a body of prior work that uses
hand-crafted policy representations, our neural network policies map directly
from raw kinematics to joint torques. Our algorithm is fully model-free, and
the amount of simulated experience required for the learning tasks on 3D bipeds
corresponds to 1-2 weeks of real time.
| John Schulman, Philipp Moritz, Sergey Levine, Michael Jordan, Pieter
Abbeel | null | 1506.02438 | null | null |
ASlib: A Benchmark Library for Algorithm Selection | cs.AI cs.LG | The task of algorithm selection involves choosing an algorithm from a set of
algorithms on a per-instance basis in order to exploit the varying performance
of algorithms over a set of instances. The algorithm selection problem is
attracting increasing attention from researchers and practitioners in AI. Years
of fruitful applications in a number of domains have resulted in a large amount
of data, but the community lacks a standard format or repository for this data.
This situation makes it difficult to share and compare different approaches
effectively, as is done in other, more established fields. It also
unnecessarily hinders new researchers who want to work in this area. To address
this problem, we introduce a standardized format for representing algorithm
selection scenarios and a repository that contains a growing number of data
sets from the literature. Our format has been designed to be able to express a
wide variety of different scenarios. Demonstrating the breadth and power of our
platform, we describe a set of example experiments that build and evaluate
algorithm selection models through a common interface. The results display the
potential of algorithm selection to achieve significant performance
improvements across a broad range of problems and algorithms.
| Bernd Bischl, Pascal Kerschke, Lars Kotthoff, Marius Lindauer, Yuri
Malitsky, Alexandre Frechette, Holger Hoos, Frank Hutter, Kevin Leyton-Brown,
Kevin Tierney, Joaquin Vanschoren | null | 1506.02465 | null | null |
SVM and ELM: Who Wins? Object Recognition with Deep Convolutional
Features from ImageNet | cs.LG cs.CV | Deep learning with a convolutional neural network (CNN) has been proved to be
very effective in feature extraction and representation of images. For image
classification problems, this work aim at finding which classifier is more
competitive based on high-level deep features of images. In this report, we
have discussed the nearest neighbor, support vector machines and extreme
learning machines for image classification under deep convolutional activation
feature representation. Specifically, we adopt the benchmark object recognition
dataset from multiple sources with domain bias for evaluating different
classifiers. The deep features of the object dataset are obtained by a
well-trained CNN with five convolutional layers and three fully-connected
layers on the challenging ImageNet. Experiments demonstrate that the ELMs
outperform SVMs in cross-domain recognition tasks. In particular,
state-of-the-art results are obtained by kernel ELM which outperforms SVMs with
about 4% of the average accuracy. The features and codes are available in
http://www.escience.cn/people/lei/index.html
| Lei Zhang and David Zhang | null | 1506.02509 | null | null |
Learning Mixtures of Ising Models using Pseudolikelihood | cs.LG stat.ML | Maximum pseudolikelihood method has been among the most important methods for
learning parameters of statistical physics models, such as Ising models. In
this paper, we study how pseudolikelihood can be derived for learning
parameters of a mixture of Ising models. The performance of the proposed
approach is demonstrated for Ising and Potts models on both synthetic and real
data.
| Onur Dikmen | null | 1506.02510 | null | null |
Learning to Transduce with Unbounded Memory | cs.NE cs.CL cs.LG | Recently, strong results have been demonstrated by Deep Recurrent Neural
Networks on natural language transduction problems. In this paper we explore
the representational power of these models using synthetic grammars designed to
exhibit phenomena similar to those found in real transduction problems such as
machine translation. These experiments lead us to propose new memory-based
recurrent networks that implement continuously differentiable analogues of
traditional data structures such as Stacks, Queues, and DeQues. We show that
these architectures exhibit superior generalisation performance to Deep RNNs
and are often able to learn the underlying generating algorithms in our
transduction experiments.
| Edward Grefenstette, Karl Moritz Hermann, Mustafa Suleyman, Phil
Blunsom | null | 1506.02516 | null | null |
Linear Convergence of the Randomized Feasible Descent Method Under the
Weak Strong Convexity Assumption | cs.LG stat.ML | In this paper we generalize the framework of the feasible descent method
(FDM) to a randomized (R-FDM) and a coordinate-wise random feasible descent
method (RC-FDM) framework. We show that the famous SDCA algorithm for
optimizing the SVM dual problem, or the stochastic coordinate descent method
for the LASSO problem, fits into the framework of RC-FDM. We prove linear
convergence for both R-FDM and RC-FDM under the weak strong convexity
assumption. Moreover, we show that the duality gap converges linearly for
RC-FDM, which implies that the duality gap also converges linearly for SDCA
applied to the SVM dual problem.
| Chenxin Ma, Rachael Tappenden, Martin Tak\'a\v{c} | null | 1506.02530 | null | null |
Efficient Learning of Ensembles with QuadBoost | cs.LG | We first present a general risk bound for ensembles that depends on the Lp
norm of the weighted combination of voters which can be selected from a
continuous set. We then propose a boosting method, called QuadBoost, which is
strongly supported by the general risk bound and has very simple rules for
assigning the voters' weights. Moreover, QuadBoost exhibits a rate of decrease
of its empirical error which is slightly faster than the one achieved by
AdaBoost. The experimental results confirm the expectation of the theory that
QuadBoost is a very efficient method for learning ensembles.
| Louis Fortier-Dubois, Fran\c{c}ois Laviolette, Mario Marchand,
Louis-Emile Robitaille, Jean-Francis Roy | null | 1506.02535 | null | null |
Learning with Group Invariant Features: A Kernel Perspective | cs.LG cs.CV stat.ML | We analyze in this paper a random feature map based on a theory of invariance
I-theory introduced recently. More specifically, a group invariant signal
signature is obtained through cumulative distributions of group transformed
random projections. Our analysis bridges invariant feature learning with kernel
methods, as we show that this feature map defines an expected Haar integration
kernel that is invariant to the specified group action. We show how this
non-linear random feature map approximates this group invariant kernel
uniformly on a set of $N$ points. Moreover, we show that it defines a function
space that is dense in the equivalent Invariant Reproducing Kernel Hilbert
Space. Finally, we quantify error rates of the convergence of the empirical
risk minimization, as well as the reduction in the sample complexity of a
learning algorithm using such an invariant representation for signal
classification, in a classical supervised learning setting.
| Youssef Mroueh, Stephen Voinea, Tomaso Poggio | null | 1506.02544 | null | null |
Regret Lower Bound and Optimal Algorithm in Dueling Bandit Problem | stat.ML cs.LG | We study the $K$-armed dueling bandit problem, a variation of the standard
stochastic bandit problem where the feedback is limited to relative comparisons
of a pair of arms. We introduce a tight asymptotic regret lower bound that is
based on the information divergence. An algorithm that is inspired by the
Deterministic Minimum Empirical Divergence algorithm (Honda and Takemura, 2010)
is proposed, and its regret is analyzed. The proposed algorithm is found to be
the first one with a regret upper bound that matches the lower bound.
Experimental comparisons of dueling bandit algorithms show that the proposed
algorithm significantly outperforms existing ones.
| Junpei Komiyama, Junya Honda, Hisashi Kashima, Hiroshi Nakagawa | null | 1506.02550 | null | null |
DUAL-LOCO: Distributing Statistical Estimation Using Random Projections | stat.ML cs.DC cs.LG | We present DUAL-LOCO, a communication-efficient algorithm for distributed
statistical estimation. DUAL-LOCO assumes that the data is distributed
according to the features rather than the samples. It requires only a single
round of communication where low-dimensional random projections are used to
approximate the dependences between features available to different workers. We
show that DUAL-LOCO has bounded approximation error which only depends weakly
on the number of workers. We compare DUAL-LOCO against a state-of-the-art
distributed optimization method on a variety of real world datasets and show
that it obtains better speedups while retaining good accuracy.
| Christina Heinze, Brian McWilliams, Nicolai Meinshausen | null | 1506.02554 | null | null |
Variational Dropout and the Local Reparameterization Trick | stat.ML cs.LG stat.CO | We investigate a local reparameterizaton technique for greatly reducing the
variance of stochastic gradients for variational Bayesian inference (SGVB) of a
posterior over model parameters, while retaining parallelizability. This local
reparameterization translates uncertainty about global parameters into local
noise that is independent across datapoints in the minibatch. Such
parameterizations can be trivially parallelized and have variance that is
inversely proportional to the minibatch size, generally leading to much faster
convergence. Additionally, we explore a connection with dropout: Gaussian
dropout objectives correspond to SGVB with local reparameterization, a
scale-invariant prior and proportionally fixed posterior variance. Our method
allows inference of more flexibly parameterized posteriors; specifically, we
propose variational dropout, a generalization of Gaussian dropout where the
dropout rates are learned, often leading to better models. The method is
demonstrated through several experiments.
| Diederik P. Kingma, Tim Salimans, Max Welling | null | 1506.02557 | null | null |
Learning to Select Pre-Trained Deep Representations with Bayesian
Evidence Framework | cs.CV cs.LG stat.ML | We propose a Bayesian evidence framework to facilitate transfer learning from
pre-trained deep convolutional neural networks (CNNs). Our framework is
formulated on top of a least squares SVM (LS-SVM) classifier, which is simple
and fast in both training and testing, and achieves competitive performance in
practice. The regularization parameters in LS-SVM is estimated automatically
without grid search and cross-validation by maximizing evidence, which is a
useful measure to select the best performing CNN out of multiple candidates for
transfer learning; the evidence is optimized efficiently by employing Aitken's
delta-squared process, which accelerates convergence of fixed point update. The
proposed Bayesian evidence framework also provides a good solution to identify
the best ensemble of heterogeneous CNNs through a greedy algorithm. Our
Bayesian evidence framework for transfer learning is tested on 12 visual
recognition datasets and illustrates the state-of-the-art performance
consistently in terms of prediction accuracy and modeling efficiency.
| Yong-Deok Kim, Taewoong Jang, Bohyung Han, and Seungjin Choi | null | 1506.02565 | null | null |
On Convergence of Emphatic Temporal-Difference Learning | cs.LG | We consider emphatic temporal-difference learning algorithms for policy
evaluation in discounted Markov decision processes with finite spaces. Such
algorithms were recently proposed by Sutton, Mahmood, and White (2015) as an
improved solution to the problem of divergence of off-policy
temporal-difference learning with linear function approximation. We present in
this paper the first convergence proofs for two emphatic algorithms,
ETD($\lambda$) and ELSTD($\lambda$). We prove, under general off-policy
conditions, the convergence in $L^1$ for ELSTD($\lambda$) iterates, and the
almost sure convergence of the approximate value functions calculated by both
algorithms using a single infinitely long trajectory. Our analysis involves new
techniques with applications beyond emphatic algorithms leading, for example,
to the first proof that standard TD($\lambda$) also converges under off-policy
training for $\lambda$ sufficiently large.
| Huizhen Yu | null | 1506.02582 | null | null |
Optimal Sparse Kernel Learning for Hyperspectral Anomaly Detection | cs.LG | In this paper, a novel framework of sparse kernel learning for Support Vector
Data Description (SVDD) based anomaly detection is presented. In this work,
optimal sparse feature selection for anomaly detection is first modeled as a
Mixed Integer Programming (MIP) problem. Due to the prohibitively high
computational complexity of the MIP, it is relaxed into a Quadratically
Constrained Linear Programming (QCLP) problem. The QCLP problem can then be
practically solved by using an iterative optimization method, in which multiple
subsets of features are iteratively found as opposed to a single subset. The
QCLP-based iterative optimization problem is solved in a finite space called
the \emph{Empirical Kernel Feature Space} (EKFS) instead of in the input space
or \emph{Reproducing Kernel Hilbert Space} (RKHS). This is possible because of
the fact that the geometrical properties of the EKFS and the corresponding RKHS
remain the same. Now, an explicit nonlinear exploitation of the data in a
finite EKFS is achievable, which results in optimal feature ranking.
Experimental results based on a hyperspectral image show that the proposed
method can provide improved performance over the current state-of-the-art
techniques.
| Zhimin Peng, Prudhvi Gurram, Heesung Kwon, Wotao Yin | null | 1506.02585 | null | null |
Path-SGD: Path-Normalized Optimization in Deep Neural Networks | cs.LG cs.CV cs.NE stat.ML | We revisit the choice of SGD for training deep neural networks by
reconsidering the appropriate geometry in which to optimize the weights. We
argue for a geometry invariant to rescaling of weights that does not affect the
output of the network, and suggest Path-SGD, which is an approximate steepest
descent method with respect to a path-wise regularizer related to max-norm
regularization. Path-SGD is easy and efficient to implement and leads to
empirical gains over SGD and AdaGrad.
| Behnam Neyshabur, Ruslan Salakhutdinov, Nathan Srebro | null | 1506.02617 | null | null |
Distributed Training of Structured SVM | stat.ML cs.DC cs.LG | Training structured prediction models is time-consuming. However, most
existing approaches only use a single machine, thus, the advantage of computing
power and the capacity for larger data sets of multiple machines have not been
exploited. In this work, we propose an efficient algorithm for distributedly
training structured support vector machines based on a distributed
block-coordinate descent method. Both theoretical and experimental results
indicate that our method is efficient.
| Ching-pei Lee, Kai-Wei Chang, Shyam Upadhyay, Dan Roth | null | 1506.02620 | null | null |
Learning both Weights and Connections for Efficient Neural Networks | cs.NE cs.CV cs.LG | Neural networks are both computationally intensive and memory intensive,
making them difficult to deploy on embedded systems. Also, conventional
networks fix the architecture before training starts; as a result, training
cannot improve the architecture. To address these limitations, we describe a
method to reduce the storage and computation required by neural networks by an
order of magnitude without affecting their accuracy by learning only the
important connections. Our method prunes redundant connections using a
three-step method. First, we train the network to learn which connections are
important. Next, we prune the unimportant connections. Finally, we retrain the
network to fine tune the weights of the remaining connections. On the ImageNet
dataset, our method reduced the number of parameters of AlexNet by a factor of
9x, from 61 million to 6.7 million, without incurring accuracy loss. Similar
experiments with VGG-16 found that the number of parameters can be reduced by
13x, from 138 million to 10.3 million, again with no loss of accuracy.
| Song Han, Jeff Pool, John Tran, William J. Dally | null | 1506.02626 | null | null |
Generalization in Adaptive Data Analysis and Holdout Reuse | cs.LG cs.DS | Overfitting is the bane of data analysts, even when data are plentiful.
Formal approaches to understanding this problem focus on statistical inference
and generalization of individual analysis procedures. Yet the practice of data
analysis is an inherently interactive and adaptive process: new analyses and
hypotheses are proposed after seeing the results of previous ones, parameters
are tuned on the basis of obtained results, and datasets are shared and reused.
An investigation of this gap has recently been initiated by the authors in
(Dwork et al., 2014), where we focused on the problem of estimating
expectations of adaptively chosen functions.
In this paper, we give a simple and practical method for reusing a holdout
(or testing) set to validate the accuracy of hypotheses produced by a learning
algorithm operating on a training set. Reusing a holdout set adaptively
multiple times can easily lead to overfitting to the holdout set itself. We
give an algorithm that enables the validation of a large number of adaptively
chosen hypotheses, while provably avoiding overfitting. We illustrate the
advantages of our algorithm over the standard use of the holdout set via a
simple synthetic experiment.
We also formalize and address the general problem of data reuse in adaptive
data analysis. We show how the differential-privacy based approach given in
(Dwork et al., 2014) is applicable much more broadly to adaptive data analysis.
We then show that a simple approach based on description length can also be
used to give guarantees of statistical validity in adaptive settings. Finally,
we demonstrate that these incomparable approaches can be unified via the notion
of approximate max-information that we introduce.
| Cynthia Dwork, Vitaly Feldman, Moritz Hardt, Toniann Pitassi, Omer
Reingold, Aaron Roth | null | 1506.02629 | null | null |
Cumulative Prospect Theory Meets Reinforcement Learning: Prediction and
Control | cs.LG math.OC | Cumulative prospect theory (CPT) is known to model human decisions well, with
substantial empirical evidence supporting this claim. CPT works by distorting
probabilities and is more general than the classic expected utility and
coherent risk measures. We bring this idea to a risk-sensitive reinforcement
learning (RL) setting and design algorithms for both estimation and control.
The RL setting presents two particular challenges when CPT is applied:
estimating the CPT objective requires estimations of the entire distribution of
the value function and finding a randomized optimal policy. The estimation
scheme that we propose uses the empirical distribution to estimate the
CPT-value of a random variable. We then use this scheme in the inner loop of a
CPT-value optimization procedure that is based on the well-known simulation
optimization idea of simultaneous perturbation stochastic approximation (SPSA).
We provide theoretical convergence guarantees for all the proposed algorithms
and also illustrate the usefulness of CPT-based criteria in a traffic signal
control application.
| Prashanth L.A., Cheng Jie, Michael Fu, Steve Marcus and Csaba
Szepesv\'ari | null | 1506.02632 | null | null |
A Topological Approach to Spectral Clustering | cs.LG stat.ML | We propose two related unsupervised clustering algorithms which, for input,
take data assumed to be sampled from a uniform distribution supported on a
metric space $X$, and output a clustering of the data based on the selection of
a topological model for the connected components of $X$. Both algorithms work
by selecting a graph on the samples from a natural one-parameter family of
graphs, using a geometric criterion in the first case and an information
theoretic criterion in the second. The estimated connected components of $X$
are identified with the kernel of the associated graph Laplacian, which allows
the algorithm to work without requiring the number of expected clusters or
other auxiliary data as input.
| Antonio Rieser | 10.3934/fods.2021005 | 1506.02633 | null | null |
Faster SGD Using Sketched Conditioning | cs.NA cs.LG | We propose a novel method for speeding up stochastic optimization algorithms
via sketching methods, which recently became a powerful tool for accelerating
algorithms for numerical linear algebra. We revisit the method of conditioning
for accelerating first-order methods and suggest the use of sketching methods
for constructing a cheap conditioner that attains a significant speedup with
respect to the Stochastic Gradient Descent (SGD) algorithm. While our
theoretical guarantees assume convexity, we discuss the applicability of our
method to deep neural networks, and experimentally demonstrate its merits.
| Alon Gonen, Shai Shalev-Shwartz | null | 1506.02649 | null | null |
The LICORS Cabinet: Nonparametric Algorithms for Spatio-temporal
Prediction | stat.ML cs.LG | Spatio-temporal data is intrinsically high dimensional, so unsupervised
modeling is only feasible if we can exploit structure in the process. When the
dynamics are local in both space and time, this structure can be exploited by
splitting the global field into many lower-dimensional "light cones". We review
light cone decompositions for predictive state reconstruction, introducing
three simple light cone algorithms. These methods allow for tractable inference
of spatio-temporal data, such as full-frame video. The algorithms make few
assumptions on the underlying process yet have good predictive performance and
can provide distributions over spatio-temporal data, enabling sophisticated
probabilistic inference.
| George D. Montanez, Cosma Rohilla Shalizi | null | 1506.02686 | null | null |
Adaptive Normalized Risk-Averting Training For Deep Neural Networks | cs.LG cs.NE stat.ML | This paper proposes a set of new error criteria and learning approaches,
Adaptive Normalized Risk-Averting Training (ANRAT), to attack the non-convex
optimization problem in training deep neural networks (DNNs). Theoretically, we
demonstrate its effectiveness on global and local convexity lower-bounded by
the standard $L_p$-norm error. By analyzing the gradient on the convexity index
$\lambda$, we explain the reason why to learn $\lambda$ adaptively using
gradient descent works. In practice, we show how this method improves training
of deep neural networks to solve visual recognition tasks on the MNIST and
CIFAR-10 datasets. Without using pretraining or other tricks, we obtain results
comparable or superior to those reported in recent literature on the same tasks
using standard ConvNets + MSE/cross entropy. Performance on deep/shallow
multilayer perceptrons and Denoised Auto-encoders is also explored. ANRAT can
be combined with other quasi-Newton training methods, innovative network
variants, regularization techniques and other specific tricks in DNNs. Other
than unsupervised pretraining, it provides a new perspective to address the
non-convex optimization problem in DNNs.
| Zhiguang Wang, Tim Oates, James Lo | null | 1506.02690 | null | null |
An Improved BKW Algorithm for LWE with Applications to Cryptography and
Lattices | cs.CR cs.DS cs.LG | In this paper, we study the Learning With Errors problem and its binary
variant, where secrets and errors are binary or taken in a small interval. We
introduce a new variant of the Blum, Kalai and Wasserman algorithm, relying on
a quantization step that generalizes and fine-tunes modulus switching. In
general this new technique yields a significant gain in the constant in front
of the exponent in the overall complexity. We illustrate this by solving p
within half a day a LWE instance with dimension n = 128, modulus $q = n^2$,
Gaussian noise $\alpha = 1/(\sqrt{n/\pi} \log^2 n)$ and binary secret, using
$2^{28}$ samples, while the previous best result based on BKW claims a time
complexity of $2^{74}$ with $2^{60}$ samples for the same parameters. We then
introduce variants of BDD, GapSVP and UniqueSVP, where the target point is
required to lie in the fundamental parallelepiped, and show how the previous
algorithm is able to solve these variants in subexponential time. Moreover, we
also show how the previous algorithm can be used to solve the BinaryLWE problem
with n samples in subexponential time $2^{(\ln 2/2+o(1))n/\log \log n}$. This
analysis does not require any heuristic assumption, contrary to other algebraic
approaches; instead, it uses a variant of an idea by Lyubashevsky to generate
many samples from a small number of samples. This makes it possible to
asymptotically and heuristically break the NTRU cryptosystem in subexponential
time (without contradicting its security assumption). We are also able to solve
subset sum problems in subexponential time for density $o(1)$, which is of
independent interest: for such density, the previous best algorithm requires
exponential time. As a direct application, we can solve in subexponential time
the parameters of a cryptosystem based on this problem proposed at TCC 2010.
| Paul Kirchner and Pierre-Alain Fouque | null | 1506.02717 | null | null |
Non-parametric Revenue Optimization for Generalized Second Price
Auctions | cs.LG cs.GT | We present an extensive analysis of the key problem of learning optimal
reserve prices for generalized second price auctions. We describe two
algorithms for this task: one based on density estimation, and a novel
algorithm benefiting from solid theoretical guarantees and with a very
favorable running-time complexity of $O(n S \log (n S))$, where $n$ is the
sample size and $S$ the number of slots. Our theoretical guarantees are more
favorable than those previously presented in the literature. Additionally, we
show that even if bidders do not play at an equilibrium, our second algorithm
is still well defined and minimizes a quantity of interest. To our knowledge,
this is the first attempt to apply learning algorithms to the problem of
reserve price optimization in GSP auctions. Finally, we present the first
convergence analysis of empirical equilibrium bidding functions to the unique
symmetric Bayesian-Nash equilibrium of a GSP.
| Mehryar Mohri and Andres Munoz Medina | null | 1506.02719 | null | null |
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