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A survey on feature weighting based K-Means algorithms | cs.LG | In a real-world data set there is always the possibility, rather high in our
opinion, that different features may have different degrees of relevance. Most
machine learning algorithms deal with this fact by either selecting or
deselecting features in the data preprocessing phase. However, we maintain that
even among relevant features there may be different degrees of relevance, and
this should be taken into account during the clustering process. With over 50
years of history, K-Means is arguably the most popular partitional clustering
algorithm there is. The first K-Means based clustering algorithm to compute
feature weights was designed just over 30 years ago. Various such algorithms
have been designed since but there has not been, to our knowledge, a survey
integrating empirical evidence of cluster recovery ability, common flaws, and
possible directions for future research. This paper elaborates on the concept
of feature weighting and addresses these issues by critically analysing some of
the most popular, or innovative, feature weighting mechanisms based in K-Means.
| Renato Cordeiro de Amorim | null | 1601.03483 | null | null |
Creativity in Machine Learning | cs.CV cs.LG | Recent machine learning techniques can be modified to produce creative
results. Those results did not exist before; it is not a trivial combination of
the data which was fed into the machine learning system. The obtained results
come in multiple forms: As images, as text and as audio.
This paper gives a high level overview of how they are created and gives some
examples. It is meant to be a summary of the current work and give people who
are new to machine learning some starting points.
| Martin Thoma | null | 1601.03642 | null | null |
Improved Relation Classification by Deep Recurrent Neural Networks with
Data Augmentation | cs.CL cs.LG | Nowadays, neural networks play an important role in the task of relation
classification. By designing different neural architectures, researchers have
improved the performance to a large extent in comparison with traditional
methods. However, existing neural networks for relation classification are
usually of shallow architectures (e.g., one-layer convolutional neural networks
or recurrent networks). They may fail to explore the potential representation
space in different abstraction levels. In this paper, we propose deep recurrent
neural networks (DRNNs) for relation classification to tackle this challenge.
Further, we propose a data augmentation method by leveraging the directionality
of relations. We evaluated our DRNNs on the SemEval-2010 Task~8, and achieve an
F1-score of 86.1%, outperforming previous state-of-the-art recorded results.
| Yan Xu, Ran Jia, Lili Mou, Ge Li, Yunchuan Chen, Yangyang Lu, Zhi Jin | null | 1601.03651 | null | null |
Dual-tree $k$-means with bounded iteration runtime | cs.DS cs.LG | k-means is a widely used clustering algorithm, but for $k$ clusters and a
dataset size of $N$, each iteration of Lloyd's algorithm costs $O(kN)$ time.
Although there are existing techniques to accelerate single Lloyd iterations,
none of these are tailored to the case of large $k$, which is increasingly
common as dataset sizes grow. We propose a dual-tree algorithm that gives the
exact same results as standard $k$-means; when using cover trees, we use
adaptive analysis techniques to, under some assumptions, bound the
single-iteration runtime of the algorithm as $O(N + k log k)$. To our knowledge
these are the first sub-$O(kN)$ bounds for exact Lloyd iterations. We then show
that this theoretically favorable algorithm performs competitively in practice,
especially for large $N$ and $k$ in low dimensions. Further, the algorithm is
tree-independent, so any type of tree may be used.
| Ryan R. Curtin | null | 1601.03754 | null | null |
Linear Algebraic Structure of Word Senses, with Applications to Polysemy | cs.CL cs.LG stat.ML | Word embeddings are ubiquitous in NLP and information retrieval, but it is
unclear what they represent when the word is polysemous. Here it is shown that
multiple word senses reside in linear superposition within the word embedding
and simple sparse coding can recover vectors that approximately capture the
senses. The success of our approach, which applies to several embedding
methods, is mathematically explained using a variant of the random walk on
discourses model (Arora et al., 2016). A novel aspect of our technique is that
each extracted word sense is accompanied by one of about 2000 "discourse atoms"
that gives a succinct description of which other words co-occur with that word
sense. Discourse atoms can be of independent interest, and make the method
potentially more useful. Empirical tests are used to verify and support the
theory.
| Sanjeev Arora, Yuanzhi Li, Yingyu Liang, Tengyu Ma, Andrej Risteski | null | 1601.03764 | null | null |
Generation of a Supervised Classification Algorithm for Time-Series
Variable Stars with an Application to the LINEAR Dataset | astro-ph.IM cs.LG | With the advent of digital astronomy, new benefits and new problems have been
presented to the modern day astronomer. While data can be captured in a more
efficient and accurate manor using digital means, the efficiency of data
retrieval has led to an overload of scientific data for processing and storage.
This paper will focus on the construction and application of a supervised
pattern classification algorithm for the identification of variable stars.
Given the reduction of a survey of stars into a standard feature space, the
problem of using prior patterns to identify new observed patterns can be
reduced to time tested classification methodologies and algorithms. Such
supervised methods, so called because the user trains the algorithms prior to
application using patterns with known classes or labels, provide a means to
probabilistically determine the estimated class type of new observations. This
paper will demonstrate the construction and application of a supervised
classification algorithm on variable star data. The classifier is applied to a
set of 192,744 LINEAR data points. Of the original samples, 34,451 unique stars
were classified with high confidence (high level of probability of being the
true class).
| Kyle B Johnston and Hakeem M Oluseyi | 10.1016/j.newast.2016.10.004 | 1601.03769 | null | null |
Trust from the past: Bayesian Personalized Ranking based Link Prediction
in Knowledge Graphs | cs.LG cs.AI cs.IR | Link prediction, or predicting the likelihood of a link in a knowledge graph
based on its existing state is a key research task. It differs from a
traditional link prediction task in that the links in a knowledge graph are
categorized into different predicates and the link prediction performance of
different predicates in a knowledge graph generally varies widely. In this
work, we propose a latent feature embedding based link prediction model which
considers the prediction task for each predicate disjointly. To learn the model
parameters it utilizes a Bayesian personalized ranking based optimization
technique. Experimental results on large-scale knowledge bases such as YAGO2
show that our link prediction approach achieves substantially higher
performance than several state-of-art approaches. We also show that for a given
predicate the topological properties of the knowledge graph induced by the
given predicate edges are key indicators of the link prediction performance of
that predicate in the knowledge graph.
| Baichuan Zhang, Sutanay Choudhury, Mohammad Al Hasan, Xia Ning,
Khushbu Agarwal, Sumit Purohit, Paola Pesntez Cabrera | null | 1601.03778 | null | null |
ActiveClean: Interactive Data Cleaning While Learning Convex Loss Models | cs.DB cs.LG | Data cleaning is often an important step to ensure that predictive models,
such as regression and classification, are not affected by systematic errors
such as inconsistent, out-of-date, or outlier data. Identifying dirty data is
often a manual and iterative process, and can be challenging on large datasets.
However, many data cleaning workflows can introduce subtle biases into the
training processes due to violation of independence assumptions. We propose
ActiveClean, a progressive cleaning approach where the model is updated
incrementally instead of re-training and can guarantee accuracy on partially
cleaned data. ActiveClean supports a popular class of models called convex loss
models (e.g., linear regression and SVMs). ActiveClean also leverages the
structure of a user's model to prioritize cleaning those records likely to
affect the results. We evaluate ActiveClean on five real-world datasets UCI
Adult, UCI EEG, MNIST, Dollars For Docs, and WorldBank with both real and
synthetic errors. Our results suggest that our proposed optimizations can
improve model accuracy by up-to 2.5x for the same amount of data cleaned.
Furthermore for a fixed cleaning budget and on all real dirty datasets,
ActiveClean returns more accurate models than uniform sampling and Active
Learning.
| Sanjay Krishnan, Jiannan Wang, Eugene Wu, Michael J. Franklin, Ken
Goldberg | null | 1601.03797 | null | null |
Matrix Neural Networks | cs.LG | Traditional neural networks assume vectorial inputs as the network is
arranged as layers of single line of computing units called neurons. This
special structure requires the non-vectorial inputs such as matrices to be
converted into vectors. This process can be problematic. Firstly, the spatial
information among elements of the data may be lost during vectorisation.
Secondly, the solution space becomes very large which demands very special
treatments to the network parameters and high computational cost. To address
these issues, we propose matrix neural networks (MatNet), which takes matrices
directly as inputs. Each neuron senses summarised information through bilinear
mapping from lower layer units in exactly the same way as the classic feed
forward neural networks. Under this structure, back prorogation and gradient
descent combination can be utilised to obtain network parameters efficiently.
Furthermore, it can be conveniently extended for multimodal inputs. We apply
MatNet to MNIST handwritten digits classification and image super resolution
tasks to show its effectiveness. Without too much tweaking MatNet achieves
comparable performance as the state-of-the-art methods in both tasks with
considerably reduced complexity.
| Junbin Gao and Yi Guo and Zhiyong Wang | null | 1601.03805 | null | null |
On the consistency of inversion-free parameter estimation for Gaussian
random fields | math.ST cs.LG stat.ML stat.TH | Gaussian random fields are a powerful tool for modeling environmental
processes. For high dimensional samples, classical approaches for estimating
the covariance parameters require highly challenging and massive computations,
such as the evaluation of the Cholesky factorization or solving linear systems.
Recently, Anitescu, Chen and Stein \cite{M.Anitescu} proposed a fast and
scalable algorithm which does not need such burdensome computations. The main
focus of this article is to study the asymptotic behavior of the algorithm of
Anitescu et al. (ACS) for regular and irregular grids in the increasing domain
setting. Consistency, minimax optimality and asymptotic normality of this
algorithm are proved under mild differentiability conditions on the covariance
function. Despite the fact that ACS's method entails a non-concave
maximization, our results hold for any stationary point of the objective
function. A numerical study is presented to evaluate the efficiency of this
algorithm for large data sets.
| Hossein Keshavarz, Clayton Scott, XuanLong Nguyen | 10.1016/j.jmva.2016.06.003 | 1601.03822 | null | null |
A Relative Exponential Weighing Algorithm for Adversarial Utility-based
Dueling Bandits | cs.LG | We study the K-armed dueling bandit problem which is a variation of the
classical Multi-Armed Bandit (MAB) problem in which the learner receives only
relative feedback about the selected pairs of arms. We propose a new algorithm
called Relative Exponential-weight algorithm for Exploration and Exploitation
(REX3) to handle the adversarial utility-based formulation of this problem.
This algorithm is a non-trivial extension of the Exponential-weight algorithm
for Exploration and Exploitation (EXP3) algorithm. We prove a finite time
expected regret upper bound of order O(sqrt(K ln(K)T)) for this algorithm and a
general lower bound of order omega(sqrt(KT)). At the end, we provide
experimental results using real data from information retrieval applications.
| Pratik Gajane, Tanguy Urvoy, Fabrice Cl\'erot (FT R and D) | null | 1601.03855 | null | null |
Improved graph-based SFA: Information preservation complements the
slowness principle | cs.CV cs.LG stat.ML | Slow feature analysis (SFA) is an unsupervised-learning algorithm that
extracts slowly varying features from a multi-dimensional time series. A
supervised extension to SFA for classification and regression is graph-based
SFA (GSFA). GSFA is based on the preservation of similarities, which are
specified by a graph structure derived from the labels. It has been shown that
hierarchical GSFA (HGSFA) allows learning from images and other
high-dimensional data. The feature space spanned by HGSFA is complex due to the
composition of the nonlinearities of the nodes in the network. However, we show
that the network discards useful information prematurely before it reaches
higher nodes, resulting in suboptimal global slowness and an under-exploited
feature space.
To counteract these problems, we propose an extension called hierarchical
information-preserving GSFA (HiGSFA), where information preservation
complements the slowness-maximization goal. We build a 10-layer HiGSFA network
to estimate human age from facial photographs of the MORPH-II database,
achieving a mean absolute error of 3.50 years, improving the state-of-the-art
performance. HiGSFA and HGSFA support multiple-labels and offer a rich feature
space, feed-forward training, and linear complexity in the number of samples
and dimensions. Furthermore, HiGSFA outperforms HGSFA in terms of feature
slowness, estimation accuracy and input reconstruction, giving rise to a
promising hierarchical supervised-learning approach.
| Alberto N. Escalante-B. and Laurenz Wiskott | null | 1601.03945 | null | null |
Average Stability is Invariant to Data Preconditioning. Implications to
Exp-concave Empirical Risk Minimization | cs.LG | We show that the average stability notion introduced by
\cite{kearns1999algorithmic, bousquet2002stability} is invariant to data
preconditioning, for a wide class of generalized linear models that includes
most of the known exp-concave losses. In other words, when analyzing the
stability rate of a given algorithm, we may assume the optimal preconditioning
of the data. This implies that, at least from a statistical perspective,
explicit regularization is not required in order to compensate for
ill-conditioned data, which stands in contrast to a widely common approach that
includes a regularization for analyzing the sample complexity of generalized
linear models. Several important implications of our findings include: a) We
demonstrate that the excess risk of empirical risk minimization (ERM) is
controlled by the preconditioned stability rate. This immediately yields a
relatively short and elegant proof for the fast rates attained by ERM in our
context. b) We strengthen the recent bounds of \cite{hardt2015train} on the
stability rate of the Stochastic Gradient Descent algorithm.
| Alon Gonen, Shai Shalev-Shwartz | null | 1601.04011 | null | null |
Faster Asynchronous SGD | stat.ML cs.LG | Asynchronous distributed stochastic gradient descent methods have trouble
converging because of stale gradients. A gradient update sent to a parameter
server by a client is stale if the parameters used to calculate that gradient
have since been updated on the server. Approaches have been proposed to
circumvent this problem that quantify staleness in terms of the number of
elapsed updates. In this work, we propose a novel method that quantifies
staleness in terms of moving averages of gradient statistics. We show that this
method outperforms previous methods with respect to convergence speed and
scalability to many clients. We also discuss how an extension to this method
can be used to dramatically reduce bandwidth costs in a distributed training
context. In particular, our method allows reduction of total bandwidth usage by
a factor of 5 with little impact on cost convergence. We also describe (and
link to) a software library that we have used to simulate these algorithms
deterministically on a single machine.
| Augustus Odena | null | 1601.04033 | null | null |
Training Recurrent Neural Networks by Diffusion | cs.LG | This work presents a new algorithm for training recurrent neural networks
(although ideas are applicable to feedforward networks as well). The algorithm
is derived from a theory in nonconvex optimization related to the diffusion
equation. The contributions made in this work are two fold. First, we show how
some seemingly disconnected mechanisms used in deep learning such as smart
initialization, annealed learning rate, layerwise pretraining, and noise
injection (as done in dropout and SGD) arise naturally and automatically from
this framework, without manually crafting them into the algorithms. Second, we
present some preliminary results on comparing the proposed method against SGD.
It turns out that the new algorithm can achieve similar level of generalization
accuracy of SGD in much fewer number of epochs.
| Hossein Mobahi | null | 1601.04114 | null | null |
Engineering Safety in Machine Learning | stat.ML cs.AI cs.CY cs.LG | Machine learning algorithms are increasingly influencing our decisions and
interacting with us in all parts of our daily lives. Therefore, just like for
power plants, highways, and myriad other engineered sociotechnical systems, we
must consider the safety of systems involving machine learning. In this paper,
we first discuss the definition of safety in terms of risk, epistemic
uncertainty, and the harm incurred by unwanted outcomes. Then we examine
dimensions, such as the choice of cost function and the appropriateness of
minimizing the empirical average training cost, along which certain real-world
applications may not be completely amenable to the foundational principle of
modern statistical machine learning: empirical risk minimization. In
particular, we note an emerging dichotomy of applications: ones in which safety
is important and risk minimization is not the complete story (we name these
Type A applications), and ones in which safety is not so critical and risk
minimization is sufficient (we name these Type B applications). Finally, we
discuss how four different strategies for achieving safety in engineering
(inherently safe design, safety reserves, safe fail, and procedural safeguards)
can be mapped to the machine learning context through interpretability and
causality of predictive models, objectives beyond expected prediction accuracy,
human involvement for labeling difficult or rare examples, and user experience
design of software.
| Kush R. Varshney | null | 1601.04126 | null | null |
$\mathbf{D^3}$: Deep Dual-Domain Based Fast Restoration of
JPEG-Compressed Images | cs.CV cs.AI cs.LG | In this paper, we design a Deep Dual-Domain ($\mathbf{D^3}$) based fast
restoration model to remove artifacts of JPEG compressed images. It leverages
the large learning capacity of deep networks, as well as the problem-specific
expertise that was hardly incorporated in the past design of deep
architectures. For the latter, we take into consideration both the prior
knowledge of the JPEG compression scheme, and the successful practice of the
sparsity-based dual-domain approach. We further design the One-Step Sparse
Inference (1-SI) module, as an efficient and light-weighted feed-forward
approximation of sparse coding. Extensive experiments verify the superiority of
the proposed $D^3$ model over several state-of-the-art methods. Specifically,
our best model is capable of outperforming the latest deep model for around 1
dB in PSNR, and is 30 times faster.
| Zhangyang Wang, Ding Liu, Shiyu Chang, Qing Ling, Yingzhen Yang, and
Thomas S. Huang | null | 1601.04149 | null | null |
Studying Very Low Resolution Recognition Using Deep Networks | cs.CV cs.AI cs.LG | Visual recognition research often assumes a sufficient resolution of the
region of interest (ROI). That is usually violated in practice, inspiring us to
explore the Very Low Resolution Recognition (VLRR) problem. Typically, the ROI
in a VLRR problem can be smaller than $16 \times 16$ pixels, and is challenging
to be recognized even by human experts. We attempt to solve the VLRR problem
using deep learning methods. Taking advantage of techniques primarily in super
resolution, domain adaptation and robust regression, we formulate a dedicated
deep learning method and demonstrate how these techniques are incorporated step
by step. Any extra complexity, when introduced, is fully justified by both
analysis and simulation results. The resulting \textit{Robust Partially Coupled
Networks} achieves feature enhancement and recognition simultaneously. It
allows for both the flexibility to combat the LR-HR domain mismatch, and the
robustness to outliers. Finally, the effectiveness of the proposed models is
evaluated on three different VLRR tasks, including face identification, digit
recognition and font recognition, all of which obtain very impressive
performances.
| Zhangyang Wang, Shiyu Chang, Yingzhen Yang, Ding Liu, and Thomas S.
Huang | null | 1601.04153 | null | null |
Brain-Inspired Deep Networks for Image Aesthetics Assessment | cs.CV cs.LG cs.NE | Image aesthetics assessment has been challenging due to its subjective
nature. Inspired by the scientific advances in the human visual perception and
neuroaesthetics, we design Brain-Inspired Deep Networks (BDN) for this task.
BDN first learns attributes through the parallel supervised pathways, on a
variety of selected feature dimensions. A high-level synthesis network is
trained to associate and transform those attributes into the overall aesthetics
rating. We then extend BDN to predicting the distribution of human ratings,
since aesthetics ratings are often subjective. Another highlight is our
first-of-its-kind study of label-preserving transformations in the context of
aesthetics assessment, which leads to an effective data augmentation approach.
Experimental results on the AVA dataset show that our biological inspired and
task-specific BDN model gains significantly performance improvement, compared
to other state-of-the-art models with the same or higher parameter capacity.
| Zhangyang Wang, Shiyu Chang, Florin Dolcos, Diane Beck, Ding Liu, and
Thomas S. Huang | null | 1601.04155 | null | null |
On-line Bayesian System Identification | cs.SY cs.LG stat.AP stat.ML | We consider an on-line system identification setting, in which new data
become available at given time steps. In order to meet real-time estimation
requirements, we propose a tailored Bayesian system identification procedure,
in which the hyper-parameters are still updated through Marginal Likelihood
maximization, but after only one iteration of a suitable iterative optimization
algorithm. Both gradient methods and the EM algorithm are considered for the
Marginal Likelihood optimization. We compare this "1-step" procedure with the
standard one, in which the optimization method is run until convergence to a
local minimum. The experiments we perform confirm the effectiveness of the
approach we propose.
| Diego Romeres, Giulia Prando, Gianluigi Pillonetto, Alessandro Chiuso | null | 1601.04251 | null | null |
Learning the kernel matrix via predictive low-rank approximations | cs.LG stat.ML | Efficient and accurate low-rank approximations of multiple data sources are
essential in the era of big data. The scaling of kernel-based learning
algorithms to large datasets is limited by the O(n^2) computation and storage
complexity of the full kernel matrix, which is required by most of the recent
kernel learning algorithms.
We present the Mklaren algorithm to approximate multiple kernel matrices
learn a regression model, which is entirely based on geometrical concepts. The
algorithm does not require access to full kernel matrices yet it accounts for
the correlations between all kernels. It uses Incomplete Cholesky
decomposition, where pivot selection is based on least-angle regression in the
combined, low-dimensional feature space. The algorithm has linear complexity in
the number of data points and kernels. When explicit feature space induced by
the kernel can be constructed, a mapping from the dual to the primal Ridge
regression weights is used for model interpretation.
The Mklaren algorithm was tested on eight standard regression datasets. It
outperforms contemporary kernel matrix approximation approaches when learning
with multiple kernels. It identifies relevant kernels, achieving highest
explained variance than other multiple kernel learning methods for the same
number of iterations. Test accuracy, equivalent to the one using full kernel
matrices, was achieved with at significantly lower approximation ranks. A
difference in run times of two orders of magnitude was observed when either the
number of samples or kernels exceeds 3000.
| Martin Stra\v{z}ar, Toma\v{z} Curk | 10.1016/j.neucom.2019.02.030 | 1601.04366 | null | null |
Zero-error dissimilarity based classifiers | stat.ML cs.LG | We consider general non-Euclidean distance measures between real world
objects that need to be classified. It is assumed that objects are represented
by distances to other objects only. Conditions for zero-error dissimilarity
based classifiers are derived. Additional conditions are given under which the
zero-error decision boundary is a continues function of the distances to a
finite set of training samples. These conditions affect the objects as well as
the distance measure used. It is argued that they can be met in practice.
| Robert P.W. Duin, Elzbieta Pekalska | null | 1601.04451 | null | null |
Bandit Structured Prediction for Learning from Partial Feedback in
Statistical Machine Translation | cs.CL cs.LG | We present an approach to structured prediction from bandit feedback, called
Bandit Structured Prediction, where only the value of a task loss function at a
single predicted point, instead of a correct structure, is observed in
learning. We present an application to discriminative reranking in Statistical
Machine Translation (SMT) where the learning algorithm only has access to a
1-BLEU loss evaluation of a predicted translation instead of obtaining a gold
standard reference translation. In our experiment bandit feedback is obtained
by evaluating BLEU on reference translations without revealing them to the
algorithm. This can be thought of as a simulation of interactive machine
translation where an SMT system is personalized by a user who provides single
point feedback to predicted translations. Our experiments show that our
approach improves translation quality and is comparable to approaches that
employ more informative feedback in learning.
| Artem Sokolov and Stefan Riezler and Tanguy Urvoy | null | 1601.04468 | null | null |
Domain based classification | stat.ML cs.LG | The majority of traditional classification ru les minimizing the expected
probability of error (0-1 loss) are inappropriate if the class probability
distributions are ill-defined or impossible to estimate. We argue that in such
cases class domains should be used instead of class distributions or densities
to construct a reliable decision function. Proposals are presented for some
evaluation criteria and classifier learning schemes, illustrated by an example.
| Robert P.W. Duin, Elzbieta Pekalska | null | 1601.04530 | null | null |
Incremental Semiparametric Inverse Dynamics Learning | stat.ML cs.LG cs.RO | This paper presents a novel approach for incremental semiparametric inverse
dynamics learning. In particular, we consider the mixture of two approaches:
Parametric modeling based on rigid body dynamics equations and nonparametric
modeling based on incremental kernel methods, with no prior information on the
mechanical properties of the system. This yields to an incremental
semiparametric approach, leveraging the advantages of both the parametric and
nonparametric models. We validate the proposed technique learning the dynamics
of one arm of the iCub humanoid robot.
| Raffaello Camoriano, Silvio Traversaro, Lorenzo Rosasco, Giorgio Metta
and Francesco Nori | 10.1109/ICRA.2016.7487177 | 1601.04549 | null | null |
SimpleDS: A Simple Deep Reinforcement Learning Dialogue System | cs.AI cs.LG | This paper presents 'SimpleDS', a simple and publicly available dialogue
system trained with deep reinforcement learning. In contrast to previous
reinforcement learning dialogue systems, this system avoids manual feature
engineering by performing action selection directly from raw text of the last
system and (noisy) user responses. Our initial results, in the restaurant
domain, show that it is indeed possible to induce reasonable dialogue behaviour
with an approach that aims for high levels of automation in dialogue control
for intelligent interactive agents.
| Heriberto Cuay\'ahuitl | null | 1601.04574 | null | null |
Nonparametric Bayesian Storyline Detection from Microtexts | cs.CL cs.LG | News events and social media are composed of evolving storylines, which
capture public attention for a limited period of time. Identifying storylines
requires integrating temporal and linguistic information, and prior work takes
a largely heuristic approach. We present a novel online non-parametric Bayesian
framework for storyline detection, using the distance-dependent Chinese
Restaurant Process (dd-CRP). To ensure efficient linear-time inference, we
employ a fixed-lag Gibbs sampling procedure, which is novel for the dd-CRP. We
evaluate on the TREC Twitter Timeline Generation (TTG), obtaining encouraging
results: despite using a weak baseline retrieval model, the dd-CRP story
clustering method is competitive with the best entries in the 2014 TTG task.
| Vinodh Krishnan and Jacob Eisenstein | null | 1601.04580 | null | null |
Sparse Convex Clustering | stat.ME cs.LG stat.ML | Convex clustering, a convex relaxation of k-means clustering and hierarchical
clustering, has drawn recent attentions since it nicely addresses the
instability issue of traditional nonconvex clustering methods. Although its
computational and statistical properties have been recently studied, the
performance of convex clustering has not yet been investigated in the
high-dimensional clustering scenario, where the data contains a large number of
features and many of them carry no information about the clustering structure.
In this paper, we demonstrate that the performance of convex clustering could
be distorted when the uninformative features are included in the clustering. To
overcome it, we introduce a new clustering method, referred to as Sparse Convex
Clustering, to simultaneously cluster observations and conduct feature
selection. The key idea is to formulate convex clustering in a form of
regularization, with an adaptive group-lasso penalty term on cluster centers.
In order to optimally balance the tradeoff between the cluster fitting and
sparsity, a tuning criterion based on clustering stability is developed. In
theory, we provide an unbiased estimator for the degrees of freedom of the
proposed sparse convex clustering method. Finally, the effectiveness of the
sparse convex clustering is examined through a variety of numerical experiments
and a real data application.
| Binhuan Wang, Yilong Zhang, Will Wei Sun, Yixin Fang | 10.1080/10618600.2017.1377081 | 1601.04586 | null | null |
Spectral Theory of Unsigned and Signed Graphs. Applications to Graph
Clustering: a Survey | cs.LG cs.DS | This is a survey of the method of graph cuts and its applications to graph
clustering of weighted unsigned and signed graphs. I provide a fairly thorough
treatment of the method of normalized graph cuts, a deeply original method due
to Shi and Malik, including complete proofs. The main thrust of this paper is
the method of normalized cuts. I give a detailed account for K = 2 clusters,
and also for K > 2 clusters, based on the work of Yu and Shi. I also show how
both graph drawing and normalized cut K-clustering can be easily generalized to
handle signed graphs, which are weighted graphs in which the weight matrix W
may have negative coefficients. Intuitively, negative coefficients indicate
distance or dissimilarity. The solution is to replace the degree matrix by the
matrix in which absolute values of the weights are used, and to replace the
Laplacian by the Laplacian with the new degree matrix of absolute values. As
far as I know, the generalization of K-way normalized clustering to signed
graphs is new. Finally, I show how the method of ratio cuts, in which a cut is
normalized by the size of the cluster rather than its volume, is just a special
case of normalized cuts.
| Jean Gallier | null | 1601.04692 | null | null |
Sub-Sampled Newton Methods I: Globally Convergent Algorithms | math.OC cs.LG stat.ML | Large scale optimization problems are ubiquitous in machine learning and data
analysis and there is a plethora of algorithms for solving such problems. Many
of these algorithms employ sub-sampling, as a way to either speed up the
computations and/or to implicitly implement a form of statistical
regularization. In this paper, we consider second-order iterative optimization
algorithms and we provide bounds on the convergence of the variants of Newton's
method that incorporate uniform sub-sampling as a means to estimate the
gradient and/or Hessian. Our bounds are non-asymptotic and quantitative. Our
algorithms are global and are guaranteed to converge from any initial iterate.
Using random matrix concentration inequalities, one can sub-sample the
Hessian to preserve the curvature information. Our first algorithm incorporates
Hessian sub-sampling while using the full gradient. We also give additional
convergence results for when the sub-sampled Hessian is regularized by
modifying its spectrum or ridge-type regularization. Next, in addition to
Hessian sub-sampling, we also consider sub-sampling the gradient as a way to
further reduce the computational complexity per iteration. We use approximate
matrix multiplication results from randomized numerical linear algebra to
obtain the proper sampling strategy. In all these algorithms, computing the
update boils down to solving a large scale linear system, which can be
computationally expensive. As a remedy, for all of our algorithms, we also give
global convergence results for the case of inexact updates where such linear
system is solved only approximately.
This paper has a more advanced companion paper, [42], in which we demonstrate
that, by doing a finer-grained analysis, we can get problem-independent bounds
for local convergence of these algorithms and explore trade-offs to improve
upon the basic results of the present paper.
| Farbod Roosta-Khorasani and Michael W. Mahoney | null | 1601.04737 | null | null |
Sub-Sampled Newton Methods II: Local Convergence Rates | math.OC cs.LG stat.ML | Many data-fitting applications require the solution of an optimization
problem involving a sum of large number of functions of high dimensional
parameter. Here, we consider the problem of minimizing a sum of $n$ functions
over a convex constraint set $\mathcal{X} \subseteq \mathbb{R}^{p}$ where both
$n$ and $p$ are large. In such problems, sub-sampling as a way to reduce $n$
can offer great amount of computational efficiency.
Within the context of second order methods, we first give quantitative local
convergence results for variants of Newton's method where the Hessian is
uniformly sub-sampled. Using random matrix concentration inequalities, one can
sub-sample in a way that the curvature information is preserved. Using such
sub-sampling strategy, we establish locally Q-linear and Q-superlinear
convergence rates. We also give additional convergence results for when the
sub-sampled Hessian is regularized by modifying its spectrum or Levenberg-type
regularization.
Finally, in addition to Hessian sub-sampling, we consider sub-sampling the
gradient as way to further reduce the computational complexity per iteration.
We use approximate matrix multiplication results from randomized numerical
linear algebra (RandNLA) to obtain the proper sampling strategy and we
establish locally R-linear convergence rates. In such a setting, we also show
that a very aggressive sample size increase results in a R-superlinearly
convergent algorithm.
While the sample size depends on the condition number of the problem, our
convergence rates are problem-independent, i.e., they do not depend on the
quantities related to the problem. Hence, our analysis here can be used to
complement the results of our basic framework from the companion paper, [38],
by exploring algorithmic trade-offs that are important in practice.
| Farbod Roosta-Khorasani and Michael W. Mahoney | null | 1601.04738 | null | null |
Improved Sampling Techniques for Learning an Imbalanced Data Set | cs.LG | This paper presents the performance of a classifier built using the stackingC
algorithm in nine different data sets. Each data set is generated using a
sampling technique applied on the original imbalanced data set. Five new
sampling techniques are proposed in this paper (i.e., SMOTERandRep, Lax Random
Oversampling, Lax Random Undersampling, Combined-Lax Random Oversampling
Undersampling, and Combined-Lax Random Undersampling Oversampling) that were
based on the three sampling techniques (i.e., Random Undersampling, Random
Oversampling, and Synthetic Minority Oversampling Technique) usually used as
solutions in imbalance learning. The metrics used to evaluate the classifier's
performance were F-measure and G-mean. F-measure determines the performance of
the classifier for every class, while G-mean measures the overall performance
of the classifier. The results using F-measure showed that for the data without
a sampling technique, the classifier's performance is good only for the
majority class. It also showed that among the eight sampling techniques, RU and
LRU have the worst performance while other techniques (i.e., RO, C-LRUO and
C-LROU) performed well only on some classes. The best performing techniques in
all data sets were SMOTE, SMOTERandRep, and LRO having the lowest F-measure
values between 0.5 and 0.65. The results using G-mean showed that the
oversampling technique that attained the highest G-mean value is LRO (0.86),
next is C-LROU (0.85), then SMOTE (0.84) and finally is SMOTERandRep (0.83).
Combining the result of the two metrics (F-measure and G-mean), only the three
sampling techniques are considered as good performing (i.e., LRO, SMOTE, and
SMOTERandRep).
| Maureen Lyndel C. Lauron, Jaderick P. Pabico | null | 1601.04756 | null | null |
Top-N Recommender System via Matrix Completion | cs.IR cs.AI cs.LG stat.ML | Top-N recommender systems have been investigated widely both in industry and
academia. However, the recommendation quality is far from satisfactory. In this
paper, we propose a simple yet promising algorithm. We fill the user-item
matrix based on a low-rank assumption and simultaneously keep the original
information. To do that, a nonconvex rank relaxation rather than the nuclear
norm is adopted to provide a better rank approximation and an efficient
optimization strategy is designed. A comprehensive set of experiments on real
datasets demonstrates that our method pushes the accuracy of Top-N
recommendation to a new level.
| Zhao Kang, Chong Peng, Qiang Cheng | null | 1601.04800 | null | null |
Understanding Deep Convolutional Networks | stat.ML cs.CV cs.LG | Deep convolutional networks provide state of the art classifications and
regressions results over many high-dimensional problems. We review their
architecture, which scatters data with a cascade of linear filter weights and
non-linearities. A mathematical framework is introduced to analyze their
properties. Computations of invariants involve multiscale contractions, the
linearization of hierarchical symmetries, and sparse separations. Applications
are discussed.
| St\'ephane Mallat | 10.1098/rsta.2015.0203 | 1601.04920 | null | null |
A Theory of Local Matching: SIFT and Beyond | cs.CV cs.LG | Why has SIFT been so successful? Why its extension, DSP-SIFT, can further
improve SIFT? Is there a theory that can explain both? How can such theory
benefit real applications? Can it suggest new algorithms with reduced
computational complexity or new descriptors with better accuracy for matching?
We construct a general theory of local descriptors for visual matching. Our
theory relies on concepts in energy minimization and heat diffusion. We show
that SIFT and DSP-SIFT approximate the solution the theory suggests. In
particular, DSP-SIFT gives a better approximation to the theoretical solution;
justifying why DSP-SIFT outperforms SIFT. Using the developed theory, we derive
new descriptors that have fewer parameters and are potentially better in
handling affine deformations.
| Hossein Mobahi, Stefano Soatto | null | 1601.05116 | null | null |
Habits vs Environment: What really causes asthma? | cs.CY cs.LG | Despite considerable number of studies on risk factors for asthma onset, very
little is known about their relative importance. To have a full picture of
these factors, both categories, personal and environmental data, have to be
taken into account simultaneously, which is missing in previous studies. We
propose a framework to rank the risk factors from heterogeneous data sources of
the two categories. Established on top of EventShop and Personal EventShop,
this framework extracts about 400 features, and analyzes them by employing a
gradient boosting tree. The features come from sources including personal
profile and life-event data, and environmental data on air pollution, weather
and PM2.5 emission sources. The top ranked risk factors derived from our
framework agree well with the general medical consensus. Thus, our framework is
a reliable approach, and the discovered rankings of relative importance of risk
factors can provide insights for the prevention of asthma.
| Mengfan Tang, Pranav Agrawal, Ramesh Jain | null | 1601.05141 | null | null |
Data-driven Rank Breaking for Efficient Rank Aggregation | cs.LG stat.ML | Rank aggregation systems collect ordinal preferences from individuals to
produce a global ranking that represents the social preference. Rank-breaking
is a common practice to reduce the computational complexity of learning the
global ranking. The individual preferences are broken into pairwise comparisons
and applied to efficient algorithms tailored for independent paired
comparisons. However, due to the ignored dependencies in the data, naive
rank-breaking approaches can result in inconsistent estimates. The key idea to
produce accurate and consistent estimates is to treat the pairwise comparisons
unequally, depending on the topology of the collected data. In this paper, we
provide the optimal rank-breaking estimator, which not only achieves
consistency but also achieves the best error bound. This allows us to
characterize the fundamental tradeoff between accuracy and complexity. Further,
the analysis identifies how the accuracy depends on the spectral gap of a
corresponding comparison graph.
| Ashish Khetan and Sewoong Oh | null | 1601.05495 | null | null |
Incremental Spectral Sparsification for Large-Scale Graph-Based
Semi-Supervised Learning | stat.ML cs.LG | While the harmonic function solution performs well in many semi-supervised
learning (SSL) tasks, it is known to scale poorly with the number of samples.
Recent successful and scalable methods, such as the eigenfunction method focus
on efficiently approximating the whole spectrum of the graph Laplacian
constructed from the data. This is in contrast to various subsampling and
quantization methods proposed in the past, which may fail in preserving the
graph spectra. However, the impact of the approximation of the spectrum on the
final generalization error is either unknown, or requires strong assumptions on
the data. In this paper, we introduce Sparse-HFS, an efficient
edge-sparsification algorithm for SSL. By constructing an edge-sparse and
spectrally similar graph, we are able to leverage the approximation guarantees
of spectral sparsification methods to bound the generalization error of
Sparse-HFS. As a result, we obtain a theoretically-grounded approximation
scheme for graph-based SSL that also empirically matches the performance of
known large-scale methods.
| Daniele Calandriello, Alessandro Lazaric, Michal Valko and Ioannis
Koutis | null | 1601.05675 | null | null |
A Confidence-Based Approach for Balancing Fairness and Accuracy | cs.LG cs.CY | We study three classical machine learning algorithms in the context of
algorithmic fairness: adaptive boosting, support vector machines, and logistic
regression. Our goal is to maintain the high accuracy of these learning
algorithms while reducing the degree to which they discriminate against
individuals because of their membership in a protected group.
Our first contribution is a method for achieving fairness by shifting the
decision boundary for the protected group. The method is based on the theory of
margins for boosting. Our method performs comparably to or outperforms previous
algorithms in the fairness literature in terms of accuracy and low
discrimination, while simultaneously allowing for a fast and transparent
quantification of the trade-off between bias and error.
Our second contribution addresses the shortcomings of the bias-error
trade-off studied in most of the algorithmic fairness literature. We
demonstrate that even hopelessly naive modifications of a biased algorithm,
which cannot be reasonably said to be fair, can still achieve low bias and high
accuracy. To help to distinguish between these naive algorithms and more
sensible algorithms we propose a new measure of fairness, called resilience to
random bias (RRB). We demonstrate that RRB distinguishes well between our naive
and sensible fairness algorithms. RRB together with bias and accuracy provides
a more complete picture of the fairness of an algorithm.
| Benjamin Fish, Jeremy Kun, \'Ad\'am D. Lelkes | null | 1601.05764 | null | null |
Local Network Community Detection with Continuous Optimization of
Conductance and Weighted Kernel K-Means | cs.SI cs.LG stat.ML | Local network community detection is the task of finding a single community
of nodes concentrated around few given seed nodes in a localized way.
Conductance is a popular objective function used in many algorithms for local
community detection. This paper studies a continuous relaxation of conductance.
We show that continuous optimization of this objective still leads to discrete
communities. We investigate the relation of conductance with weighted kernel
k-means for a single community, which leads to the introduction of a new
objective function, $\sigma$-conductance. Conductance is obtained by setting
$\sigma$ to $0$. Two algorithms, EMc and PGDc, are proposed to locally optimize
$\sigma$-conductance and automatically tune the parameter $\sigma$. They are
based on expectation maximization and projected gradient descent, respectively.
We prove locality and give performance guarantees for EMc and PGDc for a class
of dense and well separated communities centered around the seeds. Experiments
are conducted on networks with ground-truth communities, comparing to
state-of-the-art graph diffusion algorithms for conductance optimization. On
large graphs, results indicate that EMc and PGDc stay localized and produce
communities most similar to the ground, while graph diffusion algorithms
generate large communities of lower quality.
| Twan van Laarhoven, Elena Marchiori | null | 1601.05775 | null | null |
When is Clustering Perturbation Robust? | cs.LG cs.CV | Clustering is a fundamental data mining tool that aims to divide data into
groups of similar items. Generally, intuition about clustering reflects the
ideal case -- exact data sets endowed with flawless dissimilarity between
individual instances.
In practice however, these cases are in the minority, and clustering
applications are typically characterized by noisy data sets with approximate
pairwise dissimilarities. As such, the efficacy of clustering methods in
practical applications necessitates robustness to perturbations.
In this paper, we perform a formal analysis of perturbation robustness,
revealing that the extent to which algorithms can exhibit this desirable
characteristic is inherently limited, and identifying the types of structures
that allow popular clustering paradigms to discover meaningful clusters in
spite of faulty data.
| Margareta Ackerman and Jarrod Moore | null | 1601.05900 | null | null |
Exploiting Low-dimensional Structures to Enhance DNN Based Acoustic
Modeling in Speech Recognition | cs.CL cs.LG stat.ML | We propose to model the acoustic space of deep neural network (DNN)
class-conditional posterior probabilities as a union of low-dimensional
subspaces. To that end, the training posteriors are used for dictionary
learning and sparse coding. Sparse representation of the test posteriors using
this dictionary enables projection to the space of training data. Relying on
the fact that the intrinsic dimensions of the posterior subspaces are indeed
very small and the matrix of all posteriors belonging to a class has a very low
rank, we demonstrate how low-dimensional structures enable further enhancement
of the posteriors and rectify the spurious errors due to mismatch conditions.
The enhanced acoustic modeling method leads to improvements in continuous
speech recognition task using hybrid DNN-HMM (hidden Markov model) framework in
both clean and noisy conditions, where upto 15.4% relative reduction in word
error rate (WER) is achieved.
| Pranay Dighe, Gil Luyet, Afsaneh Asaei and Herve Bourlard | 10.1109/ICASSP.2016.7472767 | 1601.05936 | null | null |
Recommender systems inspired by the structure of quantum theory | cs.LG cs.IT math.IT math.OC quant-ph stat.ML | Physicists use quantum models to describe the behavior of physical systems.
Quantum models owe their success to their interpretability, to their relation
to probabilistic models (quantization of classical models) and to their high
predictive power. Beyond physics, these properties are valuable in general data
science. This motivates the use of quantum models to analyze general
nonphysical datasets. Here we provide both empirical and theoretical insights
into the application of quantum models in data science. In the theoretical part
of this paper, we firstly show that quantum models can be exponentially more
efficient than probabilistic models because there exist datasets that admit
low-dimensional quantum models and only exponentially high-dimensional
probabilistic models. Secondly, we explain in what sense quantum models realize
a useful relaxation of compressed probabilistic models. Thirdly, we show that
sparse datasets admit low-dimensional quantum models and finally, we introduce
a method to compute hierarchical orderings of properties of users (e.g.,
personality traits) and items (e.g., genres of movies). In the empirical part
of the paper, we evaluate quantum models in item recommendation and observe
that the predictive power of quantum-inspired recommender systems can compete
with state-of-the-art recommender systems like SVD++ and PureSVD. Furthermore,
we make use of the interpretability of quantum models by computing hierarchical
orderings of properties of users and items. This work establishes a connection
between data science (item recommendation), information theory (communication
complexity), mathematical programming (positive semidefinite factorizations)
and physics (quantum models).
| Cyril Stark | null | 1601.06035 | null | null |
Bitwise Neural Networks | cs.LG cs.AI cs.NE | Based on the assumption that there exists a neural network that efficiently
represents a set of Boolean functions between all binary inputs and outputs, we
propose a process for developing and deploying neural networks whose weight
parameters, bias terms, input, and intermediate hidden layer output signals,
are all binary-valued, and require only basic bit logic for the feedforward
pass. The proposed Bitwise Neural Network (BNN) is especially suitable for
resource-constrained environments, since it replaces either floating or
fixed-point arithmetic with significantly more efficient bitwise operations.
Hence, the BNN requires for less spatial complexity, less memory bandwidth, and
less power consumption in hardware. In order to design such networks, we
propose to add a few training schemes, such as weight compression and noisy
backpropagation, which result in a bitwise network that performs almost as well
as its corresponding real-valued network. We test the proposed network on the
MNIST dataset, represented using binary features, and show that BNNs result in
competitive performance while offering dramatic computational savings.
| Minje Kim and Paris Smaragdis | null | 1601.06071 | null | null |
Learning Minimum Volume Sets and Anomaly Detectors from KNN Graphs | stat.ML cs.LG | We propose a non-parametric anomaly detection algorithm for high dimensional
data. We first rank scores derived from nearest neighbor graphs on $n$-point
nominal training data. We then train limited complexity models to imitate these
scores based on the max-margin learning-to-rank framework. A test-point is
declared as an anomaly at $\alpha$-false alarm level if the predicted score is
in the $\alpha$-percentile. The resulting anomaly detector is shown to be
asymptotically optimal in that for any false alarm rate $\alpha$, its decision
region converges to the $\alpha$-percentile minimum volume level set of the
unknown underlying density. In addition, we test both the statistical
performance and computational efficiency of our algorithm on a number of
synthetic and real-data experiments. Our results demonstrate the superiority of
our algorithm over existing $K$-NN based anomaly detection algorithms, with
significant computational savings.
| Jonathan Root, Venkatesh Saligrama, Jing Qian | null | 1601.06105 | null | null |
A Mathematical Formalization of Hierarchical Temporal Memory's Spatial
Pooler | stat.ML cs.LG q-bio.NC | Hierarchical temporal memory (HTM) is an emerging machine learning algorithm,
with the potential to provide a means to perform predictions on spatiotemporal
data. The algorithm, inspired by the neocortex, currently does not have a
comprehensive mathematical framework. This work brings together all aspects of
the spatial pooler (SP), a critical learning component in HTM, under a single
unifying framework. The primary learning mechanism is explored, where a maximum
likelihood estimator for determining the degree of permanence update is
proposed. The boosting mechanisms are studied and found to be only relevant
during the initial few iterations of the network. Observations are made
relating HTM to well-known algorithms such as competitive learning and
attribute bagging. Methods are provided for using the SP for classification as
well as dimensionality reduction. Empirical evidence verifies that given the
proper parameterizations, the SP may be used for feature learning.
| James Mnatzaganian, Ernest Fokou\'e, and Dhireesha Kudithipudi | null | 1601.06116 | null | null |
On the Latent Variable Interpretation in Sum-Product Networks | cs.AI cs.LG | One of the central themes in Sum-Product networks (SPNs) is the
interpretation of sum nodes as marginalized latent variables (LVs). This
interpretation yields an increased syntactic or semantic structure, allows the
application of the EM algorithm and to efficiently perform MPE inference. In
literature, the LV interpretation was justified by explicitly introducing the
indicator variables corresponding to the LVs' states. However, as pointed out
in this paper, this approach is in conflict with the completeness condition in
SPNs and does not fully specify the probabilistic model. We propose a remedy
for this problem by modifying the original approach for introducing the LVs,
which we call SPN augmentation. We discuss conditional independencies in
augmented SPNs, formally establish the probabilistic interpretation of the
sum-weights and give an interpretation of augmented SPNs as Bayesian networks.
Based on these results, we find a sound derivation of the EM algorithm for
SPNs. Furthermore, the Viterbi-style algorithm for MPE proposed in literature
was never proven to be correct. We show that this is indeed a correct
algorithm, when applied to selective SPNs, and in particular when applied to
augmented SPNs. Our theoretical results are confirmed in experiments on
synthetic data and 103 real-world datasets.
| Robert Peharz, Robert Gens, Franz Pernkopf, Pedro Domingos | null | 1601.06180 | null | null |
Universal Collaboration Strategies for Signal Detection: A Sparse
Learning Approach | cs.LG stat.ML | This paper considers the problem of high dimensional signal detection in a
large distributed network whose nodes can collaborate with their one-hop
neighboring nodes (spatial collaboration). We assume that only a small subset
of nodes communicate with the Fusion Center (FC). We design optimal
collaboration strategies which are universal for a class of deterministic
signals. By establishing the equivalence between the collaboration strategy
design problem and sparse PCA, we solve the problem efficiently and evaluate
the impact of collaboration on detection performance.
| Prashant Khanduri, Bhavya Kailkhura, Jayaraman J. Thiagarajan, Pramod
K. Varshney | 10.1109/LSP.2016.2601911 | 1601.06201 | null | null |
Rectified Gaussian Scale Mixtures and the Sparse Non-Negative Least
Squares Problem | cs.LG stat.ML | In this paper, we develop a Bayesian evidence maximization framework to solve
the sparse non-negative least squares (S-NNLS) problem. We introduce a family
of probability densities referred to as the Rectified Gaussian Scale Mixture
(R- GSM) to model the sparsity enforcing prior distribution for the solution.
The R-GSM prior encompasses a variety of heavy-tailed densities such as the
rectified Laplacian and rectified Student- t distributions with a proper choice
of the mixing density. We utilize the hierarchical representation induced by
the R-GSM prior and develop an evidence maximization framework based on the
Expectation-Maximization (EM) algorithm. Using the EM based method, we estimate
the hyper-parameters and obtain a point estimate for the solution. We refer to
the proposed method as rectified sparse Bayesian learning (R-SBL). We provide
four R- SBL variants that offer a range of options for computational complexity
and the quality of the E-step computation. These methods include the Markov
chain Monte Carlo EM, linear minimum mean-square-error estimation, approximate
message passing and a diagonal approximation. Using numerical experiments, we
show that the proposed R-SBL method outperforms existing S-NNLS solvers in
terms of both signal and support recovery performance, and is also very robust
against the structure of the design matrix.
| Alican Nalci, Igor Fedorov, Maher Al-Shoukairi, Thomas T. Liu, and
Bhaskar D. Rao | null | 1601.06207 | null | null |
Divide and Conquer Local Average Regression | cs.LG math.ST stat.TH | The divide and conquer strategy, which breaks a massive data set into a se-
ries of manageable data blocks, and then combines the independent results of
data blocks to obtain a final decision, has been recognized as a
state-of-the-art method to overcome challenges of massive data analysis. In
this paper, we merge the divide and conquer strategy with local average
regression methods to infer the regressive relationship of input-output pairs
from a massive data set. After theoretically analyzing the pros and cons, we
find that although the divide and conquer local average regression can reach
the optimal learning rate, the restric- tion to the number of data blocks is a
bit strong, which makes it only feasible for small number of data blocks. We
then propose two variants to lessen (or remove) this restriction. Our results
show that these variants can achieve the optimal learning rate with much milder
restriction (or without such restriction). Extensive experimental studies are
carried out to verify our theoretical assertions.
| Xiangyu Chang, Shaobo Lin and Yao Wang | null | 1601.06239 | null | null |
Automatic recognition of element classes and boundaries in the birdsong
with variable sequences | q-bio.NC cs.LG cs.SD | Researches on sequential vocalization often require analysis of vocalizations
in long continuous sounds. In such studies as developmental ones or studies
across generations in which days or months of vocalizations must be analyzed,
methods for automatic recognition would be strongly desired. Although methods
for automatic speech recognition for application purposes have been intensively
studied, blindly applying them for biological purposes may not be an optimal
solution. This is because, unlike human speech recognition, analysis of
sequential vocalizations often requires accurate extraction of timing
information. In the present study we propose automated systems suitable for
recognizing birdsong, one of the most intensively investigated sequential
vocalizations, focusing on the three properties of the birdsong. First, a song
is a sequence of vocal elements, called notes, which can be grouped into
categories. Second, temporal structure of birdsong is precisely controlled,
meaning that temporal information is important in song analysis. Finally, notes
are produced according to certain probabilistic rules, which may facilitate the
accurate song recognition. We divided the procedure of song recognition into
three sub-steps: local classification, boundary detection, and global
sequencing, each of which corresponds to each of the three properties of
birdsong. We compared the performances of several different ways to arrange
these three steps. As results, we demonstrated a hybrid model of a deep neural
network and a hidden Markov model is effective in recognizing birdsong with
variable note sequences. We propose suitable arrangements of methods according
to whether accurate boundary detection is needed. Also we designed the new
measure to jointly evaluate the accuracy of note classification and boundary
detection. Our methods should be applicable, with small modification and
tuning, to the songs in other species that hold the three properties of the
sequential vocalization.
| Takuya Koumura and Kazuo Okanoya | 10.1371/journal.pone.0159188 | 1601.06248 | null | null |
Minimax Lower Bounds for Linear Independence Testing | stat.ML cs.IT cs.LG math.IT math.ST stat.TH | Linear independence testing is a fundamental information-theoretic and
statistical problem that can be posed as follows: given $n$ points
$\{(X_i,Y_i)\}^n_{i=1}$ from a $p+q$ dimensional multivariate distribution
where $X_i \in \mathbb{R}^p$ and $Y_i \in\mathbb{R}^q$, determine whether $a^T
X$ and $b^T Y$ are uncorrelated for every $a \in \mathbb{R}^p, b\in
\mathbb{R}^q$ or not. We give minimax lower bound for this problem (when $p+q,n
\to \infty$, $(p+q)/n \leq \kappa < \infty$, without sparsity assumptions). In
summary, our results imply that $n$ must be at least as large as $\sqrt
{pq}/\|\Sigma_{XY}\|_F^2$ for any procedure (test) to have non-trivial power,
where $\Sigma_{XY}$ is the cross-covariance matrix of $X,Y$. We also provide
some evidence that the lower bound is tight, by connections to two-sample
testing and regression in specific settings.
| Aaditya Ramdas, David Isenberg, Aarti Singh, Larry Wasserman | null | 1601.06259 | null | null |
Fast Binary Embedding via Circulant Downsampled Matrix -- A
Data-Independent Approach | cs.IT cs.CV cs.LG math.IT | Binary embedding of high-dimensional data aims to produce low-dimensional
binary codes while preserving discriminative power. State-of-the-art methods
often suffer from high computation and storage costs. We present a simple and
fast embedding scheme by first downsampling N-dimensional data into
M-dimensional data and then multiplying the data with an MxM circulant matrix.
Our method requires O(N +M log M) computation and O(N) storage costs. We prove
if data have sparsity, our scheme can achieve similarity-preserving well.
Experiments further demonstrate that though our method is cost-effective and
fast, it still achieves comparable performance in image applications.
| Sung-Hsien Hsieh, Chun-Shien Lu, Soo-Chang Pei | null | 1601.06342 | null | null |
QUOTE: "Querying" Users as Oracles in Tag Engines - A Semi-Supervised
Learning Approach to Personalized Image Tagging | cs.IR cs.LG cs.MM cs.SI | One common trend in image tagging research is to focus on visually relevant
tags, and this tends to ignore the personal and social aspect of tags,
especially on photoblogging websites such as Flickr. Previous work has
correctly identified that many of the tags that users provide on images are not
visually relevant (i.e. representative of the salient content in the image) and
they go on to treat such tags as noise, ignoring that the users chose to
provide those tags over others that could have been more visually relevant.
Another common assumption about user generated tags for images is that the
order of these tags provides no useful information for the prediction of tags
on future images. This assumption also tends to define usefulness in terms of
what is visually relevant to the image. For general tagging or labeling
applications that focus on providing visual information about image content,
these assumptions are reasonable, but when considering personalized image
tagging applications, these assumptions are at best too rigid, ignoring user
choice and preferences.
We challenge the aforementioned assumptions, and provide a machine learning
approach to the problem of personalized image tagging with the following
contributions: 1.) We reformulate the personalized image tagging problem as a
search/retrieval ranking problem, 2.) We leverage the order of tags, which does
not always reflect visual relevance, provided by the user in the past as a cue
to their tag preferences, similar to click data, 3.) We propose a technique to
augment sparse user tag data (semi-supervision), and 4.) We demonstrate the
efficacy of our method on a subset of Flickr images, showing improvement over
previous state-of-art methods.
| Amandianeze O. Nwana and Tsuhan Chen | 10.1109/ISM.2016.0016 | 1601.06440 | null | null |
A new correlation clustering method for cancer mutation analysis | cs.LG q-bio.QM | Cancer genomes exhibit a large number of different alterations that affect
many genes in a diverse manner. It is widely believed that these alterations
follow combinatorial patterns that have a strong connection with the underlying
molecular interaction networks and functional pathways. A better understanding
of the generative mechanisms behind the mutation rules and their influence on
gene communities is of great importance for the process of driver mutations
discovery and for identification of network modules related to cancer
development and progression. We developed a new method for cancer mutation
pattern analysis based on a constrained form of correlation clustering.
Correlation clustering is an agnostic learning method that can be used for
general community detection problems in which the number of communities or
their structure is not known beforehand. The resulting algorithm, named $C^3$,
leverages mutual exclusivity of mutations, patient coverage, and driver network
concentration principles; it accepts as its input a user determined combination
of heterogeneous patient data, such as that available from TCGA (including
mutation, copy number, and gene expression information), and creates a large
number of clusters containing mutually exclusive mutated genes in a particular
type of cancer. The cluster sizes may be required to obey some useful soft size
constraints, without impacting the computational complexity of the algorithm.
To test $C^3$, we performed a detailed analysis on TCGA breast cancer and
glioblastoma data and showed that our algorithm outperforms the
state-of-the-art CoMEt method in terms of discovering mutually exclusive gene
modules and identifying driver genes. Our $C^3$ method represents a unique tool
for efficient and reliable identification of mutation patterns and driver
pathways in large-scale cancer genomics studies.
| Jack P. Hou, Amin Emad, Gregory J. Puleo, Jian Ma, Olgica Milenkovic | null | 1601.06476 | null | null |
Robust Influence Maximization | cs.SI cs.LG | In this paper, we address the important issue of uncertainty in the edge
influence probability estimates for the well studied influence maximization
problem --- the task of finding $k$ seed nodes in a social network to maximize
the influence spread. We propose the problem of robust influence maximization,
which maximizes the worst-case ratio between the influence spread of the chosen
seed set and the optimal seed set, given the uncertainty of the parameter
input. We design an algorithm that solves this problem with a
solution-dependent bound. We further study uniform sampling and adaptive
sampling methods to effectively reduce the uncertainty on parameters and
improve the robustness of the influence maximization task. Our empirical
results show that parameter uncertainty may greatly affect influence
maximization performance and prior studies that learned influence probabilities
could lead to poor performance in robust influence maximization due to
relatively large uncertainty in parameter estimates, and information cascade
based adaptive sampling method may be an effective way to improve the
robustness of influence maximization.
| Wei Chen, Tian Lin, Zihan Tan, Mingfei Zhao, Xuren Zhou | null | 1601.06551 | null | null |
Character-Level Incremental Speech Recognition with Recurrent Neural
Networks | cs.CL cs.LG cs.NE | In real-time speech recognition applications, the latency is an important
issue. We have developed a character-level incremental speech recognition (ISR)
system that responds quickly even during the speech, where the hypotheses are
gradually improved while the speaking proceeds. The algorithm employs a
speech-to-character unidirectional recurrent neural network (RNN), which is
end-to-end trained with connectionist temporal classification (CTC), and an
RNN-based character-level language model (LM). The output values of the
CTC-trained RNN are character-level probabilities, which are processed by beam
search decoding. The RNN LM augments the decoding by providing long-term
dependency information. We propose tree-based online beam search with
additional depth-pruning, which enables the system to process infinitely long
input speech with low latency. This system not only responds quickly on speech
but also can dictate out-of-vocabulary (OOV) words according to pronunciation.
The proposed model achieves the word error rate (WER) of 8.90% on the Wall
Street Journal (WSJ) Nov'92 20K evaluation set when trained on the WSJ SI-284
training set.
| Kyuyeon Hwang, Wonyong Sung | 10.1109/ICASSP.2016.7472696 | 1601.06581 | null | null |
Expected Similarity Estimation for Large-Scale Batch and Streaming
Anomaly Detection | cs.LG cs.AI | We present a novel algorithm for anomaly detection on very large datasets and
data streams. The method, named EXPected Similarity Estimation (EXPoSE), is
kernel-based and able to efficiently compute the similarity between new data
points and the distribution of regular data. The estimator is formulated as an
inner product with a reproducing kernel Hilbert space embedding and makes no
assumption about the type or shape of the underlying data distribution. We show
that offline (batch) learning with EXPoSE can be done in linear time and online
(incremental) learning takes constant time per instance and model update.
Furthermore, EXPoSE can make predictions in constant time, while it requires
only constant memory. In addition, we propose different methodologies for
concept drift adaptation on evolving data streams. On several real datasets we
demonstrate that our approach can compete with state of the art algorithms for
anomaly detection while being an order of magnitude faster than most other
approaches.
| Markus Schneider and Wolfgang Ertel and Fabio Ramos | 10.1007/s10994-016-5567-7 | 1601.06602 | null | null |
A Taxonomy of Deep Convolutional Neural Nets for Computer Vision | cs.CV cs.LG cs.MM | Traditional architectures for solving computer vision problems and the degree
of success they enjoyed have been heavily reliant on hand-crafted features.
However, of late, deep learning techniques have offered a compelling
alternative -- that of automatically learning problem-specific features. With
this new paradigm, every problem in computer vision is now being re-examined
from a deep learning perspective. Therefore, it has become important to
understand what kind of deep networks are suitable for a given problem.
Although general surveys of this fast-moving paradigm (i.e. deep-networks)
exist, a survey specific to computer vision is missing. We specifically
consider one form of deep networks widely used in computer vision -
convolutional neural networks (CNNs). We start with "AlexNet" as our base CNN
and then examine the broad variations proposed over time to suit different
applications. We hope that our recipe-style survey will serve as a guide,
particularly for novice practitioners intending to use deep-learning techniques
for computer vision.
| Suraj Srinivas, Ravi Kiran Sarvadevabhatla, Konda Reddy Mopuri, Nikita
Prabhu, Srinivas S S Kruthiventi and R. Venkatesh Babu | 10.3389/frobt.2015.00036 | 1601.06615 | null | null |
Time-Varying Gaussian Process Bandit Optimization | stat.ML cs.LG | We consider the sequential Bayesian optimization problem with bandit
feedback, adopting a formulation that allows for the reward function to vary
with time. We model the reward function using a Gaussian process whose
evolution obeys a simple Markov model. We introduce two natural extensions of
the classical Gaussian process upper confidence bound (GP-UCB) algorithm. The
first, R-GP-UCB, resets GP-UCB at regular intervals. The second, TV-GP-UCB,
instead forgets about old data in a smooth fashion. Our main contribution
comprises of novel regret bounds for these algorithms, providing an explicit
characterization of the trade-off between the time horizon and the rate at
which the function varies. We illustrate the performance of the algorithms on
both synthetic and real data, and we find the gradual forgetting of TV-GP-UCB
to perform favorably compared to the sharp resetting of R-GP-UCB. Moreover,
both algorithms significantly outperform classical GP-UCB, since it treats
stale and fresh data equally.
| Ilija Bogunovic, Jonathan Scarlett, Volkan Cevher | null | 1601.06650 | null | null |
Conditional distribution variability measures for causality detection | stat.ML cs.LG | In this paper we derive variability measures for the conditional probability
distributions of a pair of random variables, and we study its application in
the inference of causal-effect relationships. We also study the combination of
the proposed measures with standard statistical measures in the the framework
of the ChaLearn cause-effect pair challenge. The developed model obtains an AUC
score of 0.82 on the final test database and ranked second in the challenge.
| Jos\'e A. R. Fonollosa | null | 1601.06680 | null | null |
Clustering from Sparse Pairwise Measurements | cs.SI cond-mat.dis-nn cs.LG | We consider the problem of grouping items into clusters based on few random
pairwise comparisons between the items. We introduce three closely related
algorithms for this task: a belief propagation algorithm approximating the
Bayes optimal solution, and two spectral algorithms based on the
non-backtracking and Bethe Hessian operators. For the case of two symmetric
clusters, we conjecture that these algorithms are asymptotically optimal in
that they detect the clusters as soon as it is information theoretically
possible to do so. We substantiate this claim for one of the spectral
approaches we introduce.
| Alaa Saade, Marc Lelarge, Florent Krzakala and Lenka Zdeborov\'a | 10.1109/ISIT.2016.7541405 | 1601.06683 | null | null |
A Robust UCB Scheme for Active Learning in Regression from Strategic
Crowds | cs.LG stat.ML | We study the problem of training an accurate linear regression model by
procuring labels from multiple noisy crowd annotators, under a budget
constraint. We propose a Bayesian model for linear regression in crowdsourcing
and use variational inference for parameter estimation. To minimize the number
of labels crowdsourced from the annotators, we adopt an active learning
approach. In this specific context, we prove the equivalence of well-studied
criteria of active learning like entropy minimization and expected error
reduction. Interestingly, we observe that we can decouple the problems of
identifying an optimal unlabeled instance and identifying an annotator to label
it. We observe a useful connection between the multi-armed bandit framework and
the annotator selection in active learning. Due to the nature of the
distribution of the rewards on the arms, we use the Robust Upper Confidence
Bound (UCB) scheme with truncated empirical mean estimator to solve the
annotator selection problem. This yields provable guarantees on the regret. We
further apply our model to the scenario where annotators are strategic and
design suitable incentives to induce them to put in their best efforts.
| Divya Padmanabhan, Satyanath Bhat, Dinesh Garg, Shirish Shevade, Y.
Narahari | null | 1601.06750 | null | null |
Pixel Recurrent Neural Networks | cs.CV cs.LG cs.NE | Modeling the distribution of natural images is a landmark problem in
unsupervised learning. This task requires an image model that is at once
expressive, tractable and scalable. We present a deep neural network that
sequentially predicts the pixels in an image along the two spatial dimensions.
Our method models the discrete probability of the raw pixel values and encodes
the complete set of dependencies in the image. Architectural novelties include
fast two-dimensional recurrent layers and an effective use of residual
connections in deep recurrent networks. We achieve log-likelihood scores on
natural images that are considerably better than the previous state of the art.
Our main results also provide benchmarks on the diverse ImageNet dataset.
Samples generated from the model appear crisp, varied and globally coherent.
| Aaron van den Oord, Nal Kalchbrenner, Koray Kavukcuoglu | null | 1601.06759 | null | null |
Very Efficient Training of Convolutional Neural Networks using Fast
Fourier Transform and Overlap-and-Add | cs.NE cs.LG | Convolutional neural networks (CNNs) are currently state-of-the-art for
various classification tasks, but are computationally expensive. Propagating
through the convolutional layers is very slow, as each kernel in each layer
must sequentially calculate many dot products for a single forward and backward
propagation which equates to $\mathcal{O}(N^{2}n^{2})$ per kernel per layer
where the inputs are $N \times N$ arrays and the kernels are $n \times n$
arrays. Convolution can be efficiently performed as a Hadamard product in the
frequency domain. The bottleneck is the transformation which has a cost of
$\mathcal{O}(N^{2}\log_2 N)$ using the fast Fourier transform (FFT). However,
the increase in efficiency is less significant when $N\gg n$ as is the case in
CNNs. We mitigate this by using the "overlap-and-add" technique reducing the
computational complexity to $\mathcal{O}(N^2\log_2 n)$ per kernel. This method
increases the algorithm's efficiency in both the forward and backward
propagation, reducing the training and testing time for CNNs. Our empirical
results show our method reduces computational time by a factor of up to 16.3
times the traditional convolution implementation for a 8 $\times$ 8 kernel and
a 224 $\times$ 224 image.
| Tyler Highlander and Andres Rodriguez | null | 1601.06815 | null | null |
Survey on the attention based RNN model and its applications in computer
vision | cs.CV cs.LG | The recurrent neural networks (RNN) can be used to solve the sequence to
sequence problem, where both the input and the output have sequential
structures. Usually there are some implicit relations between the structures.
However, it is hard for the common RNN model to fully explore the relations
between the sequences. In this survey, we introduce some attention based RNN
models which can focus on different parts of the input for each output item, in
order to explore and take advantage of the implicit relations between the input
and the output items. The different attention mechanisms are described in
detail. We then introduce some applications in computer vision which apply the
attention based RNN models. The superiority of the attention based RNN model is
shown by the experimental results. At last some future research directions are
given.
| Feng Wang, David M.J. Tax | null | 1601.06823 | null | null |
A Novel Memetic Feature Selection Algorithm | cs.LG | Feature selection is a problem of finding efficient features among all
features in which the final feature set can improve accuracy and reduce
complexity. In feature selection algorithms search strategies are key aspects.
Since feature selection is an NP-Hard problem; therefore heuristic algorithms
have been studied to solve this problem. In this paper, we have proposed a
method based on memetic algorithm to find an efficient feature subset for a
classification problem. It incorporates a filter method in the genetic
algorithm to improve classification performance and accelerates the search in
identifying core feature subsets. Particularly, the method adds or deletes a
feature from a candidate feature subset based on the multivariate feature
information. Empirical study on commonly data sets of the university of
California, Irvine shows that the proposed method outperforms existing methods.
| Mohadeseh Montazeri, Hamid Reza Naji, Mitra Montazeri, Ahmad Faraahi | null | 1601.06933 | null | null |
Unifying Adversarial Training Algorithms with Flexible Deep Data
Gradient Regularization | cs.LG cs.NE | Many previous proposals for adversarial training of deep neural nets have
included di- rectly modifying the gradient, training on a mix of original and
adversarial examples, using contractive penalties, and approximately optimizing
constrained adversarial ob- jective functions. In this paper, we show these
proposals are actually all instances of optimizing a general, regularized
objective we call DataGrad. Our proposed DataGrad framework, which can be
viewed as a deep extension of the layerwise contractive au- toencoder penalty,
cleanly simplifies prior work and easily allows extensions such as adversarial
training with multi-task cues. In our experiments, we find that the deep gra-
dient regularization of DataGrad (which also has L1 and L2 flavors of
regularization) outperforms alternative forms of regularization, including
classical L1, L2, and multi- task, both on the original dataset as well as on
adversarial sets. Furthermore, we find that combining multi-task optimization
with DataGrad adversarial training results in the most robust performance.
| Alexander G. Ororbia II, C. Lee Giles, and Daniel Kifer | null | 1601.07213 | null | null |
Predicting Drug Interactions and Mutagenicity with Ensemble Classifiers
on Subgraphs of Molecules | stat.ML cs.LG | In this study, we intend to solve a mutual information problem in interacting
molecules of any type, such as proteins, nucleic acids, and small molecules.
Using machine learning techniques, we accurately predict pairwise interactions,
which can be of medical and biological importance. Graphs are are useful in
this problem for their generality to all types of molecules, due to the
inherent association of atoms through atomic bonds. Subgraphs can represent
different molecular domains. These domains can be biologically significant as
most molecules only have portions that are of functional significance and can
interact with other domains. Thus, we use subgraphs as features in different
machine learning algorithms to predict if two drugs interact and predict
potential single molecule effects.
| Andrew Schaumberg, Angela Yu, Tatsuhiro Koshi, Xiaochan Zong,
Santoshkalyan Rayadhurgam | null | 1601.07233 | null | null |
On the Sample Complexity of Learning Graphical Games | cs.GT cs.LG stat.ML | We analyze the sample complexity of learning graphical games from purely
behavioral data. We assume that we can only observe the players' joint actions
and not their payoffs. We analyze the sufficient and necessary number of
samples for the correct recovery of the set of pure-strategy Nash equilibria
(PSNE) of the true game. Our analysis focuses on directed graphs with $n$ nodes
and at most $k$ parents per node. Sparse graphs correspond to ${k \in O(1)}$
with respect to $n$, while dense graphs correspond to ${k \in O(n)}$. By using
VC dimension arguments, we show that if the number of samples is greater than
${O(k n \log^2{n})}$ for sparse graphs or ${O(n^2 \log{n})}$ for dense graphs,
then maximum likelihood estimation correctly recovers the PSNE with high
probability. By using information-theoretic arguments, we show that if the
number of samples is less than ${\Omega(k n \log^2{n})}$ for sparse graphs or
${\Omega(n^2 \log{n})}$ for dense graphs, then any conceivable method fails to
recover the PSNE with arbitrary probability.
| Jean Honorio | null | 1601.07243 | null | null |
Evolutionary stability implies asymptotic stability under multiplicative
weights | cs.GT cs.LG math.OC | We show that evolutionarily stable states in general (nonlinear) population
games (which can be viewed as continuous vector fields constrained on a
polytope) are asymptotically stable under a multiplicative weights dynamic
(under appropriate choices of a parameter called the learning rate or step
size, which we demonstrate to be crucial to achieve convergence, as otherwise
even chaotic behavior is possible to manifest). Our result implies that
evolutionary theories based on multiplicative weights are compatible (in
principle, more general) with those based on the notion of evolutionary
stability. However, our result further establishes multiplicative weights as a
nonlinear programming primitive (on par with standard nonlinear programming
methods) since various nonlinear optimization problems, such as finding
Nash/Wardrop equilibria in nonatomic congestion games, which are well-known to
be equipped with a convex potential function, and finding strict local maxima
of quadratic programming problems, are special cases of the problem of
computing evolutionarily stable states in nonlinear population games.
| Ioannis Avramopoulos | null | 1601.07267 | null | null |
Quantum machine learning with glow for episodic tasks and decision games | quant-ph cs.AI cs.LG | We consider a general class of models, where a reinforcement learning (RL)
agent learns from cyclic interactions with an external environment via
classical signals. Perceptual inputs are encoded as quantum states, which are
subsequently transformed by a quantum channel representing the agent's memory,
while the outcomes of measurements performed at the channel's output determine
the agent's actions. The learning takes place via stepwise modifications of the
channel properties. They are described by an update rule that is inspired by
the projective simulation (PS) model and equipped with a glow mechanism that
allows for a backpropagation of policy changes, analogous to the eligibility
traces in RL and edge glow in PS. In this way, the model combines features of
PS with the ability for generalization, offered by its physical embodiment as a
quantum system. We apply the agent to various setups of an invasion game and a
grid world, which serve as elementary model tasks allowing a direct comparison
with a basic classical PS agent.
| Jens Clausen, Hans J. Briegel | 10.1103/PhysRevA.97.022303 | 1601.07358 | null | null |
Investigating echo state networks dynamics by means of recurrence
analysis | physics.data-an cs.LG nlin.CD | In this paper, we elaborate over the well-known interpretability issue in
echo state networks. The idea is to investigate the dynamics of reservoir
neurons with time-series analysis techniques taken from research on complex
systems. Notably, we analyze time-series of neuron activations with Recurrence
Plots (RPs) and Recurrence Quantification Analysis (RQA), which permit to
visualize and characterize high-dimensional dynamical systems. We show that
this approach is useful in a number of ways. First, the two-dimensional
representation offered by RPs provides a way for visualizing the
high-dimensional dynamics of a reservoir. Our results suggest that, if the
network is stable, reservoir and input denote similar line patterns in the
respective RPs. Conversely, the more unstable the ESN, the more the RP of the
reservoir presents instability patterns. As a second result, we show that the
$\mathrm{L_{max}}$ measure is highly correlated with the well-established
maximal local Lyapunov exponent. This suggests that complexity measures based
on RP diagonal lines distribution provide a valuable tool to quantify the
degree of network stability. Finally, our analysis shows that all RQA measures
fluctuate on the proximity of the so-called edge of stability, where an ESN
typically achieves maximum computational capability. We verify that the
determination of the edge of stability provided by such RQA measures is more
accurate than two well-known criteria based on the Jacobian matrix of the
reservoir. Therefore, we claim that RPs and RQA-based analyses can be used as
valuable tools to design an effective network given a specific problem.
| Filippo Maria Bianchi and Lorenzo Livi and Cesare Alippi | 10.1109/TNNLS.2016.2630802 | 1601.07381 | null | null |
Information-theoretic limits of Bayesian network structure learning | cs.LG cs.IT math.IT stat.ML | In this paper, we study the information-theoretic limits of learning the
structure of Bayesian networks (BNs), on discrete as well as continuous random
variables, from a finite number of samples. We show that the minimum number of
samples required by any procedure to recover the correct structure grows as
$\Omega(m)$ and $\Omega(k \log m + (k^2/m))$ for non-sparse and sparse BNs
respectively, where $m$ is the number of variables and $k$ is the maximum
number of parents per node. We provide a simple recipe, based on an extension
of the Fano's inequality, to obtain information-theoretic limits of structure
recovery for any exponential family BN. We instantiate our result for specific
conditional distributions in the exponential family to characterize the
fundamental limits of learning various commonly used BNs, such as conditional
probability table based networks, gaussian BNs, noisy-OR networks, and logistic
regression networks. En route to obtaining our main results, we obtain tight
bounds on the number of sparse and non-sparse essential-DAGs. Finally, as a
byproduct, we recover the information-theoretic limits of sparse variable
selection for logistic regression.
| Asish Ghoshal and Jean Honorio | null | 1601.07460 | null | null |
Unsupervised Learning in Neuromemristive Systems | cs.ET cs.LG stat.ML | Neuromemristive systems (NMSs) currently represent the most promising
platform to achieve energy efficient neuro-inspired computation. However, since
the research field is less than a decade old, there are still countless
algorithms and design paradigms to be explored within these systems. One
particular domain that remains to be fully investigated within NMSs is
unsupervised learning. In this work, we explore the design of an NMS for
unsupervised clustering, which is a critical element of several machine
learning algorithms. Using a simple memristor crossbar architecture and
learning rule, we are able to achieve performance which is on par with MATLAB's
k-means clustering.
| Cory Merkel and Dhireesha Kudithipudi | null | 1601.07482 | null | null |
Revealing Fundamental Physics from the Daya Bay Neutrino Experiment
using Deep Neural Networks | stat.ML cs.LG physics.data-an | Experiments in particle physics produce enormous quantities of data that must
be analyzed and interpreted by teams of physicists. This analysis is often
exploratory, where scientists are unable to enumerate the possible types of
signal prior to performing the experiment. Thus, tools for summarizing,
clustering, visualizing and classifying high-dimensional data are essential. In
this work, we show that meaningful physical content can be revealed by
transforming the raw data into a learned high-level representation using deep
neural networks, with measurements taken at the Daya Bay Neutrino Experiment as
a case study. We further show how convolutional deep neural networks can
provide an effective classification filter with greater than 97% accuracy
across different classes of physics events, significantly better than other
machine learning approaches.
| Evan Racah, Seyoon Ko, Peter Sadowski, Wahid Bhimji, Craig Tull,
Sang-Yun Oh, Pierre Baldi, Prabhat | 10.1109/ICMLA.2016.0160 | 1601.07621 | null | null |
Log-Normal Matrix Completion for Large Scale Link Prediction | cs.SI cs.LG stat.ML | The ubiquitous proliferation of online social networks has led to the
widescale emergence of relational graphs expressing unique patterns in link
formation and descriptive user node features. Matrix Factorization and
Completion have become popular methods for Link Prediction due to the low rank
nature of mutual node friendship information, and the availability of parallel
computer architectures for rapid matrix processing. Current Link Prediction
literature has demonstrated vast performance improvement through the
utilization of sparsity in addition to the low rank matrix assumption. However,
the majority of research has introduced sparsity through the limited L1 or
Frobenius norms, instead of considering the more detailed distributions which
led to the graph formation and relationship evolution. In particular, social
networks have been found to express either Pareto, or more recently discovered,
Log Normal distributions. Employing the convexity-inducing Lovasz Extension, we
demonstrate how incorporating specific degree distribution information can lead
to large scale improvements in Matrix Completion based Link prediction. We
introduce Log-Normal Matrix Completion (LNMC), and solve the complex
optimization problem by employing Alternating Direction Method of Multipliers.
Using data from three popular social networks, our experiments yield up to 5%
AUC increase over top-performing non-structured sparsity based methods.
| Brian Mohtashemi, Thomas Ketseoglou | null | 1601.07714 | null | null |
Distributed Low Rank Approximation of Implicit Functions of a Matrix | cs.NA cs.LG | We study distributed low rank approximation in which the matrix to be
approximated is only implicitly represented across the different servers. For
example, each of $s$ servers may have an $n \times d$ matrix $A^t$, and we may
be interested in computing a low rank approximation to $A = f(\sum_{t=1}^s
A^t)$, where $f$ is a function which is applied entrywise to the matrix
$\sum_{t=1}^s A^t$. We show for a wide class of functions $f$ it is possible to
efficiently compute a $d \times d$ rank-$k$ projection matrix $P$ for which
$\|A - AP\|_F^2 \leq \|A - [A]_k\|_F^2 + \varepsilon \|A\|_F^2$, where $AP$
denotes the projection of $A$ onto the row span of $P$, and $[A]_k$ denotes the
best rank-$k$ approximation to $A$ given by the singular value decomposition.
The communication cost of our protocols is $d \cdot (sk/\varepsilon)^{O(1)}$,
and they succeed with high probability. Our framework allows us to efficiently
compute a low rank approximation to an entry-wise softmax, to a Gaussian kernel
expansion, and to $M$-Estimators applied entrywise (i.e., forms of robust low
rank approximation). We also show that our additive error approximation is best
possible, in the sense that any protocol achieving relative error for these
problems requires significantly more communication. Finally, we experimentally
validate our algorithms on real datasets.
| David P. Woodruff, Peilin Zhong | null | 1601.07721 | null | null |
Distributed User Association in Energy Harvesting Small Cell Networks: A
Probabilistic Model | cs.IT cs.LG math.IT | We consider a distributed downlink user association problem in a small cell
network, where small cells obtain the required energy for providing wireless
services to users through ambient energy harvesting. Since energy harvesting is
opportunistic in nature, the amount of harvested energy is a random variable,
without any a priori known characteristics. Moreover, since users arrive in the
network randomly and require different wireless services, the energy
consumption is a random variable as well. In this paper, we propose a
probabilistic framework to mathematically model and analyze the random behavior
of energy harvesting and energy consumption in dense small cell networks.
Furthermore, as acquiring (even statistical) channel and network knowledge is
very costly in a distributed dense network, we develop a bandit-theoretical
formulation for distributed user association when no information is available
at users
| Setareh Maghsudi and Ekram Hossain | 10.1109/TWC.2017.2647946 | 1601.07795 | null | null |
Joint Sensing Matrix and Sparsifying Dictionary Optimization for Tensor
Compressive Sensing | cs.LG cs.IT math.IT | Tensor Compressive Sensing (TCS) is a multidimensional framework of
Compressive Sensing (CS), and it is advantageous in terms of reducing the
amount of storage, easing hardware implementations and preserving
multidimensional structures of signals in comparison to a conventional CS
system. In a TCS system, instead of using a random sensing matrix and a
predefined dictionary, the average-case performance can be further improved by
employing an optimized multidimensional sensing matrix and a learned
multilinear sparsifying dictionary. In this paper, we propose a joint
optimization approach of the sensing matrix and dictionary for a TCS system.
For the sensing matrix design in TCS, an extended separable approach with a
closed form solution and a novel iterative non-separable method are proposed
when the multilinear dictionary is fixed. In addition, a multidimensional
dictionary learning method that takes advantages of the multidimensional
structure is derived, and the influence of sensing matrices is taken into
account in the learning process. A joint optimization is achieved via
alternately iterating the optimization of the sensing matrix and dictionary.
Numerical experiments using both synthetic data and real images demonstrate the
superiority of the proposed approaches.
| Xin Ding, Wei Chen and Ian J. Wassell | 10.1109/TSP.2017.2699639 | 1601.07804 | null | null |
Parameterized Machine Learning for High-Energy Physics | hep-ex cs.LG hep-ph | We investigate a new structure for machine learning classifiers applied to
problems in high-energy physics by expanding the inputs to include not only
measured features but also physics parameters. The physics parameters represent
a smoothly varying learning task, and the resulting parameterized classifier
can smoothly interpolate between them and replace sets of classifiers trained
at individual values. This simplifies the training process and gives improved
performance at intermediate values, even for complex problems requiring deep
learning. Applications include tools parameterized in terms of theoretical
model parameters, such as the mass of a particle, which allow for a single
network to provide improved discrimination across a range of masses. This
concept is simple to implement and allows for optimized interpolatable results.
| Pierre Baldi, Kyle Cranmer, Taylor Faucett, Peter Sadowski, Daniel
Whiteson | 10.1140/epjc/s10052-016-4099-4 | 1601.07913 | null | null |
Automating biomedical data science through tree-based pipeline
optimization | cs.LG cs.NE | Over the past decade, data science and machine learning has grown from a
mysterious art form to a staple tool across a variety of fields in academia,
business, and government. In this paper, we introduce the concept of tree-based
pipeline optimization for automating one of the most tedious parts of machine
learning---pipeline design. We implement a Tree-based Pipeline Optimization
Tool (TPOT) and demonstrate its effectiveness on a series of simulated and
real-world genetic data sets. In particular, we show that TPOT can build
machine learning pipelines that achieve competitive classification accuracy and
discover novel pipeline operators---such as synthetic feature
constructors---that significantly improve classification accuracy on these data
sets. We also highlight the current challenges to pipeline optimization, such
as the tendency to produce pipelines that overfit the data, and suggest future
research paths to overcome these challenges. As such, this work represents an
early step toward fully automating machine learning pipeline design.
| Randal S. Olson, Ryan J. Urbanowicz, Peter C. Andrews, Nicole A.
Lavender, La Creis Kidd, Jason H. Moore | null | 1601.07925 | null | null |
Information-Theoretic Lower Bounds for Recovery of Diffusion Network
Structures | cs.LG cs.IT math.IT stat.ML | We study the information-theoretic lower bound of the sample complexity of
the correct recovery of diffusion network structures. We introduce a
discrete-time diffusion model based on the Independent Cascade model for which
we obtain a lower bound of order $\Omega(k \log p)$, for directed graphs of $p$
nodes, and at most $k$ parents per node. Next, we introduce a continuous-time
diffusion model, for which a similar lower bound of order $\Omega(k \log p)$ is
obtained. Our results show that the algorithm of Pouget-Abadie et al. is
statistically optimal for the discrete-time regime. Our work also opens the
question of whether it is possible to devise an optimal algorithm for the
continuous-time regime.
| Keehwan Park and Jean Honorio | null | 1601.07932 | null | null |
Large-scale Kernel-based Feature Extraction via Budgeted Nonlinear
Subspace Tracking | stat.ML cs.LG | Kernel-based methods enjoy powerful generalization capabilities in handling a
variety of learning tasks. When such methods are provided with sufficient
training data, broadly-applicable classes of nonlinear functions can be
approximated with desired accuracy. Nevertheless, inherent to the nonparametric
nature of kernel-based estimators are computational and memory requirements
that become prohibitive with large-scale datasets. In response to this
formidable challenge, the present work puts forward a low-rank, kernel-based,
feature extraction approach that is particularly tailored for online operation,
where data streams need not be stored in memory. A novel generative model is
introduced to approximate high-dimensional (possibly infinite) features via a
low-rank nonlinear subspace, the learning of which leads to a direct kernel
function approximation. Offline and online solvers are developed for the
subspace learning task, along with affordable versions, in which the number of
stored data vectors is confined to a predefined budget. Analytical results
provide performance bounds on how well the kernel matrix as well as
kernel-based classification and regression tasks can be approximated by
leveraging budgeted online subspace learning and feature extraction schemes.
Tests on synthetic and real datasets demonstrate and benchmark the efficiency
of the proposed method when linear classification and regression is applied to
the extracted features.
| Fatemeh Sheikholeslami, Dimitris Berberidis, Georgios B.Giannakis | null | 1601.07947 | null | null |
Feature Selection: A Data Perspective | cs.LG | Feature selection, as a data preprocessing strategy, has been proven to be
effective and efficient in preparing data (especially high-dimensional data)
for various data mining and machine learning problems. The objectives of
feature selection include: building simpler and more comprehensible models,
improving data mining performance, and preparing clean, understandable data.
The recent proliferation of big data has presented some substantial challenges
and opportunities to feature selection. In this survey, we provide a
comprehensive and structured overview of recent advances in feature selection
research. Motivated by current challenges and opportunities in the era of big
data, we revisit feature selection research from a data perspective and review
representative feature selection algorithms for conventional data, structured
data, heterogeneous data and streaming data. Methodologically, to emphasize the
differences and similarities of most existing feature selection algorithms for
conventional data, we categorize them into four main groups: similarity based,
information theoretical based, sparse learning based and statistical based
methods. To facilitate and promote the research in this community, we also
present an open-source feature selection repository that consists of most of
the popular feature selection algorithms
(\url{http://featureselection.asu.edu/}). Also, we use it as an example to show
how to evaluate feature selection algorithms. At the end of the survey, we
present a discussion about some open problems and challenges that require more
attention in future research.
| Jundong Li, Kewei Cheng, Suhang Wang, Fred Morstatter, Robert P.
Trevino, Jiliang Tang, Huan Liu | 10.1145/3136625 | 1601.07996 | null | null |
System Identification through Online Sparse Gaussian Process Regression
with Input Noise | stat.ML cs.LG cs.SY | There has been a growing interest in using non-parametric regression methods
like Gaussian Process (GP) regression for system identification. GP regression
does traditionally have three important downsides: (1) it is computationally
intensive, (2) it cannot efficiently implement newly obtained measurements
online, and (3) it cannot deal with stochastic (noisy) input points. In this
paper we present an algorithm tackling all these three issues simultaneously.
The resulting Sparse Online Noisy Input GP (SONIG) regression algorithm can
incorporate new noisy measurements in constant runtime. A comparison has shown
that it is more accurate than similar existing regression algorithms. When
applied to non-linear black-box system modeling, its performance is competitive
with existing non-linear ARX models.
| Hildo Bijl, Thomas B. Sch\"on, Jan-Willem van Wingerden, Michel
Verhaegen | null | 1601.08068 | null | null |
Kernels for sequentially ordered data | stat.ML cs.DM cs.LG math.ST stat.ME stat.TH | We present a novel framework for kernel learning with sequential data of any
kind, such as time series, sequences of graphs, or strings. Our approach is
based on signature features which can be seen as an ordered variant of sample
(cross-)moments; it allows to obtain a "sequentialized" version of any static
kernel. The sequential kernels are efficiently computable for discrete
sequences and are shown to approximate a continuous moment form in a sampling
sense.
A number of known kernels for sequences arise as "sequentializations" of
suitable static kernels: string kernels may be obtained as a special case, and
alignment kernels are closely related up to a modification that resolves their
open non-definiteness issue. Our experiments indicate that our signature-based
sequential kernel framework may be a promising approach to learning with
sequential data, such as time series, that allows to avoid extensive manual
pre-processing.
| Franz J Kir\'aly, Harald Oberhauser | null | 1601.08169 | null | null |
Spectrum Estimation from Samples | cs.LG stat.ML | We consider the problem of approximating the set of eigenvalues of the
covariance matrix of a multivariate distribution (equivalently, the problem of
approximating the "population spectrum"), given access to samples drawn from
the distribution. The eigenvalues of the covariance of a distribution contain
basic information about the distribution, including the presence or lack of
structure in the distribution, the effective dimensionality of the
distribution, and the applicability of higher-level machine learning and
multivariate statistical tools. We consider this fundamental recovery problem
in the regime where the number of samples is comparable, or even sublinear in
the dimensionality of the distribution in question. First, we propose a
theoretically optimal and computationally efficient algorithm for recovering
the moments of the eigenvalues of the population covariance matrix. We then
leverage this accurate moment recovery, via a Wasserstein distance argument, to
show that the vector of eigenvalues can be accurately recovered. We provide
finite--sample bounds on the expected error of the recovered eigenvalues, which
imply that our estimator is asymptotically consistent as the dimensionality of
the distribution and sample size tend towards infinity, even in the sublinear
sample regime where the ratio of the sample size to the dimensionality tends to
zero. In addition to our theoretical results, we show that our approach
performs well in practice for a broad range of distributions and sample sizes.
| Weihao Kong and Gregory Valiant | null | 1602.00061 | null | null |
DNA-inspired online behavioral modeling and its application to spambot
detection | cs.SI cs.CR cs.LG | We propose a strikingly novel, simple, and effective approach to model online
user behavior: we extract and analyze digital DNA sequences from user online
actions and we use Twitter as a benchmark to test our proposal. We obtain an
incisive and compact DNA-inspired characterization of user actions. Then, we
apply standard DNA analysis techniques to discriminate between genuine and
spambot accounts on Twitter. An experimental campaign supports our proposal,
showing its effectiveness and viability. To the best of our knowledge, we are
the first ones to identify and adapt DNA-inspired techniques to online user
behavioral modeling. While Twitter spambot detection is a specific use case on
a specific social media, our proposed methodology is platform and technology
agnostic, hence paving the way for diverse behavioral characterization tasks.
| Stefano Cresci, Roberto Di Pietro, Marinella Petrocchi, Angelo
Spognardi, and Maurizio Tesconi | 10.1109/MIS.2016.29 | 1602.00110 | null | null |
SCOPE: Scalable Composite Optimization for Learning on Spark | stat.ML cs.LG | Many machine learning models, such as logistic regression~(LR) and support
vector machine~(SVM), can be formulated as composite optimization problems.
Recently, many distributed stochastic optimization~(DSO) methods have been
proposed to solve the large-scale composite optimization problems, which have
shown better performance than traditional batch methods. However, most of these
DSO methods are not scalable enough. In this paper, we propose a novel DSO
method, called \underline{s}calable \underline{c}omposite
\underline{op}timization for l\underline{e}arning~({SCOPE}), and implement it
on the fault-tolerant distributed platform \mbox{Spark}. SCOPE is both
computation-efficient and communication-efficient. Theoretical analysis shows
that SCOPE is convergent with linear convergence rate when the objective
function is convex. Furthermore, empirical results on real datasets show that
SCOPE can outperform other state-of-the-art distributed learning methods on
Spark, including both batch learning methods and DSO methods.
| Shen-Yi Zhao, Ru Xiang, Ying-Hao Shi, Peng Gao, Wu-Jun Li | null | 1602.00133 | null | null |
Multiple instance learning for sequence data with across bag
dependencies | cs.LG | In Multiple Instance Learning (MIL) problem for sequence data, the instances
inside the bags are sequences. In some real world applications such as
bioinformatics, comparing a random couple of sequences makes no sense. In fact,
each instance may have structural and/or functional relations with instances of
other bags. Thus, the classification task should take into account this across
bag relation. In this work, we present two novel MIL approaches for sequence
data classification named ABClass and ABSim. ABClass extracts motifs from
related instances and use them to encode sequences. A discriminative classifier
is then applied to compute a partial classification result for each set of
related sequences. ABSim uses a similarity measure to discriminate the related
instances and to compute a scores matrix. For both approaches, an aggregation
method is applied in order to generate the final classification result. We
applied both approaches to solve the problem of bacterial Ionizing Radiation
Resistance prediction. The experimental results of the presented approaches are
satisfactory.
| Manel Zoghlami, Sabeur Aridhi, Mondher Maddouri, Engelbert Mephu
Nguifo | 10.1007/s13042-019-01021-5 | 1602.00163 | null | null |
Deep Learning For Smile Recognition | cs.CV cs.LG cs.NE | Inspired by recent successes of deep learning in computer vision, we propose
a novel application of deep convolutional neural networks to facial expression
recognition, in particular smile recognition. A smile recognition test accuracy
of 99.45% is achieved for the Denver Intensity of Spontaneous Facial Action
(DISFA) database, significantly outperforming existing approaches based on
hand-crafted features with accuracies ranging from 65.55% to 79.67%. The
novelty of this approach includes a comprehensive model selection of the
architecture parameters, allowing to find an appropriate architecture for each
expression such as smile. This is feasible because all experiments were run on
a Tesla K40c GPU, allowing a speedup of factor 10 over traditional computations
on a CPU.
| Patrick O. Glauner | null | 1602.00172 | null | null |
Greedy Deep Dictionary Learning | cs.LG cs.AI stat.ML | In this work we propose a new deep learning tool called deep dictionary
learning. Multi-level dictionaries are learnt in a greedy fashion, one layer at
a time. This requires solving a simple (shallow) dictionary learning problem,
the solution to this is well known. We apply the proposed technique on some
benchmark deep learning datasets. We compare our results with other deep
learning tools like stacked autoencoder and deep belief network; and state of
the art supervised dictionary learning tools like discriminative KSVD and label
consistent KSVD. Our method yields better results than all.
| Snigdha Tariyal, Angshul Majumdar, Richa Singh and Mayank Vatsa | null | 1602.00203 | null | null |
Unsupervised Deep Hashing for Large-scale Visual Search | cs.CV cs.LG | Learning based hashing plays a pivotal role in large-scale visual search.
However, most existing hashing algorithms tend to learn shallow models that do
not seek representative binary codes. In this paper, we propose a novel hashing
approach based on unsupervised deep learning to hierarchically transform
features into hash codes. Within the heterogeneous deep hashing framework, the
autoencoder layers with specific constraints are considered to model the
nonlinear mapping between features and binary codes. Then, a Restricted
Boltzmann Machine (RBM) layer with constraints is utilized to reduce the
dimension in the hamming space. Extensive experiments on the problem of visual
search demonstrate the competitiveness of our proposed approach compared to
state-of-the-art.
| Zhaoqiang Xia, Xiaoyi Feng, Jinye Peng, Abdenour Hadid | 10.1109/IPTA.2016.7821007 | 1602.00206 | null | null |
Feature Selection for Regression Problems Based on the Morisita
Estimator of Intrinsic Dimension | stat.ML cs.LG | Data acquisition, storage and management have been improved, while the key
factors of many phenomena are not well known. Consequently, irrelevant and
redundant features artificially increase the size of datasets, which
complicates learning tasks, such as regression. To address this problem,
feature selection methods have been proposed. This paper introduces a new
supervised filter based on the Morisita estimator of intrinsic dimension. It
can identify relevant features and distinguish between redundant and irrelevant
information. Besides, it offers a clear graphical representation of the
results, and it can be easily implemented in different programming languages.
Comprehensive numerical experiments are conducted using simulated datasets
characterized by different levels of complexity, sample size and noise. The
suggested algorithm is also successfully tested on a selection of real world
applications and compared with RReliefF using extreme learning machine. In
addition, a new measure of feature relevance is presented and discussed.
| Jean Golay, Michael Leuenberger, Mikhail Kanevski | null | 1602.00216 | null | null |
A Proximal Stochastic Quasi-Newton Algorithm | cs.LG stat.ML | In this paper, we discuss the problem of minimizing the sum of two convex
functions: a smooth function plus a non-smooth function. Further, the smooth
part can be expressed by the average of a large number of smooth component
functions, and the non-smooth part is equipped with a simple proximal mapping.
We propose a proximal stochastic second-order method, which is efficient and
scalable. It incorporates the Hessian in the smooth part of the function and
exploits multistage scheme to reduce the variance of the stochastic gradient.
We prove that our method can achieve linear rate of convergence.
| Luo Luo, Zihao Chen, Zhihua Zhang, Wu-Jun Li | null | 1602.00223 | null | null |
Additive Approximations in High Dimensional Nonparametric Regression via
the SALSA | stat.ML cs.LG | High dimensional nonparametric regression is an inherently difficult problem
with known lower bounds depending exponentially in dimension. A popular
strategy to alleviate this curse of dimensionality has been to use additive
models of \emph{first order}, which model the regression function as a sum of
independent functions on each dimension. Though useful in controlling the
variance of the estimate, such models are often too restrictive in practical
settings. Between non-additive models which often have large variance and first
order additive models which have large bias, there has been little work to
exploit the trade-off in the middle via additive models of intermediate order.
In this work, we propose SALSA, which bridges this gap by allowing interactions
between variables, but controls model capacity by limiting the order of
interactions. SALSA minimises the residual sum of squares with squared RKHS
norm penalties. Algorithmically, it can be viewed as Kernel Ridge Regression
with an additive kernel. When the regression function is additive, the excess
risk is only polynomial in dimension. Using the Girard-Newton formulae, we
efficiently sum over a combinatorial number of terms in the additive expansion.
Via a comparison on $15$ real datasets, we show that our method is competitive
against $21$ other alternatives.
| Kirthevasan Kandasamy, Yaoliang Yu | null | 1602.00287 | null | null |
Bandits meet Computer Architecture: Designing a Smartly-allocated Cache | cs.LG | In many embedded systems, such as imaging sys- tems, the system has a single
designated purpose, and same threads are executed repeatedly. Profiling thread
behavior, allows the system to allocate each thread its resources in a way that
improves overall system performance. We study an online resource al-
locationproblem,wherearesourcemanagersimulta- neously allocates resources
(exploration), learns the impact on the different consumers (learning) and im-
proves allocation towards optimal performance (ex- ploitation). We build on the
rich framework of multi- armed bandits and present online and offline algo-
rithms. Through extensive experiments with both synthetic data and real-world
cache allocation to threads we show the merits and properties of our al-
gorithms
| Yonatan Glassner, Koby Crammer | null | 1602.00309 | null | null |
Adaptive Subgradient Methods for Online AUC Maximization | cs.LG | Learning for maximizing AUC performance is an important research problem in
Machine Learning and Artificial Intelligence. Unlike traditional batch learning
methods for maximizing AUC which often suffer from poor scalability, recent
years have witnessed some emerging studies that attempt to maximize AUC by
single-pass online learning approaches. Despite their encouraging results
reported, the existing online AUC maximization algorithms often adopt simple
online gradient descent approaches that fail to exploit the geometrical
knowledge of the data observed during the online learning process, and thus
could suffer from relatively larger regret. To address the above limitation, in
this work, we explore a novel algorithm of Adaptive Online AUC Maximization
(AdaOAM) which employs an adaptive gradient method that exploits the knowledge
of historical gradients to perform more informative online learning. The new
adaptive updating strategy of the AdaOAM is less sensitive to the parameter
settings and maintains the same time complexity as previous non-adaptive
counterparts. Additionally, we extend the algorithm to handle high-dimensional
sparse data (SAdaOAM) and address sparsity in the solution by performing lazy
gradient updating. We analyze the theoretical bounds and evaluate their
empirical performance on various types of data sets. The encouraging empirical
results obtained clearly highlighted the effectiveness and efficiency of the
proposed algorithms.
| Yi Ding, Peilin Zhao, Steven C.H. Hoi, Yew-Soon Ong | null | 1602.00351 | null | null |
Active Learning Algorithms for Graphical Model Selection | stat.ML cs.IT cs.LG math.IT math.ST stat.TH | The problem of learning the structure of a high dimensional graphical model
from data has received considerable attention in recent years. In many
applications such as sensor networks and proteomics it is often expensive to
obtain samples from all the variables involved simultaneously. For instance,
this might involve the synchronization of a large number of sensors or the
tagging of a large number of proteins. To address this important issue, we
initiate the study of a novel graphical model selection problem, where the goal
is to optimize the total number of scalar samples obtained by allowing the
collection of samples from only subsets of the variables. We propose a general
paradigm for graphical model selection where feedback is used to guide the
sampling to high degree vertices, while obtaining only few samples from the
ones with the low degrees. We instantiate this framework with two specific
active learning algorithms, one of which makes mild assumptions but is
computationally expensive, while the other is more computationally efficient
but requires stronger (nevertheless standard) assumptions. Whereas the sample
complexity of passive algorithms is typically a function of the maximum degree
of the graph, we show that the sample complexity of our algorithms is provable
smaller and that it depends on a novel local complexity measure that is akin to
the average degree of the graph. We finally demonstrate the efficacy of our
framework via simulations.
| Gautam Dasarathy, Aarti Singh, Maria-Florina Balcan, Jong Hyuk Park | null | 1602.00354 | null | null |
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