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Efficient Sparse Group Feature Selection via Nonconvex Optimization | cs.LG stat.ML | Sparse feature selection has been demonstrated to be effective in handling
high-dimensional data. While promising, most of the existing works use convex
methods, which may be suboptimal in terms of the accuracy of feature selection
and parameter estimation. In this paper, we expand a nonconvex paradigm to
sparse group feature selection, which is motivated by applications that require
identifying the underlying group structure and performing feature selection
simultaneously. The main contributions of this article are twofold: (1)
statistically, we introduce a nonconvex sparse group feature selection model
which can reconstruct the oracle estimator. Therefore, consistent feature
selection and parameter estimation can be achieved; (2) computationally, we
propose an efficient algorithm that is applicable to large-scale problems.
Numerical results suggest that the proposed nonconvex method compares favorably
against its competitors on synthetic data and real-world applications, thus
achieving desired goal of delivering high performance.
| Shuo Xiang, Xiaotong Shen, Jieping Ye | null | 1205.5075 | null | null |
A hybrid clustering algorithm for data mining | cs.DB cs.LG | Data clustering is a process of arranging similar data into groups. A
clustering algorithm partitions a data set into several groups such that the
similarity within a group is better than among groups. In this paper a hybrid
clustering algorithm based on K-mean and K-harmonic mean (KHM) is described.
The proposed algorithm is tested on five different datasets. The research is
focused on fast and accurate clustering. Its performance is compared with the
traditional K-means & KHM algorithm. The result obtained from proposed hybrid
algorithm is much better than the traditional K-mean & KHM algorithm.
| Ravindra Jain | null | 1205.5353 | null | null |
Language-Constraint Reachability Learning in Probabilistic Graphs | cs.AI cs.LG | The probabilistic graphs framework models the uncertainty inherent in
real-world domains by means of probabilistic edges whose value quantifies the
likelihood of the edge existence or the strength of the link it represents. The
goal of this paper is to provide a learning method to compute the most likely
relationship between two nodes in a framework based on probabilistic graphs. In
particular, given a probabilistic graph we adopted the language-constraint
reachability method to compute the probability of possible interconnections
that may exists between two nodes. Each of these connections may be viewed as
feature, or a factor, between the two nodes and the corresponding probability
as its weight. Each observed link is considered as a positive instance for its
corresponding link label. Given the training set of observed links a
L2-regularized Logistic Regression has been adopted to learn a model able to
predict unobserved link labels. The experiments on a real world collaborative
filtering problem proved that the proposed approach achieves better results
than that obtained adopting classical methods.
| Claudio Taranto, Nicola Di Mauro, Floriana Esposito | null | 1205.5367 | null | null |
Measurability Aspects of the Compactness Theorem for Sample Compression
Schemes | stat.ML cs.LG | It was proved in 1998 by Ben-David and Litman that a concept space has a
sample compression scheme of size d if and only if every finite subspace has a
sample compression scheme of size d. In the compactness theorem, measurability
of the hypotheses of the created sample compression scheme is not guaranteed;
at the same time measurability of the hypotheses is a necessary condition for
learnability. In this thesis we discuss when a sample compression scheme,
created from com- pression schemes on finite subspaces via the compactness
theorem, have measurable hypotheses. We show that if X is a standard Borel
space with a d-maximum and universally separable concept class C, then (X,C)
has a sample compression scheme of size d with universally Borel measurable
hypotheses. Additionally we introduce a new variant of compression scheme
called a copy sample compression scheme.
| Damjan Kalajdzievski | null | 1205.5819 | null | null |
Towards a Mathematical Foundation of Immunology and Amino Acid Chains | stat.ML cs.LG q-bio.GN | We attempt to set a mathematical foundation of immunology and amino acid
chains. To measure the similarities of these chains, a kernel on strings is
defined using only the sequence of the chains and a good amino acid
substitution matrix (e.g. BLOSUM62). The kernel is used in learning machines to
predict binding affinities of peptides to human leukocyte antigens DR (HLA-DR)
molecules. On both fixed allele (Nielsen and Lund 2009) and pan-allele (Nielsen
et.al. 2010) benchmark databases, our algorithm achieves the state-of-the-art
performance. The kernel is also used to define a distance on an HLA-DR allele
set based on which a clustering analysis precisely recovers the serotype
classifications assigned by WHO (Nielsen and Lund 2009, and Marsh et.al. 2010).
These results suggest that our kernel relates well the chain structure of both
peptides and HLA-DR molecules to their biological functions, and that it offers
a simple, powerful and promising methodology to immunology and amino acid chain
studies.
| Wen-Jun Shen, Hau-San Wong, Quan-Wu Xiao, Xin Guo, Stephen Smale | null | 1205.6031 | null | null |
Learning Dictionaries with Bounded Self-Coherence | stat.ML cs.LG | Sparse coding in learned dictionaries has been established as a successful
approach for signal denoising, source separation and solving inverse problems
in general. A dictionary learning method adapts an initial dictionary to a
particular signal class by iteratively computing an approximate factorization
of a training data matrix into a dictionary and a sparse coding matrix. The
learned dictionary is characterized by two properties: the coherence of the
dictionary to observations of the signal class, and the self-coherence of the
dictionary atoms. A high coherence to the signal class enables the sparse
coding of signal observations with a small approximation error, while a low
self-coherence of the atoms guarantees atom recovery and a more rapid residual
error decay rate for the sparse coding algorithm. The two goals of high signal
coherence and low self-coherence are typically in conflict, therefore one seeks
a trade-off between them, depending on the application. We present a dictionary
learning method with an effective control over the self-coherence of the
trained dictionary, enabling a trade-off between maximizing the sparsity of
codings and approximating an equiangular tight frame.
| Christian D. Sigg and Tomas Dikk and Joachim M. Buhmann | 10.1109/LSP.2012.2223757 | 1205.6210 | null | null |
A Framework for Evaluating Approximation Methods for Gaussian Process
Regression | stat.ML cs.LG stat.CO | Gaussian process (GP) predictors are an important component of many Bayesian
approaches to machine learning. However, even a straightforward implementation
of Gaussian process regression (GPR) requires O(n^2) space and O(n^3) time for
a dataset of n examples. Several approximation methods have been proposed, but
there is a lack of understanding of the relative merits of the different
approximations, and in what situations they are most useful. We recommend
assessing the quality of the predictions obtained as a function of the compute
time taken, and comparing to standard baselines (e.g., Subset of Data and
FITC). We empirically investigate four different approximation algorithms on
four different prediction problems, and make our code available to encourage
future comparisons.
| Krzysztof Chalupka, Christopher K. I. Williams and Iain Murray | null | 1205.6326 | null | null |
Multiclass Learning Approaches: A Theoretical Comparison with
Implications | cs.LG | We theoretically analyze and compare the following five popular multiclass
classification methods: One vs. All, All Pairs, Tree-based classifiers, Error
Correcting Output Codes (ECOC) with randomly generated code matrices, and
Multiclass SVM. In the first four methods, the classification is based on a
reduction to binary classification. We consider the case where the binary
classifier comes from a class of VC dimension $d$, and in particular from the
class of halfspaces over $\reals^d$. We analyze both the estimation error and
the approximation error of these methods. Our analysis reveals interesting
conclusions of practical relevance, regarding the success of the different
approaches under various conditions. Our proof technique employs tools from VC
theory to analyze the \emph{approximation error} of hypothesis classes. This is
in sharp contrast to most, if not all, previous uses of VC theory, which only
deal with estimation error.
| Amit Daniely and Sivan Sabato and Shai Shalev Shwartz | null | 1205.6432 | null | null |
Finding Important Genes from High-Dimensional Data: An Appraisal of
Statistical Tests and Machine-Learning Approaches | stat.ML cs.LG q-bio.QM | Over the past decades, statisticians and machine-learning researchers have
developed literally thousands of new tools for the reduction of
high-dimensional data in order to identify the variables most responsible for a
particular trait. These tools have applications in a plethora of settings,
including data analysis in the fields of business, education, forensics, and
biology (such as microarray, proteomics, brain imaging), to name a few.
In the present work, we focus our investigation on the limitations and
potential misuses of certain tools in the analysis of the benchmark colon
cancer data (2,000 variables; Alon et al., 1999) and the prostate cancer data
(6,033 variables; Efron, 2010, 2008). Our analysis demonstrates that models
that produce 100% accuracy measures often select different sets of genes and
cannot stand the scrutiny of parameter estimates and model stability.
Furthermore, we created a host of simulation datasets and "artificial
diseases" to evaluate the reliability of commonly used statistical and data
mining tools. We found that certain widely used models can classify the data
with 100% accuracy without using any of the variables responsible for the
disease. With moderate sample size and suitable pre-screening, stochastic
gradient boosting will be shown to be a superior model for gene selection and
variable screening from high-dimensional datasets.
| Chamont Wang, Jana Gevertz, Chaur-Chin Chen, Leonardo Auslender | null | 1205.6523 | null | null |
A Brief Summary of Dictionary Learning Based Approach for Classification
(revised) | cs.CV cs.LG | This note presents some representative methods which are based on dictionary
learning (DL) for classification. We do not review the sophisticated methods or
frameworks that involve DL for classification, such as online DL and spatial
pyramid matching (SPM), but rather, we concentrate on the direct DL-based
classification methods. Here, the "so-called direct DL-based method" is the
approach directly deals with DL framework by adding some meaningful penalty
terms. By listing some representative methods, we can roughly divide them into
two categories, i.e. (1) directly making the dictionary discriminative and (2)
forcing the sparse coefficients discriminative to push the discrimination power
of the dictionary. From this taxonomy, we can expect some extensions of them as
future researches.
| Shu Kong, Donghui Wang | null | 1205.6544 | null | null |
Beyond $\ell_1$-norm minimization for sparse signal recovery | cs.IT cs.LG math.IT | Sparse signal recovery has been dominated by the basis pursuit denoise (BPDN)
problem formulation for over a decade. In this paper, we propose an algorithm
that outperforms BPDN in finding sparse solutions to underdetermined linear
systems of equations at no additional computational cost. Our algorithm, called
WSPGL1, is a modification of the spectral projected gradient for $\ell_1$
minimization (SPGL1) algorithm in which the sequence of LASSO subproblems are
replaced by a sequence of weighted LASSO subproblems with constant weights
applied to a support estimate. The support estimate is derived from the data
and is updated at every iteration. The algorithm also modifies the Pareto curve
at every iteration to reflect the new weighted $\ell_1$ minimization problem
that is being solved. We demonstrate through extensive simulations that the
sparse recovery performance of our algorithm is superior to that of $\ell_1$
minimization and approaches the recovery performance of iterative re-weighted
$\ell_1$ (IRWL1) minimization of Cand{\`e}s, Wakin, and Boyd, although it does
not match it in general. Moreover, our algorithm has the computational cost of
a single BPDN problem.
| Hassan Mansour | null | 1205.6849 | null | null |
Posterior contraction of the population polytope in finite admixture
models | math.ST cs.LG stat.TH | We study the posterior contraction behavior of the latent population
structure that arises in admixture models as the amount of data increases. We
adopt the geometric view of admixture models - alternatively known as topic
models - as a data generating mechanism for points randomly sampled from the
interior of a (convex) population polytope, whose extreme points correspond to
the population structure variables of interest. Rates of posterior contraction
are established with respect to Hausdorff metric and a minimum matching
Euclidean metric defined on polytopes. Tools developed include posterior
asymptotics of hierarchical models and arguments from convex geometry.
| XuanLong Nguyen | 10.3150/13-BEJ582 | 1206.0068 | null | null |
Sparse Trace Norm Regularization | cs.LG stat.ML | We study the problem of estimating multiple predictive functions from a
dictionary of basis functions in the nonparametric regression setting. Our
estimation scheme assumes that each predictive function can be estimated in the
form of a linear combination of the basis functions. By assuming that the
coefficient matrix admits a sparse low-rank structure, we formulate the
function estimation problem as a convex program regularized by the trace norm
and the $\ell_1$-norm simultaneously. We propose to solve the convex program
using the accelerated gradient (AG) method and the alternating direction method
of multipliers (ADMM) respectively; we also develop efficient algorithms to
solve the key components in both AG and ADMM. In addition, we conduct
theoretical analysis on the proposed function estimation scheme: we derive a
key property of the optimal solution to the convex program; based on an
assumption on the basis functions, we establish a performance bound of the
proposed function estimation scheme (via the composite regularization).
Simulation studies demonstrate the effectiveness and efficiency of the proposed
algorithms.
| Jianhui Chen and Jieping Ye | null | 1206.0333 | null | null |
A Route Confidence Evaluation Method for Reliable Hierarchical Text
Categorization | cs.IR cs.LG | Hierarchical Text Categorization (HTC) is becoming increasingly important
with the rapidly growing amount of text data available in the World Wide Web.
Among the different strategies proposed to cope with HTC, the Local Classifier
per Node (LCN) approach attains good performance by mirroring the underlying
class hierarchy while enforcing a top-down strategy in the testing step.
However, the problem of embedding hierarchical information (parent-child
relationship) to improve the performance of HTC systems still remains open. A
confidence evaluation method for a selected route in the hierarchy is proposed
to evaluate the reliability of the final candidate labels in an HTC system. In
order to take into account the information embedded in the hierarchy, weight
factors are used to take into account the importance of each level. An
acceptance/rejection strategy in the top-down decision making process is
proposed, which improves the overall categorization accuracy by rejecting a few
percentage of samples, i.e., those with low reliability score. Experimental
results on the Reuters benchmark dataset (RCV1- v2) confirm the effectiveness
of the proposed method, compared to other state-of-the art HTC methods.
| Nima Hatami, Camelia Chira and Giuliano Armano | null | 1206.0335 | null | null |
Poisson noise reduction with non-local PCA | cs.CV cs.LG stat.CO | Photon-limited imaging arises when the number of photons collected by a
sensor array is small relative to the number of detector elements. Photon
limitations are an important concern for many applications such as spectral
imaging, night vision, nuclear medicine, and astronomy. Typically a Poisson
distribution is used to model these observations, and the inherent
heteroscedasticity of the data combined with standard noise removal methods
yields significant artifacts. This paper introduces a novel denoising algorithm
for photon-limited images which combines elements of dictionary learning and
sparse patch-based representations of images. The method employs both an
adaptation of Principal Component Analysis (PCA) for Poisson noise and recently
developed sparsity-regularized convex optimization algorithms for
photon-limited images. A comprehensive empirical evaluation of the proposed
method helps characterize the performance of this approach relative to other
state-of-the-art denoising methods. The results reveal that, despite its
conceptual simplicity, Poisson PCA-based denoising appears to be highly
competitive in very low light regimes.
| Joseph Salmon and Zachary Harmany and Charles-Alban Deledalle and
Rebecca Willett | null | 1206.0338 | null | null |
Learning in Hierarchical Social Networks | cs.SI cs.IT cs.LG math.IT | We study a social network consisting of agents organized as a hierarchical
M-ary rooted tree, common in enterprise and military organizational structures.
The goal is to aggregate information to solve a binary hypothesis testing
problem. Each agent at a leaf of the tree, and only such an agent, makes a
direct measurement of the underlying true hypothesis. The leaf agent then makes
a decision and sends it to its supervising agent, at the next level of the
tree. Each supervising agent aggregates the decisions from the M members of its
group, produces a summary message, and sends it to its supervisor at the next
level, and so on. Ultimately, the agent at the root of the tree makes an
overall decision. We derive upper and lower bounds for the Type I and II error
probabilities associated with this decision with respect to the number of leaf
agents, which in turn characterize the converge rates of the Type I, Type II,
and total error probabilities. We also provide a message-passing scheme
involving non-binary message alphabets and characterize the exponent of the
error probability with respect to the message alphabet size.
| Zhenliang Zhang, Edwin K. P. Chong, Ali Pezeshki, William Moran, and
Stephen D. Howard | 10.1109/JSTSP.2013.2245859 | 1206.0652 | null | null |
Topological graph clustering with thin position | math.GT cs.LG stat.ML | A clustering algorithm partitions a set of data points into smaller sets
(clusters) such that each subset is more tightly packed than the whole. Many
approaches to clustering translate the vector data into a graph with edges
reflecting a distance or similarity metric on the points, then look for highly
connected subgraphs. We introduce such an algorithm based on ideas borrowed
from the topological notion of thin position for knots and 3-dimensional
manifolds.
| Jesse Johnson | null | 1206.0771 | null | null |
A Mixed Observability Markov Decision Process Model for Musical Pitch | cs.AI cs.LG | Partially observable Markov decision processes have been widely used to
provide models for real-world decision making problems. In this paper, we will
provide a method in which a slightly different version of them called Mixed
observability Markov decision process, MOMDP, is going to join with our
problem. Basically, we aim at offering a behavioural model for interaction of
intelligent agents with musical pitch environment and we will show that how
MOMDP can shed some light on building up a decision making model for musical
pitch conveniently.
| Pouyan Rafiei Fard, Keyvan Yahya | null | 1206.0855 | null | null |
Nearly optimal solutions for the Chow Parameters Problem and low-weight
approximation of halfspaces | cs.CC cs.DS cs.LG | The \emph{Chow parameters} of a Boolean function $f: \{-1,1\}^n \to \{-1,1\}$
are its $n+1$ degree-0 and degree-1 Fourier coefficients. It has been known
since 1961 (Chow, Tannenbaum) that the (exact values of the) Chow parameters of
any linear threshold function $f$ uniquely specify $f$ within the space of all
Boolean functions, but until recently (O'Donnell and Servedio) nothing was
known about efficient algorithms for \emph{reconstructing} $f$ (exactly or
approximately) from exact or approximate values of its Chow parameters. We
refer to this reconstruction problem as the \emph{Chow Parameters Problem.}
Our main result is a new algorithm for the Chow Parameters Problem which,
given (sufficiently accurate approximations to) the Chow parameters of any
linear threshold function $f$, runs in time $\tilde{O}(n^2)\cdot
(1/\eps)^{O(\log^2(1/\eps))}$ and with high probability outputs a
representation of an LTF $f'$ that is $\eps$-close to $f$. The only previous
algorithm (O'Donnell and Servedio) had running time $\poly(n) \cdot
2^{2^{\tilde{O}(1/\eps^2)}}.$
As a byproduct of our approach, we show that for any linear threshold
function $f$ over $\{-1,1\}^n$, there is a linear threshold function $f'$ which
is $\eps$-close to $f$ and has all weights that are integers at most $\sqrt{n}
\cdot (1/\eps)^{O(\log^2(1/\eps))}$. This significantly improves the best
previous result of Diakonikolas and Servedio which gave a $\poly(n) \cdot
2^{\tilde{O}(1/\eps^{2/3})}$ weight bound, and is close to the known lower
bound of $\max\{\sqrt{n},$ $(1/\eps)^{\Omega(\log \log (1/\eps))}\}$ (Goldberg,
Servedio). Our techniques also yield improved algorithms for related problems
in learning theory.
| Anindya De, Ilias Diakonikolas, Vitaly Feldman, Rocco A. Servedio | null | 1206.0985 | null | null |
An Optimization Framework for Semi-Supervised and Transfer Learning
using Multiple Classifiers and Clusterers | cs.LG | Unsupervised models can provide supplementary soft constraints to help
classify new, "target" data since similar instances in the target set are more
likely to share the same class label. Such models can also help detect possible
differences between training and target distributions, which is useful in
applications where concept drift may take place, as in transfer learning
settings. This paper describes a general optimization framework that takes as
input class membership estimates from existing classifiers learnt on previously
encountered "source" data, as well as a similarity matrix from a cluster
ensemble operating solely on the target data to be classified, and yields a
consensus labeling of the target data. This framework admits a wide range of
loss functions and classification/clustering methods. It exploits properties of
Bregman divergences in conjunction with Legendre duality to yield a principled
and scalable approach. A variety of experiments show that the proposed
framework can yield results substantially superior to those provided by popular
transductive learning techniques or by naively applying classifiers learnt on
the original task to the target data.
| Ayan Acharya, Eduardo R. Hruschka, Joydeep Ghosh, Sreangsu Acharyya | null | 1206.0994 | null | null |
A Machine Learning Approach For Opinion Holder Extraction In Arabic
Language | cs.IR cs.LG | Opinion mining aims at extracting useful subjective information from reliable
amounts of text. Opinion mining holder recognition is a task that has not been
considered yet in Arabic Language. This task essentially requires deep
understanding of clauses structures. Unfortunately, the lack of a robust,
publicly available, Arabic parser further complicates the research. This paper
presents a leading research for the opinion holder extraction in Arabic news
independent from any lexical parsers. We investigate constructing a
comprehensive feature set to compensate the lack of parsing structural
outcomes. The proposed feature set is tuned from English previous works coupled
with our proposed semantic field and named entities features. Our feature
analysis is based on Conditional Random Fields (CRF) and semi-supervised
pattern recognition techniques. Different research models are evaluated via
cross-validation experiments achieving 54.03 F-measure. We publicly release our
own research outcome corpus and lexicon for opinion mining community to
encourage further research.
| Mohamed Elarnaoty, Samir AbdelRahman, and Aly Fahmy | 10.5121/ijaia.2012.3205 | 1206.1011 | null | null |
Bayesian Structure Learning for Markov Random Fields with a Spike and
Slab Prior | stat.ML cs.LG | In recent years a number of methods have been developed for automatically
learning the (sparse) connectivity structure of Markov Random Fields. These
methods are mostly based on L1-regularized optimization which has a number of
disadvantages such as the inability to assess model uncertainty and expensive
cross-validation to find the optimal regularization parameter. Moreover, the
model's predictive performance may degrade dramatically with a suboptimal value
of the regularization parameter (which is sometimes desirable to induce
sparseness). We propose a fully Bayesian approach based on a "spike and slab"
prior (similar to L0 regularization) that does not suffer from these
shortcomings. We develop an approximate MCMC method combining Langevin dynamics
and reversible jump MCMC to conduct inference in this model. Experiments show
that the proposed model learns a good combination of the structure and
parameter values without the need for separate hyper-parameter tuning.
Moreover, the model's predictive performance is much more robust than L1-based
methods with hyper-parameter settings that induce highly sparse model
structures.
| Yutian Chen, Max Welling | null | 1206.1088 | null | null |
No More Pesky Learning Rates | stat.ML cs.LG | The performance of stochastic gradient descent (SGD) depends critically on
how learning rates are tuned and decreased over time. We propose a method to
automatically adjust multiple learning rates so as to minimize the expected
error at any one time. The method relies on local gradient variations across
samples. In our approach, learning rates can increase as well as decrease,
making it suitable for non-stationary problems. Using a number of convex and
non-convex learning tasks, we show that the resulting algorithm matches the
performance of SGD or other adaptive approaches with their best settings
obtained through systematic search, and effectively removes the need for
learning rate tuning.
| Tom Schaul, Sixin Zhang and Yann LeCun | null | 1206.1106 | null | null |
Comparison of the C4.5 and a Naive Bayes Classifier for the Prediction
of Lung Cancer Survivability | cs.LG | Numerous data mining techniques have been developed to extract information
and identify patterns and predict trends from large data sets. In this study,
two classification techniques, the J48 implementation of the C4.5 algorithm and
a Naive Bayes classifier are applied to predict lung cancer survivability from
an extensive data set with fifteen years of patient records. The purpose of the
project is to verify the predictive effectiveness of the two techniques on
real, historical data. Besides the performance outcome that renders J48
marginally better than the Naive Bayes technique, there is a detailed
description of the data and the required pre-processing activities. The
performance results confirm expectations while some of the issues that appeared
during experimentation, underscore the value of having domain-specific
understanding to leverage any domain-specific characteristics inherent in the
data.
| George Dimitoglou, James A. Adams, Carol M. Jim | null | 1206.1121 | null | null |
Memory-Efficient Topic Modeling | cs.LG cs.IR | As one of the simplest probabilistic topic modeling techniques, latent
Dirichlet allocation (LDA) has found many important applications in text
mining, computer vision and computational biology. Recent training algorithms
for LDA can be interpreted within a unified message passing framework. However,
message passing requires storing previous messages with a large amount of
memory space, increasing linearly with the number of documents or the number of
topics. Therefore, the high memory usage is often a major problem for topic
modeling of massive corpora containing a large number of topics. To reduce the
space complexity, we propose a novel algorithm without storing previous
messages for training LDA: tiny belief propagation (TBP). The basic idea of TBP
relates the message passing algorithms with the non-negative matrix
factorization (NMF) algorithms, which absorb the message updating into the
message passing process, and thus avoid storing previous messages. Experimental
results on four large data sets confirm that TBP performs comparably well or
even better than current state-of-the-art training algorithms for LDA but with
a much less memory consumption. TBP can do topic modeling when massive corpora
cannot fit in the computer memory, for example, extracting thematic topics from
7 GB PUBMED corpora on a common desktop computer with 2GB memory.
| Jia Zeng, Zhi-Qiang Liu and Xiao-Qin Cao | null | 1206.1147 | null | null |
Cumulative Step-size Adaptation on Linear Functions: Technical Report | cs.LG | The CSA-ES is an Evolution Strategy with Cumulative Step size Adaptation,
where the step size is adapted measuring the length of a so-called cumulative
path. The cumulative path is a combination of the previous steps realized by
the algorithm, where the importance of each step decreases with time. This
article studies the CSA-ES on composites of strictly increasing with affine
linear functions through the investigation of its underlying Markov chains.
Rigorous results on the change and the variation of the step size are derived
with and without cumulation. The step-size diverges geometrically fast in most
cases. Furthermore, the influence of the cumulation parameter is studied.
| Alexandre Adrien Chotard (LRI, INRIA Saclay - Ile de France), Anne
Auger (INRIA Saclay - Ile de France), Nikolaus Hansen (LRI, INRIA Saclay -
Ile de France, MSR - INRIA) | null | 1206.1208 | null | null |
Factoring nonnegative matrices with linear programs | math.OC cs.LG stat.ML | This paper describes a new approach, based on linear programming, for
computing nonnegative matrix factorizations (NMFs). The key idea is a
data-driven model for the factorization where the most salient features in the
data are used to express the remaining features. More precisely, given a data
matrix X, the algorithm identifies a matrix C such that X approximately equals
CX and some linear constraints. The constraints are chosen to ensure that the
matrix C selects features; these features can then be used to find a low-rank
NMF of X. A theoretical analysis demonstrates that this approach has guarantees
similar to those of the recent NMF algorithm of Arora et al. (2012). In
contrast with this earlier work, the proposed method extends to more general
noise models and leads to efficient, scalable algorithms. Experiments with
synthetic and real datasets provide evidence that the new approach is also
superior in practice. An optimized C++ implementation can factor a
multigigabyte matrix in a matter of minutes.
| Victor Bittorf and Benjamin Recht and Christopher Re and Joel A. Tropp | null | 1206.1270 | null | null |
A New Greedy Algorithm for Multiple Sparse Regression | stat.ML cs.LG | This paper proposes a new algorithm for multiple sparse regression in high
dimensions, where the task is to estimate the support and values of several
(typically related) sparse vectors from a few noisy linear measurements. Our
algorithm is a "forward-backward" greedy procedure that -- uniquely -- operates
on two distinct classes of objects. In particular, we organize our target
sparse vectors as a matrix; our algorithm involves iterative addition and
removal of both (a) individual elements, and (b) entire rows (corresponding to
shared features), of the matrix.
Analytically, we establish that our algorithm manages to recover the supports
(exactly) and values (approximately) of the sparse vectors, under assumptions
similar to existing approaches based on convex optimization. However, our
algorithm has a much smaller computational complexity. Perhaps most
interestingly, it is seen empirically to require visibly fewer samples. Ours
represents the first attempt to extend greedy algorithms to the class of models
that can only/best be represented by a combination of component structural
assumptions (sparse and group-sparse, in our case).
| Ali Jalali and Sujay Sanghavi | null | 1206.1402 | null | null |
Sparse projections onto the simplex | cs.LG stat.ML | Most learning methods with rank or sparsity constraints use convex
relaxations, which lead to optimization with the nuclear norm or the
$\ell_1$-norm. However, several important learning applications cannot benefit
from this approach as they feature these convex norms as constraints in
addition to the non-convex rank and sparsity constraints. In this setting, we
derive efficient sparse projections onto the simplex and its extension, and
illustrate how to use them to solve high-dimensional learning problems in
quantum tomography, sparse density estimation and portfolio selection with
non-convex constraints.
| Anastasios Kyrillidis, Stephen Becker, Volkan Cevher and, Christoph
Koch | null | 1206.1529 | null | null |
Proximal Newton-type methods for minimizing composite functions | stat.ML cs.DS cs.LG cs.NA math.OC | We generalize Newton-type methods for minimizing smooth functions to handle a
sum of two convex functions: a smooth function and a nonsmooth function with a
simple proximal mapping. We show that the resulting proximal Newton-type
methods inherit the desirable convergence behavior of Newton-type methods for
minimizing smooth functions, even when search directions are computed
inexactly. Many popular methods tailored to problems arising in bioinformatics,
signal processing, and statistical learning are special cases of proximal
Newton-type methods, and our analysis yields new convergence results for some
of these methods.
| Jason D. Lee, Yuekai Sun, Michael A. Saunders | null | 1206.1623 | null | null |
Dimension Reduction by Mutual Information Discriminant Analysis | cs.CV cs.IT cs.LG math.IT | In the past few decades, researchers have proposed many discriminant analysis
(DA) algorithms for the study of high-dimensional data in a variety of
problems. Most DA algorithms for feature extraction are based on
transformations that simultaneously maximize the between-class scatter and
minimize the withinclass scatter matrices. This paper presents a novel DA
algorithm for feature extraction using mutual information (MI). However, it is
not always easy to obtain an accurate estimation for high-dimensional MI. In
this paper, we propose an efficient method for feature extraction that is based
on one-dimensional MI estimations. We will refer to this algorithm as mutual
information discriminant analysis (MIDA). The performance of this proposed
method was evaluated using UCI databases. The results indicate that MIDA
provides robust performance over different data sets with different
characteristics and that MIDA always performs better than, or at least
comparable to, the best performing algorithms.
| Ali Shadvar | null | 1206.2058 | null | null |
Communication-Efficient Parallel Belief Propagation for Latent Dirichlet
Allocation | cs.LG | This paper presents a novel communication-efficient parallel belief
propagation (CE-PBP) algorithm for training latent Dirichlet allocation (LDA).
Based on the synchronous belief propagation (BP) algorithm, we first develop a
parallel belief propagation (PBP) algorithm on the parallel architecture.
Because the extensive communication delay often causes a low efficiency of
parallel topic modeling, we further use Zipf's law to reduce the total
communication cost in PBP. Extensive experiments on different data sets
demonstrate that CE-PBP achieves a higher topic modeling accuracy and reduces
more than 80% communication cost than the state-of-the-art parallel Gibbs
sampling (PGS) algorithm.
| Jian-feng Yan, Zhi-Qiang Liu, Yang Gao, Jia Zeng | null | 1206.2190 | null | null |
Fast Cross-Validation via Sequential Testing | cs.LG stat.ML | With the increasing size of today's data sets, finding the right parameter
configuration in model selection via cross-validation can be an extremely
time-consuming task. In this paper we propose an improved cross-validation
procedure which uses nonparametric testing coupled with sequential analysis to
determine the best parameter set on linearly increasing subsets of the data. By
eliminating underperforming candidates quickly and keeping promising candidates
as long as possible, the method speeds up the computation while preserving the
capability of the full cross-validation. Theoretical considerations underline
the statistical power of our procedure. The experimental evaluation shows that
our method reduces the computation time by a factor of up to 120 compared to a
full cross-validation with a negligible impact on the accuracy.
| Tammo Krueger, Danny Panknin, Mikio Braun | null | 1206.2248 | null | null |
PRISMA: PRoximal Iterative SMoothing Algorithm | math.OC cs.LG | Motivated by learning problems including max-norm regularized matrix
completion and clustering, robust PCA and sparse inverse covariance selection,
we propose a novel optimization algorithm for minimizing a convex objective
which decomposes into three parts: a smooth part, a simple non-smooth Lipschitz
part, and a simple non-smooth non-Lipschitz part. We use a time variant
smoothing strategy that allows us to obtain a guarantee that does not depend on
knowing in advance the total number of iterations nor a bound on the domain.
| Francesco Orabona and Andreas Argyriou and Nathan Srebro | null | 1206.2372 | null | null |
IDS: An Incremental Learning Algorithm for Finite Automata | cs.LG cs.DS cs.FL | We present a new algorithm IDS for incremental learning of deterministic
finite automata (DFA). This algorithm is based on the concept of distinguishing
sequences introduced in (Angluin81). We give a rigorous proof that two versions
of this learning algorithm correctly learn in the limit. Finally we present an
empirical performance analysis that compares these two algorithms, focussing on
learning times and different types of learning queries. We conclude that IDS is
an efficient algorithm for software engineering applications of automata
learning, such as testing and model inference.
| Muddassar A. Sindhu, Karl Meinke | null | 1206.2691 | null | null |
Practical Bayesian Optimization of Machine Learning Algorithms | stat.ML cs.LG | Machine learning algorithms frequently require careful tuning of model
hyperparameters, regularization terms, and optimization parameters.
Unfortunately, this tuning is often a "black art" that requires expert
experience, unwritten rules of thumb, or sometimes brute-force search. Much
more appealing is the idea of developing automatic approaches which can
optimize the performance of a given learning algorithm to the task at hand. In
this work, we consider the automatic tuning problem within the framework of
Bayesian optimization, in which a learning algorithm's generalization
performance is modeled as a sample from a Gaussian process (GP). The tractable
posterior distribution induced by the GP leads to efficient use of the
information gathered by previous experiments, enabling optimal choices about
what parameters to try next. Here we show how the effects of the Gaussian
process prior and the associated inference procedure can have a large impact on
the success or failure of Bayesian optimization. We show that thoughtful
choices can lead to results that exceed expert-level performance in tuning
machine learning algorithms. We also describe new algorithms that take into
account the variable cost (duration) of learning experiments and that can
leverage the presence of multiple cores for parallel experimentation. We show
that these proposed algorithms improve on previous automatic procedures and can
reach or surpass human expert-level optimization on a diverse set of
contemporary algorithms including latent Dirichlet allocation, structured SVMs
and convolutional neural networks.
| Jasper Snoek, Hugo Larochelle and Ryan P. Adams | null | 1206.2944 | null | null |
Statistical Consistency of Finite-dimensional Unregularized Linear
Classification | cs.LG stat.ML | This manuscript studies statistical properties of linear classifiers obtained
through minimization of an unregularized convex risk over a finite sample.
Although the results are explicitly finite-dimensional, inputs may be passed
through feature maps; in this way, in addition to treating the consistency of
logistic regression, this analysis also handles boosting over a finite weak
learning class with, for instance, the exponential, logistic, and hinge losses.
In this finite-dimensional setting, it is still possible to fit arbitrary
decision boundaries: scaling the complexity of the weak learning class with the
sample size leads to the optimal classification risk almost surely.
| Matus Telgarsky | null | 1206.3072 | null | null |
Sparse Distributed Learning Based on Diffusion Adaptation | cs.LG cs.DC | This article proposes diffusion LMS strategies for distributed estimation
over adaptive networks that are able to exploit sparsity in the underlying
system model. The approach relies on convex regularization, common in
compressive sensing, to enhance the detection of sparsity via a diffusive
process over the network. The resulting algorithms endow networks with learning
abilities and allow them to learn the sparse structure from the incoming data
in real-time, and also to track variations in the sparsity of the model. We
provide convergence and mean-square performance analysis of the proposed method
and show under what conditions it outperforms the unregularized diffusion
version. We also show how to adaptively select the regularization parameter.
Simulation results illustrate the advantage of the proposed filters for sparse
data recovery.
| Paolo Di Lorenzo and Ali H. Sayed | 10.1109/TSP.2012.2232663 | 1206.3099 | null | null |
Identifiability and Unmixing of Latent Parse Trees | stat.ML cs.LG | This paper explores unsupervised learning of parsing models along two
directions. First, which models are identifiable from infinite data? We use a
general technique for numerically checking identifiability based on the rank of
a Jacobian matrix, and apply it to several standard constituency and dependency
parsing models. Second, for identifiable models, how do we estimate the
parameters efficiently? EM suffers from local optima, while recent work using
spectral methods cannot be directly applied since the topology of the parse
tree varies across sentences. We develop a strategy, unmixing, which deals with
this additional complexity for restricted classes of parsing models.
| Daniel Hsu and Sham M. Kakade and Percy Liang | null | 1206.3137 | null | null |
Improved Spectral-Norm Bounds for Clustering | cs.LG cs.DS | Aiming to unify known results about clustering mixtures of distributions
under separation conditions, Kumar and Kannan[2010] introduced a deterministic
condition for clustering datasets. They showed that this single deterministic
condition encompasses many previously studied clustering assumptions. More
specifically, their proximity condition requires that in the target
$k$-clustering, the projection of a point $x$ onto the line joining its cluster
center $\mu$ and some other center $\mu'$, is a large additive factor closer to
$\mu$ than to $\mu'$. This additive factor can be roughly described as $k$
times the spectral norm of the matrix representing the differences between the
given (known) dataset and the means of the (unknown) target clustering.
Clearly, the proximity condition implies center separation -- the distance
between any two centers must be as large as the above mentioned bound.
In this paper we improve upon the work of Kumar and Kannan along several
axes. First, we weaken the center separation bound by a factor of $\sqrt{k}$,
and secondly we weaken the proximity condition by a factor of $k$. Using these
weaker bounds we still achieve the same guarantees when all points satisfy the
proximity condition. We also achieve better guarantees when only
$(1-\epsilon)$-fraction of the points satisfy the weaker proximity condition.
The bulk of our analysis relies only on center separation under which one can
produce a clustering which (i) has low error, (ii) has low $k$-means cost, and
(iii) has centers very close to the target centers.
Our improved separation condition allows us to match the results of the
Planted Partition Model of McSherry[2001], improve upon the results of
Ostrovsky et al[2006], and improve separation results for mixture of Gaussian
models in a particular setting.
| Pranjal Awasthi, Or Sheffet | null | 1206.3204 | null | null |
CORL: A Continuous-state Offset-dynamics Reinforcement Learner | cs.LG stat.ML | Continuous state spaces and stochastic, switching dynamics characterize a
number of rich, realworld domains, such as robot navigation across varying
terrain. We describe a reinforcementlearning algorithm for learning in these
domains and prove for certain environments the algorithm is probably
approximately correct with a sample complexity that scales polynomially with
the state-space dimension. Unfortunately, no optimal planning techniques exist
in general for such problems; instead we use fitted value iteration to solve
the learned MDP, and include the error due to approximate planning in our
bounds. Finally, we report an experiment using a robotic car driving over
varying terrain to demonstrate that these dynamics representations adequately
capture real-world dynamics and that our algorithm can be used to efficiently
solve such problems.
| Emma Brunskill, Bethany Leffler, Lihong Li, Michael L. Littman,
Nicholas Roy | null | 1206.3231 | null | null |
Learning Inclusion-Optimal Chordal Graphs | cs.LG cs.DS stat.ML | Chordal graphs can be used to encode dependency models that are representable
by both directed acyclic and undirected graphs. This paper discusses a very
simple and efficient algorithm to learn the chordal structure of a
probabilistic model from data. The algorithm is a greedy hill-climbing search
algorithm that uses the inclusion boundary neighborhood over chordal graphs. In
the limit of a large sample size and under appropriate hypotheses on the
scoring criterion, we prove that the algorithm will find a structure that is
inclusion-optimal when the dependency model of the data-generating distribution
can be represented exactly by an undirected graph. The algorithm is evaluated
on simulated datasets.
| Vincent Auvray, Louis Wehenkel | null | 1206.3236 | null | null |
Clique Matrices for Statistical Graph Decomposition and Parameterising
Restricted Positive Definite Matrices | cs.DM cs.LG stat.ML | We introduce Clique Matrices as an alternative representation of undirected
graphs, being a generalisation of the incidence matrix representation. Here we
use clique matrices to decompose a graph into a set of possibly overlapping
clusters, de ned as well-connected subsets of vertices. The decomposition is
based on a statistical description which encourages clusters to be well
connected and few in number. Inference is carried out using a variational
approximation. Clique matrices also play a natural role in parameterising
positive de nite matrices under zero constraints on elements of the matrix. We
show that clique matrices can parameterise all positive de nite matrices
restricted according to a decomposable graph and form a structured Factor
Analysis approximation in the non-decomposable case.
| David Barber | null | 1206.3237 | null | null |
Greedy Block Coordinate Descent for Large Scale Gaussian Process
Regression | cs.LG stat.ML | We propose a variable decomposition algorithm -greedy block coordinate
descent (GBCD)- in order to make dense Gaussian process regression practical
for large scale problems. GBCD breaks a large scale optimization into a series
of small sub-problems. The challenge in variable decomposition algorithms is
the identification of a subproblem (the active set of variables) that yields
the largest improvement. We analyze the limitations of existing methods and
cast the active set selection into a zero-norm constrained optimization problem
that we solve using greedy methods. By directly estimating the decrease in the
objective function, we obtain not only efficient approximate solutions for
GBCD, but we are also able to demonstrate that the method is globally
convergent. Empirical comparisons against competing dense methods like
Conjugate Gradient or SMO show that GBCD is an order of magnitude faster.
Comparisons against sparse GP methods show that GBCD is both accurate and
capable of handling datasets of 100,000 samples or more.
| Liefeng Bo, Cristian Sminchisescu | null | 1206.3238 | null | null |
Approximating the Partition Function by Deleting and then Correcting for
Model Edges | cs.LG stat.ML | We propose an approach for approximating the partition function which is
based on two steps: (1) computing the partition function of a simplified model
which is obtained by deleting model edges, and (2) rectifying the result by
applying an edge-by-edge correction. The approach leads to an intuitive
framework in which one can trade-off the quality of an approximation with the
complexity of computing it. It also includes the Bethe free energy
approximation as a degenerate case. We develop the approach theoretically in
this paper and provide a number of empirical results that reveal its practical
utility.
| Arthur Choi, Adnan Darwiche | null | 1206.3241 | null | null |
Multi-View Learning in the Presence of View Disagreement | cs.LG stat.ML | Traditional multi-view learning approaches suffer in the presence of view
disagreement,i.e., when samples in each view do not belong to the same class
due to view corruption, occlusion or other noise processes. In this paper we
present a multi-view learning approach that uses a conditional entropy
criterion to detect view disagreement. Once detected, samples with view
disagreement are filtered and standard multi-view learning methods can be
successfully applied to the remaining samples. Experimental evaluation on
synthetic and audio-visual databases demonstrates that the detection and
filtering of view disagreement considerably increases the performance of
traditional multi-view learning approaches.
| C. Christoudias, Raquel Urtasun, Trevor Darrell | null | 1206.3242 | null | null |
Bounds on the Bethe Free Energy for Gaussian Networks | cs.LG stat.ML | We address the problem of computing approximate marginals in Gaussian
probabilistic models by using mean field and fractional Bethe approximations.
As an extension of Welling and Teh (2001), we define the Gaussian fractional
Bethe free energy in terms of the moment parameters of the approximate
marginals and derive an upper and lower bound for it. We give necessary
conditions for the Gaussian fractional Bethe free energies to be bounded from
below. It turns out that the bounding condition is the same as the pairwise
normalizability condition derived by Malioutov et al. (2006) as a sufficient
condition for the convergence of the message passing algorithm. By giving a
counterexample, we disprove the conjecture in Welling and Teh (2001): even when
the Bethe free energy is not bounded from below, it can possess a local minimum
to which the minimization algorithms can converge.
| Botond Cseke, Tom Heskes | null | 1206.3243 | null | null |
Learning Convex Inference of Marginals | cs.LG stat.ML | Graphical models trained using maximum likelihood are a common tool for
probabilistic inference of marginal distributions. However, this approach
suffers difficulties when either the inference process or the model is
approximate. In this paper, the inference process is first defined to be the
minimization of a convex function, inspired by free energy approximations.
Learning is then done directly in terms of the performance of the inference
process at univariate marginal prediction. The main novelty is that this is a
direct minimization of emperical risk, where the risk measures the accuracy of
predicted marginals.
| Justin Domke | null | 1206.3247 | null | null |
Projected Subgradient Methods for Learning Sparse Gaussians | cs.LG stat.ML | Gaussian Markov random fields (GMRFs) are useful in a broad range of
applications. In this paper we tackle the problem of learning a sparse GMRF in
a high-dimensional space. Our approach uses the l1-norm as a regularization on
the inverse covariance matrix. We utilize a novel projected gradient method,
which is faster than previous methods in practice and equal to the best
performing of these in asymptotic complexity. We also extend the l1-regularized
objective to the problem of sparsifying entire blocks within the inverse
covariance matrix. Our methods generalize fairly easily to this case, while
other methods do not. We demonstrate that our extensions give better
generalization performance on two real domains--biological network analysis and
a 2D-shape modeling image task.
| John Duchi, Stephen Gould, Daphne Koller | null | 1206.3249 | null | null |
Convex Point Estimation using Undirected Bayesian Transfer Hierarchies | cs.LG stat.ML | When related learning tasks are naturally arranged in a hierarchy, an
appealing approach for coping with scarcity of instances is that of transfer
learning using a hierarchical Bayes framework. As fully Bayesian computations
can be difficult and computationally demanding, it is often desirable to use
posterior point estimates that facilitate (relatively) efficient prediction.
However, the hierarchical Bayes framework does not always lend itself naturally
to this maximum aposteriori goal. In this work we propose an undirected
reformulation of hierarchical Bayes that relies on priors in the form of
similarity measures. We introduce the notion of "degree of transfer" weights on
components of these similarity measures, and show how they can be automatically
learned within a joint probabilistic framework. Importantly, our reformulation
results in a convex objective for many learning problems, thus facilitating
optimal posterior point estimation using standard optimization techniques. In
addition, we no longer require proper priors, allowing for flexible and
straightforward specification of joint distributions over transfer hierarchies.
We show that our framework is effective for learning models that are part of
transfer hierarchies for two real-life tasks: object shape modeling using
Gaussian density estimation and document classification.
| Gal Elidan, Ben Packer, Geremy Heitz, Daphne Koller | null | 1206.3252 | null | null |
Latent Topic Models for Hypertext | cs.IR cs.CL cs.LG stat.ML | Latent topic models have been successfully applied as an unsupervised topic
discovery technique in large document collections. With the proliferation of
hypertext document collection such as the Internet, there has also been great
interest in extending these approaches to hypertext [6, 9]. These approaches
typically model links in an analogous fashion to how they model words - the
document-link co-occurrence matrix is modeled in the same way that the
document-word co-occurrence matrix is modeled in standard topic models. In this
paper we present a probabilistic generative model for hypertext document
collections that explicitly models the generation of links. Specifically, links
from a word w to a document d depend directly on how frequent the topic of w is
in d, in addition to the in-degree of d. We show how to perform EM learning on
this model efficiently. By not modeling links as analogous to words, we end up
using far fewer free parameters and obtain better link prediction results.
| Amit Gruber, Michal Rosen-Zvi, Yair Weiss | null | 1206.3254 | null | null |
Multi-View Learning over Structured and Non-Identical Outputs | cs.LG stat.ML | In many machine learning problems, labeled training data is limited but
unlabeled data is ample. Some of these problems have instances that can be
factored into multiple views, each of which is nearly sufficent in determining
the correct labels. In this paper we present a new algorithm for probabilistic
multi-view learning which uses the idea of stochastic agreement between views
as regularization. Our algorithm works on structured and unstructured problems
and easily generalizes to partial agreement scenarios. For the full agreement
case, our algorithm minimizes the Bhattacharyya distance between the models of
each view, and performs better than CoBoosting and two-view Perceptron on
several flat and structured classification problems.
| Kuzman Ganchev, Joao Graca, John Blitzer, Ben Taskar | null | 1206.3256 | null | null |
Constrained Approximate Maximum Entropy Learning of Markov Random Fields | cs.LG stat.ML | Parameter estimation in Markov random fields (MRFs) is a difficult task, in
which inference over the network is run in the inner loop of a gradient descent
procedure. Replacing exact inference with approximate methods such as loopy
belief propagation (LBP) can suffer from poor convergence. In this paper, we
provide a different approach for combining MRF learning and Bethe
approximation. We consider the dual of maximum likelihood Markov network
learning - maximizing entropy with moment matching constraints - and then
approximate both the objective and the constraints in the resulting
optimization problem. Unlike previous work along these lines (Teh & Welling,
2003), our formulation allows parameter sharing between features in a general
log-linear model, parameter regularization and conditional training. We show
that piecewise training (Sutton & McCallum, 2005) is a very restricted special
case of this formulation. We study two optimization strategies: one based on a
single convex approximation and one that uses repeated convex approximations.
We show results on several real-world networks that demonstrate that these
algorithms can significantly outperform learning with loopy and piecewise. Our
results also provide a framework for analyzing the trade-offs of different
relaxations of the entropy objective and of the constraints.
| Varun Ganapathi, David Vickrey, John Duchi, Daphne Koller | null | 1206.3257 | null | null |
Cumulative distribution networks and the derivative-sum-product
algorithm | cs.LG stat.ML | We introduce a new type of graphical model called a "cumulative distribution
network" (CDN), which expresses a joint cumulative distribution as a product of
local functions. Each local function can be viewed as providing evidence about
possible orderings, or rankings, of variables. Interestingly, we find that the
conditional independence properties of CDNs are quite different from other
graphical models. We also describe a messagepassing algorithm that efficiently
computes conditional cumulative distributions. Due to the unique independence
properties of the CDN, these messages do not in general have a one-to-one
correspondence with messages exchanged in standard algorithms, such as belief
propagation. We demonstrate the application of CDNs for structured ranking
learning using a previously-studied multi-player gaming dataset.
| Jim Huang, Brendan J. Frey | null | 1206.3259 | null | null |
Causal discovery of linear acyclic models with arbitrary distributions | stat.ML cs.AI cs.LG | An important task in data analysis is the discovery of causal relationships
between observed variables. For continuous-valued data, linear acyclic causal
models are commonly used to model the data-generating process, and the
inference of such models is a well-studied problem. However, existing methods
have significant limitations. Methods based on conditional independencies
(Spirtes et al. 1993; Pearl 2000) cannot distinguish between
independence-equivalent models, whereas approaches purely based on Independent
Component Analysis (Shimizu et al. 2006) are inapplicable to data which is
partially Gaussian. In this paper, we generalize and combine the two
approaches, to yield a method able to learn the model structure in many cases
for which the previous methods provide answers that are either incorrect or are
not as informative as possible. We give exact graphical conditions for when two
distinct models represent the same family of distributions, and empirically
demonstrate the power of our method through thorough simulations.
| Patrik O. Hoyer, Aapo Hyvarinen, Richard Scheines, Peter L. Spirtes,
Joseph Ramsey, Gustavo Lacerda, Shohei Shimizu | null | 1206.3260 | null | null |
Convergent Message-Passing Algorithms for Inference over General Graphs
with Convex Free Energies | cs.LG stat.ML | Inference problems in graphical models can be represented as a constrained
optimization of a free energy function. It is known that when the Bethe free
energy is used, the fixedpoints of the belief propagation (BP) algorithm
correspond to the local minima of the free energy. However BP fails to converge
in many cases of interest. Moreover, the Bethe free energy is non-convex for
graphical models with cycles thus introducing great difficulty in deriving
efficient algorithms for finding local minima of the free energy for general
graphs. In this paper we introduce two efficient BP-like algorithms, one
sequential and the other parallel, that are guaranteed to converge to the
global minimum, for any graph, over the class of energies known as "convex free
energies". In addition, we propose an efficient heuristic for setting the
parameters of the convex free energy based on the structure of the graph.
| Tamir Hazan, Amnon Shashua | null | 1206.3262 | null | null |
Bayesian Out-Trees | cs.LG stat.ML | A Bayesian treatment of latent directed graph structure for non-iid data is
provided where each child datum is sampled with a directed conditional
dependence on a single unknown parent datum. The latent graph structure is
assumed to lie in the family of directed out-tree graphs which leads to
efficient Bayesian inference. The latent likelihood of the data and its
gradients are computable in closed form via Tutte's directed matrix tree
theorem using determinants and inverses of the out-Laplacian. This novel
likelihood subsumes iid likelihood, is exchangeable and yields efficient
unsupervised and semi-supervised learning algorithms. In addition to handling
taxonomy and phylogenetic datasets the out-tree assumption performs
surprisingly well as a semi-parametric density estimator on standard iid
datasets. Experiments with unsupervised and semisupervised learning are shown
on various UCI and taxonomy datasets.
| Tony S. Jebara | null | 1206.3269 | null | null |
Estimation and Clustering with Infinite Rankings | cs.LG stat.ML | This paper presents a natural extension of stagewise ranking to the the case
of infinitely many items. We introduce the infinite generalized Mallows model
(IGM), describe its properties and give procedures to estimate it from data.
For estimation of multimodal distributions we introduce the
Exponential-Blurring-Mean-Shift nonparametric clustering algorithm. The
experiments highlight the properties of the new model and demonstrate that
infinite models can be simple, elegant and practical.
| Marina Meila, Le Bao | null | 1206.3270 | null | null |
Small Sample Inference for Generalization Error in Classification Using
the CUD Bound | cs.LG stat.ML | Confidence measures for the generalization error are crucial when small
training samples are used to construct classifiers. A common approach is to
estimate the generalization error by resampling and then assume the resampled
estimator follows a known distribution to form a confidence set [Kohavi 1995,
Martin 1996,Yang 2006]. Alternatively, one might bootstrap the resampled
estimator of the generalization error to form a confidence set. Unfortunately,
these methods do not reliably provide sets of the desired confidence. The poor
performance appears to be due to the lack of smoothness of the generalization
error as a function of the learned classifier. This results in a non-normal
distribution of the estimated generalization error. We construct a confidence
set for the generalization error by use of a smooth upper bound on the
deviation between the resampled estimate and generalization error. The
confidence set is formed by bootstrapping this upper bound. In cases in which
the approximation class for the classifier can be represented as a parametric
additive model, we provide a computationally efficient algorithm. This method
exhibits superior performance across a series of test and simulated data sets.
| Eric B. Laber, Susan A. Murphy | null | 1206.3274 | null | null |
Learning Hidden Markov Models for Regression using Path Aggregation | cs.LG cs.CE q-bio.QM | We consider the task of learning mappings from sequential data to real-valued
responses. We present and evaluate an approach to learning a type of hidden
Markov model (HMM) for regression. The learning process involves inferring the
structure and parameters of a conventional HMM, while simultaneously learning a
regression model that maps features that characterize paths through the model
to continuous responses. Our results, in both synthetic and biological domains,
demonstrate the value of jointly learning the two components of our approach.
| Keith Noto, Mark Craven | null | 1206.3275 | null | null |
The Phylogenetic Indian Buffet Process: A Non-Exchangeable Nonparametric
Prior for Latent Features | cs.LG stat.ML | Nonparametric Bayesian models are often based on the assumption that the
objects being modeled are exchangeable. While appropriate in some applications
(e.g., bag-of-words models for documents), exchangeability is sometimes assumed
simply for computational reasons; non-exchangeable models might be a better
choice for applications based on subject matter. Drawing on ideas from
graphical models and phylogenetics, we describe a non-exchangeable prior for a
class of nonparametric latent feature models that is nearly as efficient
computationally as its exchangeable counterpart. Our model is applicable to the
general setting in which the dependencies between objects can be expressed
using a tree, where edge lengths indicate the strength of relationships. We
demonstrate an application to modeling probabilistic choice.
| Kurt T. Miller, Thomas Griffiths, Michael I. Jordan | null | 1206.3279 | null | null |
Dyna-Style Planning with Linear Function Approximation and Prioritized
Sweeping | cs.AI cs.LG cs.SY | We consider the problem of efficiently learning optimal control policies and
value functions over large state spaces in an online setting in which estimates
must be available after each interaction with the world. This paper develops an
explicitly model-based approach extending the Dyna architecture to linear
function approximation. Dynastyle planning proceeds by generating imaginary
experience from the world model and then applying model-free reinforcement
learning algorithms to the imagined state transitions. Our main results are to
prove that linear Dyna-style planning converges to a unique solution
independent of the generating distribution, under natural conditions. In the
policy evaluation setting, we prove that the limit point is the least-squares
(LSTD) solution. An implication of our results is that prioritized-sweeping can
be soundly extended to the linear approximation case, backing up to preceding
features rather than to preceding states. We introduce two versions of
prioritized sweeping with linear Dyna and briefly illustrate their performance
empirically on the Mountain Car and Boyan Chain problems.
| Richard S. Sutton, Csaba Szepesvari, Alborz Geramifard, Michael P.
Bowling | null | 1206.3285 | null | null |
Learning the Bayesian Network Structure: Dirichlet Prior versus Data | cs.LG stat.ME stat.ML | In the Bayesian approach to structure learning of graphical models, the
equivalent sample size (ESS) in the Dirichlet prior over the model parameters
was recently shown to have an important effect on the maximum-a-posteriori
estimate of the Bayesian network structure. In our first contribution, we
theoretically analyze the case of large ESS-values, which complements previous
work: among other results, we find that the presence of an edge in a Bayesian
network is favoured over its absence even if both the Dirichlet prior and the
data imply independence, as long as the conditional empirical distribution is
notably different from uniform. In our second contribution, we focus on
realistic ESS-values, and provide an analytical approximation to the "optimal"
ESS-value in a predictive sense (its accuracy is also validated
experimentally): this approximation provides an understanding as to which
properties of the data have the main effect determining the "optimal"
ESS-value.
| Harald Steck | null | 1206.3287 | null | null |
Modelling local and global phenomena with sparse Gaussian processes | cs.LG stat.ML | Much recent work has concerned sparse approximations to speed up the Gaussian
process regression from the unfavorable O(n3) scaling in computational time to
O(nm2). Thus far, work has concentrated on models with one covariance function.
However, in many practical situations additive models with multiple covariance
functions may perform better, since the data may contain both long and short
length-scale phenomena. The long length-scales can be captured with global
sparse approximations, such as fully independent conditional (FIC), and the
short length-scales can be modeled naturally by covariance functions with
compact support (CS). CS covariance functions lead to naturally sparse
covariance matrices, which are computationally cheaper to handle than full
covariance matrices. In this paper, we propose a new sparse Gaussian process
model with two additive components: FIC for the long length-scales and CS
covariance function for the short length-scales. We give theoretical and
experimental results and show that under certain conditions the proposed model
has the same computational complexity as FIC. We also compare the model
performance of the proposed model to additive models approximated by fully and
partially independent conditional (PIC). We use real data sets and show that
our model outperforms FIC and PIC approximations for data sets with two
additive phenomena.
| Jarno Vanhatalo, Aki Vehtari | null | 1206.3290 | null | null |
Flexible Priors for Exemplar-based Clustering | cs.LG stat.ML | Exemplar-based clustering methods have been shown to produce state-of-the-art
results on a number of synthetic and real-world clustering problems. They are
appealing because they offer computational benefits over latent-mean models and
can handle arbitrary pairwise similarity measures between data points. However,
when trying to recover underlying structure in clustering problems, tailored
similarity measures are often not enough; we also desire control over the
distribution of cluster sizes. Priors such as Dirichlet process priors allow
the number of clusters to be unspecified while expressing priors over data
partitions. To our knowledge, they have not been applied to exemplar-based
models. We show how to incorporate priors, including Dirichlet process priors,
into the recently introduced affinity propagation algorithm. We develop an
efficient maxproduct belief propagation algorithm for our new model and
demonstrate experimentally how the expanded range of clustering priors allows
us to better recover true clusterings in situations where we have some
information about the generating process.
| Daniel Tarlow, Richard S. Zemel, Brendan J. Frey | null | 1206.3294 | null | null |
Hybrid Variational/Gibbs Collapsed Inference in Topic Models | cs.LG stat.ML | Variational Bayesian inference and (collapsed) Gibbs sampling are the two
important classes of inference algorithms for Bayesian networks. Both have
their advantages and disadvantages: collapsed Gibbs sampling is unbiased but is
also inefficient for large count values and requires averaging over many
samples to reduce variance. On the other hand, variational Bayesian inference
is efficient and accurate for large count values but suffers from bias for
small counts. We propose a hybrid algorithm that combines the best of both
worlds: it samples very small counts and applies variational updates to large
counts. This hybridization is shown to significantly improve testset perplexity
relative to variational inference at no computational cost.
| Max Welling, Yee Whye Teh, Hilbert Kappen | null | 1206.3297 | null | null |
Continuous Time Dynamic Topic Models | cs.IR cs.LG stat.ML | In this paper, we develop the continuous time dynamic topic model (cDTM). The
cDTM is a dynamic topic model that uses Brownian motion to model the latent
topics through a sequential collection of documents, where a "topic" is a
pattern of word use that we expect to evolve over the course of the collection.
We derive an efficient variational approximate inference algorithm that takes
advantage of the sparsity of observations in text, a property that lets us
easily handle many time points. In contrast to the cDTM, the original
discrete-time dynamic topic model (dDTM) requires that time be discretized.
Moreover, the complexity of variational inference for the dDTM grows quickly as
time granularity increases, a drawback which limits fine-grained
discretization. We demonstrate the cDTM on two news corpora, reporting both
predictive perplexity and the novel task of time stamp prediction.
| Chong Wang, David Blei, David Heckerman | null | 1206.3298 | null | null |
Simple Regret Optimization in Online Planning for Markov Decision
Processes | cs.AI cs.LG | We consider online planning in Markov decision processes (MDPs). In online
planning, the agent focuses on its current state only, deliberates about the
set of possible policies from that state onwards and, when interrupted, uses
the outcome of that exploratory deliberation to choose what action to perform
next. The performance of algorithms for online planning is assessed in terms of
simple regret, which is the agent's expected performance loss when the chosen
action, rather than an optimal one, is followed.
To date, state-of-the-art algorithms for online planning in general MDPs are
either best effort, or guarantee only polynomial-rate reduction of simple
regret over time. Here we introduce a new Monte-Carlo tree search algorithm,
BRUE, that guarantees exponential-rate reduction of simple regret and error
probability. This algorithm is based on a simple yet non-standard state-space
sampling scheme, MCTS2e, in which different parts of each sample are dedicated
to different exploratory objectives. Our empirical evaluation shows that BRUE
not only provides superior performance guarantees, but is also very effective
in practice and favorably compares to state-of-the-art. We then extend BRUE
with a variant of "learning by forgetting." The resulting set of algorithms,
BRUE(alpha), generalizes BRUE, improves the exponential factor in the upper
bound on its reduction rate, and exhibits even more attractive empirical
performance.
| Zohar Feldman, Carmel Domshlak | null | 1206.3382 | null | null |
A Novel Approach for Protein Structure Prediction | cs.LG q-bio.BM | The idea of this project is to study the protein structure and sequence
relationship using the hidden markov model and artificial neural network. In
this context we have assumed two hidden markov models. In first model we have
taken protein secondary structures as hidden and protein sequences as observed.
In second model we have taken protein sequences as hidden and protein
structures as observed. The efficiencies for both the hidden markov models have
been calculated. The results show that the efficiencies of first model is
greater that the second one .These efficiencies are cross validated using
artificial neural network. This signifies the importance of protein secondary
structures as the main hidden controlling factors due to which we observe a
particular amino acid sequence. This also signifies that protein secondary
structure is more conserved in comparison to amino acid sequence.
| Saurabh Sarkar, Prateek Malhotra, Virender Guman | null | 1206.3509 | null | null |
Decentralized Learning for Multi-player Multi-armed Bandits | math.OC cs.LG cs.SY | We consider the problem of distributed online learning with multiple players
in multi-armed bandits (MAB) models. Each player can pick among multiple arms.
When a player picks an arm, it gets a reward. We consider both i.i.d. reward
model and Markovian reward model. In the i.i.d. model each arm is modelled as
an i.i.d. process with an unknown distribution with an unknown mean. In the
Markovian model, each arm is modelled as a finite, irreducible, aperiodic and
reversible Markov chain with an unknown probability transition matrix and
stationary distribution. The arms give different rewards to different players.
If two players pick the same arm, there is a "collision", and neither of them
get any reward. There is no dedicated control channel for coordination or
communication among the players. Any other communication between the users is
costly and will add to the regret. We propose an online index-based distributed
learning policy called ${\tt dUCB_4}$ algorithm that trades off
\textit{exploration v. exploitation} in the right way, and achieves expected
regret that grows at most as near-$O(\log^2 T)$. The motivation comes from
opportunistic spectrum access by multiple secondary users in cognitive radio
networks wherein they must pick among various wireless channels that look
different to different users. This is the first distributed learning algorithm
for multi-player MABs to the best of our knowledge.
| Dileep Kalathil, Naumaan Nayyar and Rahul Jain | 10.1109/CDC.2012.6426587 | 1206.3582 | null | null |
Unsupervised adaptation of brain machine interface decoders | cs.LG q-bio.NC | The performance of neural decoders can degrade over time due to
nonstationarities in the relationship between neuronal activity and behavior.
In this case, brain-machine interfaces (BMI) require adaptation of their
decoders to maintain high performance across time. One way to achieve this is
by use of periodical calibration phases, during which the BMI system (or an
external human demonstrator) instructs the user to perform certain movements or
behaviors. This approach has two disadvantages: (i) calibration phases
interrupt the autonomous operation of the BMI and (ii) between two calibration
phases the BMI performance might not be stable but continuously decrease. A
better alternative would be that the BMI decoder is able to continuously adapt
in an unsupervised manner during autonomous BMI operation, i.e. without knowing
the movement intentions of the user.
In the present article, we present an efficient method for such unsupervised
training of BMI systems for continuous movement control. The proposed method
utilizes a cost function derived from neuronal recordings, which guides a
learning algorithm to evaluate the decoding parameters. We verify the
performance of our adaptive method by simulating a BMI user with an optimal
feedback control model and its interaction with our adaptive BMI decoder. The
simulation results show that the cost function and the algorithm yield fast and
precise trajectories towards targets at random orientations on a 2-dimensional
computer screen. For initially unknown and non-stationary tuning parameters,
our unsupervised method is still able to generate precise trajectories and to
keep its performance stable in the long term. The algorithm can optionally work
also with neuronal error signals instead or in conjunction with the proposed
unsupervised adaptation.
| Tayfun G\"urel, Carsten Mehring | null | 1206.3666 | null | null |
Learning the Structure and Parameters of Large-Population Graphical
Games from Behavioral Data | cs.LG cs.GT stat.ML | We consider learning, from strictly behavioral data, the structure and
parameters of linear influence games (LIGs), a class of parametric graphical
games introduced by Irfan and Ortiz (2014). LIGs facilitate causal strategic
inference (CSI): Making inferences from causal interventions on stable behavior
in strategic settings. Applications include the identification of the most
influential individuals in large (social) networks. Such tasks can also support
policy-making analysis. Motivated by the computational work on LIGs, we cast
the learning problem as maximum-likelihood estimation (MLE) of a generative
model defined by pure-strategy Nash equilibria (PSNE). Our simple formulation
uncovers the fundamental interplay between goodness-of-fit and model
complexity: good models capture equilibrium behavior within the data while
controlling the true number of equilibria, including those unobserved. We
provide a generalization bound establishing the sample complexity for MLE in
our framework. We propose several algorithms including convex loss minimization
(CLM) and sigmoidal approximations. We prove that the number of exact PSNE in
LIGs is small, with high probability; thus, CLM is sound. We illustrate our
approach on synthetic data and real-world U.S. congressional voting records. We
briefly discuss our learning framework's generality and potential applicability
to general graphical games.
| Jean Honorio and Luis Ortiz | null | 1206.3713 | null | null |
How important are Deformable Parts in the Deformable Parts Model? | cs.CV cs.AI cs.LG | The main stated contribution of the Deformable Parts Model (DPM) detector of
Felzenszwalb et al. (over the Histogram-of-Oriented-Gradients approach of Dalal
and Triggs) is the use of deformable parts. A secondary contribution is the
latent discriminative learning. Tertiary is the use of multiple components. A
common belief in the vision community (including ours, before this study) is
that their ordering of contributions reflects the performance of detector in
practice. However, what we have experimentally found is that the ordering of
importance might actually be the reverse. First, we show that by increasing the
number of components, and switching the initialization step from their
aspect-ratio, left-right flipping heuristics to appearance-based clustering,
considerable improvement in performance is obtained. But more intriguingly, we
show that with these new components, the part deformations can now be
completely switched off, yet obtaining results that are almost on par with the
original DPM detector. Finally, we also show initial results for using multiple
components on a different problem -- scene classification, suggesting that this
idea might have wider applications in addition to object detection.
| Santosh K. Divvala and Alexei A. Efros and Martial Hebert | null | 1206.3714 | null | null |
Constraint-free Graphical Model with Fast Learning Algorithm | cs.LG stat.ML | In this paper, we propose a simple, versatile model for learning the
structure and parameters of multivariate distributions from a data set.
Learning a Markov network from a given data set is not a simple problem,
because Markov networks rigorously represent Markov properties, and this rigor
imposes complex constraints on the design of the networks. Our proposed model
removes these constraints, acquiring important aspects from the information
geometry. The proposed parameter- and structure-learning algorithms are simple
to execute as they are based solely on local computation at each node.
Experiments demonstrate that our algorithms work appropriately.
| Kazuya Takabatake and Shotaro Akaho | null | 1206.3721 | null | null |
DANCo: Dimensionality from Angle and Norm Concentration | cs.LG stat.ML | In the last decades the estimation of the intrinsic dimensionality of a
dataset has gained considerable importance. Despite the great deal of research
work devoted to this task, most of the proposed solutions prove to be
unreliable when the intrinsic dimensionality of the input dataset is high and
the manifold where the points lie is nonlinearly embedded in a higher
dimensional space. In this paper we propose a novel robust intrinsic
dimensionality estimator that exploits the twofold complementary information
conveyed both by the normalized nearest neighbor distances and by the angles
computed on couples of neighboring points, providing also closed-forms for the
Kullback-Leibler divergences of the respective distributions. Experiments
performed on both synthetic and real datasets highlight the robustness and the
effectiveness of the proposed algorithm when compared to state of the art
methodologies.
| Claudio Ceruti and Simone Bassis and Alessandro Rozza and Gabriele
Lombardi and Elena Casiraghi and Paola Campadelli | null | 1206.3881 | null | null |
A Linear Approximation to the chi^2 Kernel with Geometric Convergence | cs.LG cs.CV stat.ML | We propose a new analytical approximation to the $\chi^2$ kernel that
converges geometrically. The analytical approximation is derived with
elementary methods and adapts to the input distribution for optimal convergence
rate. Experiments show the new approximation leads to improved performance in
image classification and semantic segmentation tasks using a random Fourier
feature approximation of the $\exp-\chi^2$ kernel. Besides, out-of-core
principal component analysis (PCA) methods are introduced to reduce the
dimensionality of the approximation and achieve better performance at the
expense of only an additional constant factor to the time complexity. Moreover,
when PCA is performed jointly on the training and unlabeled testing data,
further performance improvements can be obtained. Experiments conducted on the
PASCAL VOC 2010 segmentation and the ImageNet ILSVRC 2010 datasets show
statistically significant improvements over alternative approximation methods.
| Fuxin Li, Guy Lebanon, Cristian Sminchisescu | null | 1206.4074 | null | null |
ConeRANK: Ranking as Learning Generalized Inequalities | cs.LG cs.IR | We propose a new data mining approach in ranking documents based on the
concept of cone-based generalized inequalities between vectors. A partial
ordering between two vectors is made with respect to a proper cone and thus
learning the preferences is formulated as learning proper cones. A pairwise
learning-to-rank algorithm (ConeRank) is proposed to learn a non-negative
subspace, formulated as a polyhedral cone, over document-pair differences. The
algorithm is regularized by controlling the `volume' of the cone. The
experimental studies on the latest and largest ranking dataset LETOR 4.0 shows
that ConeRank is competitive against other recent ranking approaches.
| Truyen T. Tran and Duc Son Pham | null | 1206.4110 | null | null |
Clustered Bandits | cs.LG | We consider a multi-armed bandit setting that is inspired by real-world
applications in e-commerce. In our setting, there are a few types of users,
each with a specific response to the different arms. When a user enters the
system, his type is unknown to the decision maker. The decision maker can
either treat each user separately ignoring the previously observed users, or
can attempt to take advantage of knowing that only few types exist and cluster
the users according to their response to the arms. We devise algorithms that
combine the usual exploration-exploitation tradeoff with clustering of users
and demonstrate the value of clustering. In the process of developing
algorithms for the clustered setting, we propose and analyze simple algorithms
for the setup where a decision maker knows that a user belongs to one of few
types, but does not know which one.
| Loc Bui, Ramesh Johari, Shie Mannor | null | 1206.4169 | null | null |
Parsimonious Mahalanobis Kernel for the Classification of High
Dimensional Data | cs.NA cs.LG | The classification of high dimensional data with kernel methods is considered
in this article. Exploit- ing the emptiness property of high dimensional
spaces, a kernel based on the Mahalanobis distance is proposed. The computation
of the Mahalanobis distance requires the inversion of a covariance matrix. In
high dimensional spaces, the estimated covariance matrix is ill-conditioned and
its inversion is unstable or impossible. Using a parsimonious statistical
model, namely the High Dimensional Discriminant Analysis model, the specific
signal and noise subspaces are estimated for each considered class making the
inverse of the class specific covariance matrix explicit and stable, leading to
the definition of a parsimonious Mahalanobis kernel. A SVM based framework is
used for selecting the hyperparameters of the parsimonious Mahalanobis kernel
by optimizing the so-called radius-margin bound. Experimental results on three
high dimensional data sets show that the proposed kernel is suitable for
classifying high dimensional data, providing better classification accuracies
than the conventional Gaussian kernel.
| M. Fauvel, A. Villa, J. Chanussot and J. A. Benediktsson | null | 1206.4481 | null | null |
Residual Component Analysis: Generalising PCA for more flexible
inference in linear-Gaussian models | cs.LG stat.ML | Probabilistic principal component analysis (PPCA) seeks a low dimensional
representation of a data set in the presence of independent spherical Gaussian
noise. The maximum likelihood solution for the model is an eigenvalue problem
on the sample covariance matrix. In this paper we consider the situation where
the data variance is already partially explained by other actors, for example
sparse conditional dependencies between the covariates, or temporal
correlations leaving some residual variance. We decompose the residual variance
into its components through a generalised eigenvalue problem, which we call
residual component analysis (RCA). We explore a range of new algorithms that
arise from the framework, including one that factorises the covariance of a
Gaussian density into a low-rank and a sparse-inverse component. We illustrate
the ideas on the recovery of a protein-signaling network, a gene expression
time-series data set and the recovery of the human skeleton from motion capture
3-D cloud data.
| Alfredo Kalaitzis (University of Sheffield), Neil Lawrence (University
of Sheffield) | null | 1206.4560 | null | null |
A Unified Robust Classification Model | cs.LG stat.ML | A wide variety of machine learning algorithms such as support vector machine
(SVM), minimax probability machine (MPM), and Fisher discriminant analysis
(FDA), exist for binary classification. The purpose of this paper is to provide
a unified classification model that includes the above models through a robust
optimization approach. This unified model has several benefits. One is that the
extensions and improvements intended for SVM become applicable to MPM and FDA,
and vice versa. Another benefit is to provide theoretical results to above
learning methods at once by dealing with the unified model. We give a
statistical interpretation of the unified classification model and propose a
non-convex optimization algorithm that can be applied to non-convex variants of
existing learning methods.
| Akiko Takeda (Keio University), Hiroyuki Mitsugi (Keio University),
Takafumi Kanamori (Nagoya University) | null | 1206.4599 | null | null |
Bayesian Nonexhaustive Learning for Online Discovery and Modeling of
Emerging Classes | cs.LG stat.ML | We present a framework for online inference in the presence of a
nonexhaustively defined set of classes that incorporates supervised
classification with class discovery and modeling. A Dirichlet process prior
(DPP) model defined over class distributions ensures that both known and
unknown class distributions originate according to a common base distribution.
In an attempt to automatically discover potentially interesting class
formations, the prior model is coupled with a suitably chosen data model, and
sequential Monte Carlo sampling is used to perform online inference. Our
research is driven by a biodetection application, where a new class of pathogen
may suddenly appear, and the rapid increase in the number of samples
originating from this class indicates the onset of an outbreak.
| Murat Dundar (IUPUI), Ferit Akova (IUPUI), Alan Qi (Purdue), Bartek
Rajwa (Purdue) | null | 1206.4600 | null | null |
Convex Multitask Learning with Flexible Task Clusters | cs.LG stat.ML | Traditionally, multitask learning (MTL) assumes that all the tasks are
related. This can lead to negative transfer when tasks are indeed incoherent.
Recently, a number of approaches have been proposed that alleviate this problem
by discovering the underlying task clusters or relationships. However, they are
limited to modeling these relationships at the task level, which may be
restrictive in some applications. In this paper, we propose a novel MTL
formulation that captures task relationships at the feature-level. Depending on
the interactions among tasks and features, the proposed method construct
different task clusters for different features, without even the need of
pre-specifying the number of clusters. Computationally, the proposed
formulation is strongly convex, and can be efficiently solved by accelerated
proximal methods. Experiments are performed on a number of synthetic and
real-world data sets. Under various degrees of task relationships, the accuracy
of the proposed method is consistently among the best. Moreover, the
feature-specific task clusters obtained agree with the known/plausible task
structures of the data.
| Wenliang Zhong (HKUST), James Kwok (HKUST) | null | 1206.4601 | null | null |
Quasi-Newton Methods: A New Direction | cs.NA cs.LG stat.ML | Four decades after their invention, quasi-Newton methods are still state of
the art in unconstrained numerical optimization. Although not usually
interpreted thus, these are learning algorithms that fit a local quadratic
approximation to the objective function. We show that many, including the most
popular, quasi-Newton methods can be interpreted as approximations of Bayesian
linear regression under varying prior assumptions. This new notion elucidates
some shortcomings of classical algorithms, and lights the way to a novel
nonparametric quasi-Newton method, which is able to make more efficient use of
available information at computational cost similar to its predecessors.
| Philipp Hennig (MPI Intelligent Systems), Martin Kiefel (MPI for
Intelligent Systems) | null | 1206.4602 | null | null |
Learning the Experts for Online Sequence Prediction | cs.LG cs.AI | Online sequence prediction is the problem of predicting the next element of a
sequence given previous elements. This problem has been extensively studied in
the context of individual sequence prediction, where no prior assumptions are
made on the origin of the sequence. Individual sequence prediction algorithms
work quite well for long sequences, where the algorithm has enough time to
learn the temporal structure of the sequence. However, they might give poor
predictions for short sequences. A possible remedy is to rely on the general
model of prediction with expert advice, where the learner has access to a set
of $r$ experts, each of which makes its own predictions on the sequence. It is
well known that it is possible to predict almost as well as the best expert if
the sequence length is order of $\log(r)$. But, without firm prior knowledge on
the problem, it is not clear how to choose a small set of {\em good} experts.
In this paper we describe and analyze a new algorithm that learns a good set of
experts using a training set of previously observed sequences. We demonstrate
the merits of our approach by applying it on the task of click prediction on
the web.
| Elad Eban (Hebrew University), Aharon Birnbaum (Hebrew University),
Shai Shalev-Shwartz (Hebrew University), Amir Globerson (Hebrew University) | null | 1206.4604 | null | null |
TrueLabel + Confusions: A Spectrum of Probabilistic Models in Analyzing
Multiple Ratings | cs.LG cs.AI stat.ML | This paper revisits the problem of analyzing multiple ratings given by
different judges. Different from previous work that focuses on distilling the
true labels from noisy crowdsourcing ratings, we emphasize gaining diagnostic
insights into our in-house well-trained judges. We generalize the well-known
DawidSkene model (Dawid & Skene, 1979) to a spectrum of probabilistic models
under the same "TrueLabel + Confusion" paradigm, and show that our proposed
hierarchical Bayesian model, called HybridConfusion, consistently outperforms
DawidSkene on both synthetic and real-world data sets.
| Chao Liu (Tencent Inc.), Yi-Min Wang (Microsoft Research) | null | 1206.4606 | null | null |
Distributed Tree Kernels | cs.LG stat.ML | In this paper, we propose the distributed tree kernels (DTK) as a novel
method to reduce time and space complexity of tree kernels. Using a linear
complexity algorithm to compute vectors for trees, we embed feature spaces of
tree fragments in low-dimensional spaces where the kernel computation is
directly done with dot product. We show that DTKs are faster, correlate with
tree kernels, and obtain a statistically similar performance in two natural
language processing tasks.
| Fabio Massimo Zanzotto (University of Rome-Tor Vergata), Lorenzo
Dell'Arciprete (University of Rome-Tor Vergata) | null | 1206.4607 | null | null |
A Hybrid Algorithm for Convex Semidefinite Optimization | cs.LG cs.DS cs.NA stat.ML | We present a hybrid algorithm for optimizing a convex, smooth function over
the cone of positive semidefinite matrices. Our algorithm converges to the
global optimal solution and can be used to solve general large-scale
semidefinite programs and hence can be readily applied to a variety of machine
learning problems. We show experimental results on three machine learning
problems (matrix completion, metric learning, and sparse PCA) . Our approach
outperforms state-of-the-art algorithms.
| Soeren Laue (Friedrich-Schiller-University) | null | 1206.4608 | null | null |
On multi-view feature learning | cs.CV cs.LG stat.ML | Sparse coding is a common approach to learning local features for object
recognition. Recently, there has been an increasing interest in learning
features from spatio-temporal, binocular, or other multi-observation data,
where the goal is to encode the relationship between images rather than the
content of a single image. We provide an analysis of multi-view feature
learning, which shows that hidden variables encode transformations by detecting
rotation angles in the eigenspaces shared among multiple image warps. Our
analysis helps explain recent experimental results showing that
transformation-specific features emerge when training complex cell models on
videos. Our analysis also shows that transformation-invariant features can
emerge as a by-product of learning representations of transformations.
| Roland Memisevic (University of Frankfurt) | null | 1206.4609 | null | null |
Manifold Relevance Determination | cs.LG cs.CV stat.ML | In this paper we present a fully Bayesian latent variable model which
exploits conditional nonlinear(in)-dependence structures to learn an efficient
latent representation. The latent space is factorized to represent shared and
private information from multiple views of the data. In contrast to previous
approaches, we introduce a relaxation to the discrete segmentation and allow
for a "softly" shared latent space. Further, Bayesian techniques allow us to
automatically estimate the dimensionality of the latent spaces. The model is
capable of capturing structure underlying extremely high dimensional spaces.
This is illustrated by modelling unprocessed images with tenths of thousands of
pixels. This also allows us to directly generate novel images from the trained
model by sampling from the discovered latent spaces. We also demonstrate the
model by prediction of human pose in an ambiguous setting. Our Bayesian
framework allows us to perform disambiguation in a principled manner by
including latent space priors which incorporate the dynamic nature of the data.
| Andreas Damianou (University of Sheffield), Carl Ek (KTH), Michalis
Titsias (University of Oxford), Neil Lawrence (University of Sheffield) | null | 1206.4610 | null | null |
A Convex Feature Learning Formulation for Latent Task Structure
Discovery | cs.LG stat.ML | This paper considers the multi-task learning problem and in the setting where
some relevant features could be shared across few related tasks. Most of the
existing methods assume the extent to which the given tasks are related or
share a common feature space to be known apriori. In real-world applications
however, it is desirable to automatically discover the groups of related tasks
that share a feature space. In this paper we aim at searching the exponentially
large space of all possible groups of tasks that may share a feature space. The
main contribution is a convex formulation that employs a graph-based
regularizer and simultaneously discovers few groups of related tasks, having
close-by task parameters, as well as the feature space shared within each
group. The regularizer encodes an important structure among the groups of tasks
leading to an efficient algorithm for solving it: if there is no feature space
under which a group of tasks has close-by task parameters, then there does not
exist such a feature space for any of its supersets. An efficient active set
algorithm that exploits this simplification and performs a clever search in the
exponentially large space is presented. The algorithm is guaranteed to solve
the proposed formulation (within some precision) in a time polynomial in the
number of groups of related tasks discovered. Empirical results on benchmark
datasets show that the proposed formulation achieves good generalization and
outperforms state-of-the-art multi-task learning algorithms in some cases.
| Pratik Jawanpuria (IIT Bombay), J. Saketha Nath (IIT Bombay) | null | 1206.4611 | null | null |
Exact Soft Confidence-Weighted Learning | cs.LG | In this paper, we propose a new Soft Confidence-Weighted (SCW) online
learning scheme, which enables the conventional confidence-weighted learning
method to handle non-separable cases. Unlike the previous confidence-weighted
learning algorithms, the proposed soft confidence-weighted learning method
enjoys all the four salient properties: (i) large margin training, (ii)
confidence weighting, (iii) capability to handle non-separable data, and (iv)
adaptive margin. Our experimental results show that the proposed SCW algorithms
significantly outperform the original CW algorithm. When comparing with a
variety of state-of-the-art algorithms (including AROW, NAROW and NHERD), we
found that SCW generally achieves better or at least comparable predictive
accuracy, but enjoys significant advantage of computational efficiency (i.e.,
smaller number of updates and lower time cost).
| Jialei Wang (NTU), Peilin Zhao (NTU), Steven C.H. Hoi (NTU) | null | 1206.4612 | null | null |
Near-Optimal BRL using Optimistic Local Transitions | cs.AI cs.LG stat.ML | Model-based Bayesian Reinforcement Learning (BRL) allows a found
formalization of the problem of acting optimally while facing an unknown
environment, i.e., avoiding the exploration-exploitation dilemma. However,
algorithms explicitly addressing BRL suffer from such a combinatorial explosion
that a large body of work relies on heuristic algorithms. This paper introduces
BOLT, a simple and (almost) deterministic heuristic algorithm for BRL which is
optimistic about the transition function. We analyze BOLT's sample complexity,
and show that under certain parameters, the algorithm is near-optimal in the
Bayesian sense with high probability. Then, experimental results highlight the
key differences of this method compared to previous work.
| Mauricio Araya (LORIA/INRIA), Olivier Buffet (LORIA/INRIA), Vincent
Thomas (LORIA/INRIA) | null | 1206.4613 | null | null |
Information-theoretic Semi-supervised Metric Learning via Entropy
Regularization | cs.LG stat.ML | We propose a general information-theoretic approach called Seraph
(SEmi-supervised metRic leArning Paradigm with Hyper-sparsity) for metric
learning that does not rely upon the manifold assumption. Given the probability
parameterized by a Mahalanobis distance, we maximize the entropy of that
probability on labeled data and minimize it on unlabeled data following entropy
regularization, which allows the supervised and unsupervised parts to be
integrated in a natural and meaningful way. Furthermore, Seraph is regularized
by encouraging a low-rank projection induced from the metric. The optimization
of Seraph is solved efficiently and stably by an EM-like scheme with the
analytical E-Step and convex M-Step. Experiments demonstrate that Seraph
compares favorably with many well-known global and local metric learning
methods.
| Gang Niu (Tokyo Institute of Technology), Bo Dai (Purdue University),
Makoto Yamada (Tokyo Institute of Technology), Masashi Sugiyama (Tokyo
Institute of Technology) | null | 1206.4614 | null | null |
Levy Measure Decompositions for the Beta and Gamma Processes | stat.ME cs.LG math.ST stat.TH | We develop new representations for the Levy measures of the beta and gamma
processes. These representations are manifested in terms of an infinite sum of
well-behaved (proper) beta and gamma distributions. Further, we demonstrate how
these infinite sums may be truncated in practice, and explicitly characterize
truncation errors. We also perform an analysis of the characteristics of
posterior distributions, based on the proposed decompositions. The
decompositions provide new insights into the beta and gamma processes (and
their generalizations), and we demonstrate how the proposed representation
unifies some properties of the two. This paper is meant to provide a rigorous
foundation for and new perspectives on Levy processes, as these are of
increasing importance in machine learning.
| Yingjian Wang (Duke University), Lawrence Carin (Duke University) | null | 1206.4615 | null | null |
A Hierarchical Dirichlet Process Model with Multiple Levels of
Clustering for Human EEG Seizure Modeling | stat.AP cs.LG stat.ML | Driven by the multi-level structure of human intracranial
electroencephalogram (iEEG) recordings of epileptic seizures, we introduce a
new variant of a hierarchical Dirichlet Process---the multi-level clustering
hierarchical Dirichlet Process (MLC-HDP)---that simultaneously clusters
datasets on multiple levels. Our seizure dataset contains brain activity
recorded in typically more than a hundred individual channels for each seizure
of each patient. The MLC-HDP model clusters over channels-types, seizure-types,
and patient-types simultaneously. We describe this model and its implementation
in detail. We also present the results of a simulation study comparing the
MLC-HDP to a similar model, the Nested Dirichlet Process and finally
demonstrate the MLC-HDP's use in modeling seizures across multiple patients. We
find the MLC-HDP's clustering to be comparable to independent human physician
clusterings. To our knowledge, the MLC-HDP model is the first in the epilepsy
literature capable of clustering seizures within and between patients.
| Drausin Wulsin (University of Pennsylvania), Shane Jensen (University
of Pennsylvania), Brian Litt (University of Pennsylvania) | null | 1206.4616 | null | null |
Continuous Inverse Optimal Control with Locally Optimal Examples | cs.LG cs.AI stat.ML | Inverse optimal control, also known as inverse reinforcement learning, is the
problem of recovering an unknown reward function in a Markov decision process
from expert demonstrations of the optimal policy. We introduce a probabilistic
inverse optimal control algorithm that scales gracefully with task
dimensionality, and is suitable for large, continuous domains where even
computing a full policy is impractical. By using a local approximation of the
reward function, our method can also drop the assumption that the
demonstrations are globally optimal, requiring only local optimality. This
allows it to learn from examples that are unsuitable for prior methods.
| Sergey Levine (Stanford University), Vladlen Koltun (Stanford
University) | null | 1206.4617 | null | null |
Compact Hyperplane Hashing with Bilinear Functions | cs.LG stat.ML | Hyperplane hashing aims at rapidly searching nearest points to a hyperplane,
and has shown practical impact in scaling up active learning with SVMs.
Unfortunately, the existing randomized methods need long hash codes to achieve
reasonable search accuracy and thus suffer from reduced search speed and large
memory overhead. To this end, this paper proposes a novel hyperplane hashing
technique which yields compact hash codes. The key idea is the bilinear form of
the proposed hash functions, which leads to higher collision probability than
the existing hyperplane hash functions when using random projections. To
further increase the performance, we propose a learning based framework in
which the bilinear functions are directly learned from the data. This results
in short yet discriminative codes, and also boosts the search performance over
the random projection based solutions. Large-scale active learning experiments
carried out on two datasets with up to one million samples demonstrate the
overall superiority of the proposed approach.
| Wei Liu (Columbia University), Jun Wang (IBM T. J. Watson Research
Center), Yadong Mu (Columbia University), Sanjiv Kumar (Google), Shih-Fu
Chang (Columbia University) | null | 1206.4618 | null | null |
Inductive Kernel Low-rank Decomposition with Priors: A Generalized
Nystrom Method | cs.LG | Low-rank matrix decomposition has gained great popularity recently in scaling
up kernel methods to large amounts of data. However, some limitations could
prevent them from working effectively in certain domains. For example, many
existing approaches are intrinsically unsupervised, which does not incorporate
side information (e.g., class labels) to produce task specific decompositions;
also, they typically work "transductively", i.e., the factorization does not
generalize to new samples, so the complete factorization needs to be recomputed
when new samples become available. To solve these problems, in this paper we
propose an"inductive"-flavored method for low-rank kernel decomposition with
priors. We achieve this by generalizing the Nystr\"om method in a novel way. On
the one hand, our approach employs a highly flexible, nonparametric structure
that allows us to generalize the low-rank factors to arbitrarily new samples;
on the other hand, it has linear time and space complexities, which can be
orders of magnitudes faster than existing approaches and renders great
efficiency in learning a low-rank kernel decomposition. Empirical results
demonstrate the efficacy and efficiency of the proposed method.
| Kai Zhang (Siemens), Liang Lan (temple university), Jun Liu (Siemens),
andreas Rauber (TU Wien), Fabian Moerchen (Siemens Corporate Research and
Technology) | null | 1206.4619 | null | null |
Improved Information Gain Estimates for Decision Tree Induction | cs.LG stat.ML | Ensembles of classification and regression trees remain popular machine
learning methods because they define flexible non-parametric models that
predict well and are computationally efficient both during training and
testing. During induction of decision trees one aims to find predicates that
are maximally informative about the prediction target. To select good
predicates most approaches estimate an information-theoretic scoring function,
the information gain, both for classification and regression problems. We point
out that the common estimation procedures are biased and show that by replacing
them with improved estimators of the discrete and the differential entropy we
can obtain better decision trees. In effect our modifications yield improved
predictive performance and are simple to implement in any decision tree code.
| Sebastian Nowozin (Microsoft Research Cambridge) | null | 1206.4620 | null | null |
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