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21,502 | Bayesian Classification and Regression with High Dimensional Features | stat.ML | This thesis responds to the challenges of using a large number, such as
thousands, of features in regression and classification problems.
There are two situations where such high dimensional features arise. One is
when high dimensional measurements are available, for example, gene expression
data produced by microarr... | computer science |
21,503 | Simulated Annealing: Rigorous finite-time guarantees for optimization on
continuous domains | stat.ML | Simulated annealing is a popular method for approaching the solution of a
global optimization problem. Existing results on its performance apply to
discrete combinatorial optimization where the optimization variables can assume
only a finite set of possible values. We introduce a new general formulation of
simulated an... | computer science |
21,504 | Pac-Bayesian Supervised Classification: The Thermodynamics of
Statistical Learning | stat.ML | This monograph deals with adaptive supervised classification, using tools
borrowed from statistical mechanics and information theory, stemming from the
PACBayesian approach pioneered by David McAllester and applied to a conception
of statistical learning theory forged by Vladimir Vapnik. Using convex analysis
on the se... | computer science |
21,505 | Classification Constrained Dimensionality Reduction | stat.ML | Dimensionality reduction is a topic of recent interest. In this paper, we
present the classification constrained dimensionality reduction (CCDR)
algorithm to account for label information. The algorithm can account for
multiple classes as well as the semi-supervised setting. We present an
out-of-sample expressions for ... | computer science |
21,506 | Testing for Homogeneity with Kernel Fisher Discriminant Analysis | stat.ML | We propose to investigate test statistics for testing homogeneity in
reproducing kernel Hilbert spaces. Asymptotic null distributions under null
hypothesis are derived, and consistency against fixed and local alternatives is
assessed. Finally, experimental evidence of the performance of the proposed
approach on both ar... | computer science |
21,507 | On the underestimation of model uncertainty by Bayesian K-nearest
neighbors | stat.ML | When using the K-nearest neighbors method, one often ignores uncertainty in
the choice of K. To account for such uncertainty, Holmes and Adams (2002)
proposed a Bayesian framework for K-nearest neighbors (KNN). Their Bayesian KNN
(BKNN) approach uses a pseudo-likelihood function, and standard Markov chain
Monte Carlo (... | computer science |
21,508 | Information Preserving Component Analysis: Data Projections for Flow
Cytometry Analysis | stat.ML | Flow cytometry is often used to characterize the malignant cells in leukemia
and lymphoma patients, traced to the level of the individual cell. Typically,
flow cytometric data analysis is performed through a series of 2-dimensional
projections onto the axes of the data set. Through the years, clinicians have
determined... | computer science |
21,509 | Random projection trees for vector quantization | stat.ML | A simple and computationally efficient scheme for tree-structured vector
quantization is presented. Unlike previous methods, its quantization error
depends only on the intrinsic dimension of the data distribution, rather than
the apparent dimension of the space in which the data happen to lie. | computer science |
21,510 | Manifold Learning: The Price of Normalization | stat.ML | We analyze the performance of a class of manifold-learning algorithms that
find their output by minimizing a quadratic form under some normalization
constraints. This class consists of Locally Linear Embedding (LLE), Laplacian
Eigenmap, Local Tangent Space Alignment (LTSA), Hessian Eigenmaps (HLLE), and
Diffusion maps.... | computer science |
21,511 | Local Procrustes for Manifold Embedding: A Measure of Embedding Quality
and Embedding Algorithms | stat.ML | We present the Procrustes measure, a novel measure based on Procrustes
rotation that enables quantitative comparison of the output of manifold-based
embedding algorithms (such as LLE (Roweis and Saul, 2000) and Isomap (Tenenbaum
et al, 2000)). The measure also serves as a natural tool when choosing
dimension-reduction ... | computer science |
21,512 | Supervised functional classification: A theoretical remark and some
comparisons | stat.ML | The problem of supervised classification (or discrimination) with functional
data is considered, with a special interest on the popular k-nearest neighbors
(k-NN) classifier. First, relying on a recent result by Cerou and Guyader
(2006), we prove the consistency of the k-NN classifier for functional data
whose distribu... | computer science |
21,513 | High-dimensional additive modeling | stat.ML | We propose a new sparsity-smoothness penalty for high-dimensional generalized
additive models. The combination of sparsity and smoothness is crucial for
mathematical theory as well as performance for finite-sample data. We present a
computationally efficient algorithm, with provable numerical convergence
properties, fo... | computer science |
21,514 | Improved Estimation of High-dimensional Ising Models | stat.ML | We consider the problem of jointly estimating the parameters as well as the
structure of binary valued Markov Random Fields, in contrast to earlier work
that focus on one of the two problems. We formulate the problem as a
maximization of $\ell_1$-regularized surrogate likelihood that allows us to
find a sparse solution... | computer science |
21,515 | Kernel Regression by Mode Calculation of the Conditional Probability
Distribution | stat.ML | The most direct way to express arbitrary dependencies in datasets is to
estimate the joint distribution and to apply afterwards the argmax-function to
obtain the mode of the corresponding conditional distribution. This method is
in practice difficult, because it requires a global optimization of a
complicated function,... | computer science |
21,516 | Entropy inference and the James-Stein estimator, with application to
nonlinear gene association networks | stat.ML | We present a procedure for effective estimation of entropy and mutual
information from small-sample data, and apply it to the problem of inferring
high-dimensional gene association networks. Specifically, we develop a
James-Stein-type shrinkage estimator, resulting in a procedure that is highly
efficient statistically ... | computer science |
21,517 | Random Forests: some methodological insights | stat.ML | This paper examines from an experimental perspective random forests, the
increasingly used statistical method for classification and regression problems
introduced by Leo Breiman in 2001. It first aims at confirming, known but
sparse, advice for using random forests and at proposing some complementary
remarks for both ... | computer science |
21,518 | An information-theoretic derivation of min-cut based clustering | stat.ML | Min-cut clustering, based on minimizing one of two heuristic cost-functions
proposed by Shi and Malik, has spawned tremendous research, both analytic and
algorithmic, in the graph partitioning and image segmentation communities over
the last decade. It is however unclear if these heuristics can be derived from
a more g... | computer science |
21,519 | On the Geometry of Discrete Exponential Families with Application to
Exponential Random Graph Models | stat.ML | There has been an explosion of interest in statistical models for analyzing
network data, and considerable interest in the class of exponential random
graph (ERG) models, especially in connection with difficulties in computing
maximum likelihood estimates. The issues associated with these difficulties
relate to the bro... | computer science |
21,520 | Reconstruction of Epsilon-Machines in Predictive Frameworks and
Decisional States | stat.ML | This article introduces both a new algorithm for reconstructing
epsilon-machines from data, as well as the decisional states. These are defined
as the internal states of a system that lead to the same decision, based on a
user-provided utility or pay-off function. The utility function encodes some a
priori knowledge ex... | computer science |
21,521 | Lanczos Approximations for the Speedup of Kernel Partial Least Squares
Regression | stat.ML | The runtime for Kernel Partial Least Squares (KPLS) to compute the fit is
quadratic in the number of examples. However, the necessity of obtaining
sensitivity measures as degrees of freedom for model selection or confidence
intervals for more detailed analysis requires cubic runtime, and thus
constitutes a computationa... | computer science |
21,522 | Escaping the curse of dimensionality with a tree-based regressor | stat.ML | We present the first tree-based regressor whose convergence rate depends only
on the intrinsic dimension of the data, namely its Assouad dimension. The
regressor uses the RPtree partitioning procedure, a simple randomized variant
of k-d trees. | computer science |
21,523 | Finding Exogenous Variables in Data with Many More Variables than
Observations | stat.ML | Many statistical methods have been proposed to estimate causal models in
classical situations with fewer variables than observations (p<n, p: the number
of variables and n: the number of observations). However, modern datasets
including gene expression data need high-dimensional causal modeling in
challenging situation... | computer science |
21,524 | Structured Variable Selection with Sparsity-Inducing Norms | stat.ML | We consider the empirical risk minimization problem for linear supervised
learning, with regularization by structured sparsity-inducing norms. These are
defined as sums of Euclidean norms on certain subsets of variables, extending
the usual $\ell_1$-norm and the group $\ell_1$-norm by allowing the subsets to
overlap. T... | computer science |
21,525 | Supplementary material for Markov equivalence for ancestral graphs | stat.ML | We prove that the criterion for Markov equivalence provided by Zhao et al.
(2005) may involve a set of features of a graph that is exponential in the
number of vertices. | computer science |
21,526 | A more robust boosting algorithm | stat.ML | We present a new boosting algorithm, motivated by the large margins theory
for boosting. We give experimental evidence that the new algorithm is
significantly more robust against label noise than existing boosting algorithm. | computer science |
21,527 | Classification by Set Cover: The Prototype Vector Machine | stat.ML | We introduce a new nearest-prototype classifier, the prototype vector machine
(PVM). It arises from a combinatorial optimization problem which we cast as a
variant of the set cover problem. We propose two algorithms for approximating
its solution. The PVM selects a relatively small number of representative
points which... | computer science |
21,528 | Convex Multiview Fisher Discriminant Analysis | stat.ML | Section 1.3 was incorrect, and 2.1 will be removed from further submissions.
A rewritten version will be posted in the future. | computer science |
21,529 | Relative Expected Improvement in Kriging Based Optimization | stat.ML | We propose an extension of the concept of Expected Improvement criterion
commonly used in Kriging based optimization. We extend it for more complex
Kriging models, e.g. models using derivatives. The target field of application
are CFD problems, where objective function are extremely expensive to evaluate,
but the theor... | computer science |
21,530 | Learning Bayesian Networks with the bnlearn R Package | stat.ML | bnlearn is an R package which includes several algorithms for learning the
structure of Bayesian networks with either discrete or continuous variables.
Both constraint-based and score-based algorithms are implemented, and can use
the functionality provided by the snow package to improve their performance via
parallel c... | computer science |
21,531 | Causal Inference on Discrete Data using Additive Noise Models | stat.ML | Inferring the causal structure of a set of random variables from a finite
sample of the joint distribution is an important problem in science. Recently,
methods using additive noise models have been suggested to approach the case of
continuous variables. In many situations, however, the variables of interest
are discre... | computer science |
21,532 | How slow is slow? SFA detects signals that are slower than the driving
force | stat.ML | Slow feature analysis (SFA) is a method for extracting slowly varying driving
forces from quickly varying nonstationary time series. We show here that it is
possible for SFA to detect a component which is even slower than the driving
force itself (e.g. the envelope of a modulated sine wave). It is shown that it
depends... | computer science |
21,533 | Sparse Convolved Multiple Output Gaussian Processes | stat.ML | Recently there has been an increasing interest in methods that deal with
multiple outputs. This has been motivated partly by frameworks like multitask
learning, multisensor networks or structured output data. From a Gaussian
processes perspective, the problem reduces to specifying an appropriate
covariance function tha... | computer science |
21,534 | Positive Definite Kernels in Machine Learning | stat.ML | This survey is an introduction to positive definite kernels and the set of
methods they have inspired in the machine learning literature, namely kernel
methods. We first discuss some properties of positive definite kernels as well
as reproducing kernel Hibert spaces, the natural extension of the set of
functions $\{k(x... | computer science |
21,535 | Under-determined reverberant audio source separation using a full-rank
spatial covariance model | stat.ML | This article addresses the modeling of reverberant recording environments in
the context of under-determined convolutive blind source separation. We model
the contribution of each source to all mixture channels in the time-frequency
domain as a zero-mean Gaussian random variable whose covariance encodes the
spatial cha... | computer science |
21,536 | Hyper-sparse optimal aggregation | stat.ML | In this paper, we consider the problem of "hyper-sparse aggregation". Namely,
given a dictionary $F = \{f_1, ..., f_M \}$ of functions, we look for an
optimal aggregation algorithm that writes $\tilde f = \sum_{j=1}^M \theta_j
f_j$ with as many zero coefficients $\theta_j$ as possible. This problem is of
particular int... | computer science |
21,537 | Multi-Way, Multi-View Learning | stat.ML | We extend multi-way, multivariate ANOVA-type analysis to cases where one
covariate is the view, with features of each view coming from different,
high-dimensional domains. The different views are assumed to be connected by
having paired samples; this is a common setup in recent bioinformatics
experiments, of which we a... | computer science |
21,538 | Variational Inducing Kernels for Sparse Convolved Multiple Output
Gaussian Processes | stat.ML | Interest in multioutput kernel methods is increasing, whether under the guise
of multitask learning, multisensor networks or structured output data. From the
Gaussian process perspective a multioutput Mercer kernel is a covariance
function over correlated output functions. One way of constructing such kernels
is based ... | computer science |
21,539 | Composite Binary Losses | stat.ML | We study losses for binary classification and class probability estimation
and extend the understanding of them from margin losses to general composite
losses which are the composition of a proper loss with a link function. We
characterise when margin losses can be proper composite losses, explicitly show
how to determ... | computer science |
21,540 | A Geometric Proof of Calibration | stat.ML | We provide yet another proof of the existence of calibrated forecasters; it
has two merits. First, it is valid for an arbitrary finite number of outcomes.
Second, it is short and simple and it follows from a direct application of
Blackwell's approachability theorem to carefully chosen vector-valued payoff
function and ... | computer science |
21,541 | Probabilistic Recovery of Multiple Subspaces in Point Clouds by
Geometric lp Minimization | stat.ML | We assume data independently sampled from a mixture distribution on the unit
ball of the D-dimensional Euclidean space with K+1 components: the first
component is a uniform distribution on that ball representing outliers and the
other K components are uniform distributions along K d-dimensional linear
subspaces restric... | computer science |
21,542 | Robust Independent Component Analysis by Iterative Maximization of the
Kurtosis Contrast with Algebraic Optimal Step Size | stat.ML | Independent component analysis (ICA) aims at decomposing an observed random
vector into statistically independent variables. Deflation-based
implementations, such as the popular one-unit FastICA algorithm and its
variants, extract the independent components one after another. A novel method
for deflationary ICA, referr... | computer science |
21,543 | On the Schoenberg Transformations in Data Analysis: Theory and
Illustrations | stat.ML | The class of Schoenberg transformations, embedding Euclidean distances into
higher dimensional Euclidean spaces, is presented, and derived from theorems on
positive definite and conditionally negative definite matrices. Original
results on the arc lengths, angles and curvature of the transformations are
proposed, and v... | computer science |
21,544 | Visualization of Manifold-Valued Elements by Multidimensional Scaling | stat.ML | The present contribution suggests the use of a multidimensional scaling (MDS)
algorithm as a visualization tool for manifold-valued elements. A visualization
tool of this kind is useful in signal processing and machine learning whenever
learning/adaptation algorithms insist on high-dimensional parameter manifolds. | computer science |
21,545 | Strong Consistency of Prototype Based Clustering in Probabilistic Space | stat.ML | In this paper we formulate in general terms an approach to prove strong
consistency of the Empirical Risk Minimisation inductive principle applied to
the prototype or distance based clustering. This approach was motivated by the
Divisive Information-Theoretic Feature Clustering model in probabilistic space
with Kullbac... | computer science |
21,546 | Sparse Linear Identifiable Multivariate Modeling | stat.ML | In this paper we consider sparse and identifiable linear latent variable
(factor) and linear Bayesian network models for parsimonious analysis of
multivariate data. We propose a computationally efficient method for joint
parameter and model inference, and model comparison. It consists of a fully
Bayesian hierarchy for ... | computer science |
21,547 | Training linear ranking SVMs in linearithmic time using red-black trees | stat.ML | We introduce an efficient method for training the linear ranking support
vector machine. The method combines cutting plane optimization with red-black
tree based approach to subgradient calculations, and has O(m*s+m*log(m)) time
complexity, where m is the number of training examples, and s the average
number of non-zer... | computer science |
21,548 | Improving the Johnson-Lindenstrauss Lemma | stat.ML | The Johnson-Lindenstrauss Lemma allows for the projection of $n$ points in
$p-$dimensional Euclidean space onto a $k-$dimensional Euclidean space, with $k
\ge \frac{24\ln \emph{n}}{3\epsilon^2-2\epsilon^3}$, so that the pairwise
distances are preserved within a factor of $1\pm\epsilon$. Here, working
directly with the ... | computer science |
21,549 | Refinements of Universal Approximation Results for Deep Belief Networks
and Restricted Boltzmann Machines | stat.ML | We improve recently published results about resources of Restricted Boltzmann
Machines (RBM) and Deep Belief Networks (DBN) required to make them Universal
Approximators. We show that any distribution p on the set of binary vectors of
length n can be arbitrarily well approximated by an RBM with k-1 hidden units,
where ... | computer science |
21,550 | Stability Approach to Regularization Selection (StARS) for High
Dimensional Graphical Models | stat.ML | A challenging problem in estimating high-dimensional graphical models is to
choose the regularization parameter in a data-dependent way. The standard
techniques include $K$-fold cross-validation ($K$-CV), Akaike information
criterion (AIC), and Bayesian information criterion (BIC). Though these methods
work well for lo... | computer science |
21,551 | Gaussian Mixture Modeling with Gaussian Process Latent Variable Models | stat.ML | Density modeling is notoriously difficult for high dimensional data. One
approach to the problem is to search for a lower dimensional manifold which
captures the main characteristics of the data. Recently, the Gaussian Process
Latent Variable Model (GPLVM) has successfully been used to find low
dimensional manifolds in... | computer science |
21,552 | Proximal Methods for Hierarchical Sparse Coding | stat.ML | Sparse coding consists in representing signals as sparse linear combinations
of atoms selected from a dictionary. We consider an extension of this framework
where the atoms are further assumed to be embedded in a tree. This is achieved
using a recently introduced tree-structured sparse regularization norm, which
has pr... | computer science |
21,553 | Calibrated Surrogate Losses for Classification with Label-Dependent
Costs | stat.ML | We present surrogate regret bounds for arbitrary surrogate losses in the
context of binary classification with label-dependent costs. Such bounds relate
a classifier's risk, assessed with respect to a surrogate loss, to its
cost-sensitive classification risk. Two approaches to surrogate regret bounds
are developed. The... | computer science |
21,554 | Fast Sparse Decomposition by Iterative Detection-Estimation | stat.ML | Finding sparse solutions of underdetermined systems of linear equations is a
fundamental problem in signal processing and statistics which has become a
subject of interest in recent years. In general, these systems have infinitely
many solutions. However, it may be shown that sufficiently sparse solutions may
be identi... | computer science |
21,555 | Task-Driven Dictionary Learning | stat.ML | Modeling data with linear combinations of a few elements from a learned
dictionary has been the focus of much recent research in machine learning,
neuroscience and signal processing. For signals such as natural images that
admit such sparse representations, it is now well established that these models
are well suited t... | computer science |
21,556 | Kernel Bayes' rule | stat.ML | A nonparametric kernel-based method for realizing Bayes' rule is proposed,
based on representations of probabilities in reproducing kernel Hilbert spaces.
Probabilities are uniquely characterized by the mean of the canonical map to
the RKHS. The prior and conditional probabilities are expressed in terms of
RKHS functio... | computer science |
21,557 | Concentration inequalities of the cross-validation estimator for
Empirical Risk Minimiser | stat.ML | In this article, we derive concentration inequalities for the
cross-validation estimate of the generalization error for empirical risk
minimizers. In the general setting, we prove sanity-check bounds in the spirit
of \cite{KR99} \textquotedblleft\textit{bounds showing that the worst-case
error of this estimate is not m... | computer science |
21,558 | The Lasso under Heteroscedasticity | stat.ML | The performance of the Lasso is well understood under the assumptions of the
standard linear model with homoscedastic noise. However, in several
applications, the standard model does not describe the important features of
the data. This paper examines how the Lasso performs on a non-standard model
that is motivated by ... | computer science |
21,559 | An Introduction to Conditional Random Fields | stat.ML | Often we wish to predict a large number of variables that depend on each
other as well as on other observed variables. Structured prediction methods are
essentially a combination of classification and graphical modeling, combining
the ability of graphical models to compactly model multivariate data with the
ability of ... | computer science |
21,560 | Concentration inequalities of the cross-validation estimate for stable
predictors | stat.ML | In this article, we derive concentration inequalities for the
cross-validation estimate of the generalization error for stable predictors in
the context of risk assessment. The notion of stability has been first
introduced by \cite{DEWA79} and extended by \cite{KEA95}, \cite{BE01} and
\cite{KUNIY02} to characterize cla... | computer science |
21,561 | Estimating Subagging by cross-validation | stat.ML | In this article, we derive concentration inequalities for the
cross-validation estimate of the generalization error for subagged estimators,
both for classification and regressor. General loss functions and class of
predictors with both finite and infinite VC-dimension are considered. We
slightly generalize the formali... | computer science |
21,562 | Cross-Domain Object Matching with Model Selection | stat.ML | The goal of cross-domain object matching (CDOM) is to find correspondence
between two sets of objects in different domains in an unsupervised way. Photo
album summarization is a typical application of CDOM, where photos are
automatically aligned into a designed frame expressed in the Cartesian
coordinate system. CDOM i... | computer science |
21,563 | Translating biomarkers between multi-way time-series experiments | stat.ML | Translating potential disease biomarkers between multi-species 'omics'
experiments is a new direction in biomedical research. The existing methods are
limited to simple experimental setups such as basic healthy-diseased
comparisons. Most of these methods also require an a priori matching of the
variables (e.g., genes o... | computer science |
21,564 | Fast Convergent Algorithms for Expectation Propagation Approximate
Bayesian Inference | stat.ML | We propose a novel algorithm to solve the expectation propagation relaxation
of Bayesian inference for continuous-variable graphical models. In contrast to
most previous algorithms, our method is provably convergent. By marrying
convergent EP ideas from (Opper&Winther 05) with covariance decoupling
techniques (Wipf&Nag... | computer science |
21,565 | Estimating Networks With Jumps | stat.ML | We study the problem of estimating a temporally varying coefficient and
varying structure (VCVS) graphical model underlying nonstationary time series
data, such as social states of interacting individuals or microarray expression
profiles of gene networks, as opposed to i.i.d. data from an invariant model
widely consid... | computer science |
21,566 | Ultra-high Dimensional Multiple Output Learning With Simultaneous
Orthogonal Matching Pursuit: A Sure Screening Approach | stat.ML | We propose a novel application of the Simultaneous Orthogonal Matching
Pursuit (S-OMP) procedure for sparsistant variable selection in ultra-high
dimensional multi-task regression problems. Screening of variables, as
introduced in \cite{fan08sis}, is an efficient and highly scalable way to
remove many irrelevant variab... | computer science |
21,567 | A convex model for non-negative matrix factorization and dimensionality
reduction on physical space | stat.ML | A collaborative convex framework for factoring a data matrix $X$ into a
non-negative product $AS$, with a sparse coefficient matrix $S$, is proposed.
We restrict the columns of the dictionary matrix $A$ to coincide with certain
columns of the data matrix $X$, thereby guaranteeing a physically meaningful
dictionary and ... | computer science |
21,568 | Large Scale Correlation Screening | stat.ML | This paper treats the problem of screening for variables with high
correlations in high dimensional data in which there can be many fewer samples
than variables. We focus on threshold-based correlation screening methods for
three related applications: screening for variables with large correlations
within a single trea... | computer science |
21,569 | On Nonparametric Guidance for Learning Autoencoder Representations | stat.ML | Unsupervised discovery of latent representations, in addition to being useful
for density modeling, visualisation and exploratory data analysis, is also
increasingly important for learning features relevant to discriminative tasks.
Autoencoders, in particular, have proven to be an effective way to learn latent
codes th... | computer science |
21,570 | Predictive Active Set Selection Methods for Gaussian Processes | stat.ML | We propose an active set selection framework for Gaussian process
classification for cases when the dataset is large enough to render its
inference prohibitive. Our scheme consists of a two step alternating procedure
of active set update rules and hyperparameter optimization based upon marginal
likelihood maximization.... | computer science |
21,571 | Fast Convergence Rate of Multiple Kernel Learning with Elastic-net
Regularization | stat.ML | We investigate the learning rate of multiple kernel leaning (MKL) with
elastic-net regularization, which consists of an $\ell_1$-regularizer for
inducing the sparsity and an $\ell_2$-regularizer for controlling the
smoothness. We focus on a sparse setting where the total number of kernels is
large but the number of non... | computer science |
21,572 | The Local Rademacher Complexity of Lp-Norm Multiple Kernel Learning | stat.ML | We derive an upper bound on the local Rademacher complexity of $\ell_p$-norm
multiple kernel learning, which yields a tighter excess risk bound than global
approaches. Previous local approaches aimed at analyzed the case $p=1$ only
while our analysis covers all cases $1\leq p\leq\infty$, assuming the different
feature ... | computer science |
21,573 | Multiple Kernel Learning: A Unifying Probabilistic Viewpoint | stat.ML | We present a probabilistic viewpoint to multiple kernel learning unifying
well-known regularised risk approaches and recent advances in approximate
Bayesian inference relaxations. The framework proposes a general objective
function suitable for regression, robust regression and classification that is
lower bound of the... | computer science |
21,574 | Additive Kernels for Gaussian Process Modeling | stat.ML | Gaussian Process (GP) models are often used as mathematical approximations of
computationally expensive experiments. Provided that its kernel is suitably
chosen and that enough data is available to obtain a reasonable fit of the
simulator, a GP model can beneficially be used for tasks such as prediction,
optimization, ... | computer science |
21,575 | Theoretical Properties of the Overlapping Groups Lasso | stat.ML | We present two sets of theoretical results on the grouped lasso with overlap
of Jacob, Obozinski and Vert (2009) in the linear regression setting. This
method allows for joint selection of predictors in sparse regression, allowing
for complex structured sparsity over the predictors encoded as a set of groups.
This flex... | computer science |
21,576 | The Discrete Infinite Logistic Normal Distribution | stat.ML | We present the discrete infinite logistic normal distribution (DILN), a
Bayesian nonparametric prior for mixed membership models. DILN is a
generalization of the hierarchical Dirichlet process (HDP) that models
correlation structure between the weights of the atoms at the group level. We
derive a representation of DILN... | computer science |
21,577 | Sufficient Component Analysis for Supervised Dimension Reduction | stat.ML | The purpose of sufficient dimension reduction (SDR) is to find the
low-dimensional subspace of input features that is sufficient for predicting
output values. In this paper, we propose a novel distribution-free SDR method
called sufficient component analysis (SCA), which is computationally more
efficient than existing ... | computer science |
21,578 | Sharp Convergence Rate and Support Consistency of Multiple Kernel
Learning with Sparse and Dense Regularization | stat.ML | We theoretically investigate the convergence rate and support consistency
(i.e., correctly identifying the subset of non-zero coefficients in the large
sample limit) of multiple kernel learning (MKL). We focus on MKL with block-l1
regularization (inducing sparse kernel combination), block-l2 regularization
(inducing un... | computer science |
21,579 | Fast Learning Rate of lp-MKL and its Minimax Optimality | stat.ML | In this paper, we give a new sharp generalization bound of lp-MKL which is a
generalized framework of multiple kernel learning (MKL) and imposes
lp-mixed-norm regularization instead of l1-mixed-norm regularization. We
utilize localization techniques to obtain the sharp learning rate. The bound is
characterized by the d... | computer science |
21,580 | Least-Squares Independence Regression for Non-Linear Causal Inference
under Non-Gaussian Noise | stat.ML | The discovery of non-linear causal relationship under additive non-Gaussian
noise models has attracted considerable attention recently because of their
high flexibility. In this paper, we propose a novel causal inference algorithm
called least-squares independence regression (LSIR). LSIR learns the additive
noise model... | computer science |
21,581 | Auto-associative models, nonlinear Principal component analysis,
manifolds and projection pursuit | stat.ML | In this paper, auto-associative models are proposed as candidates to the
generalization of Principal Component Analysis. We show that these models are
dedicated to the approximation of the dataset by a manifold. Here, the word
"manifold" refers to the topology properties of the structure. The
approximating manifold is ... | computer science |
21,582 | Multi-scale Mining of fMRI data with Hierarchical Structured Sparsity | stat.ML | Inverse inference, or "brain reading", is a recent paradigm for analyzing
functional magnetic resonance imaging (fMRI) data, based on pattern recognition
and statistical learning. By predicting some cognitive variables related to
brain activation maps, this approach aims at decoding brain activity. Inverse
inference ta... | computer science |
21,583 | A Risk Comparison of Ordinary Least Squares vs Ridge Regression | stat.ML | We compare the risk of ridge regression to a simple variant of ordinary least
squares, in which one simply projects the data onto a finite dimensional
subspace (as specified by a Principal Component Analysis) and then performs an
ordinary (un-regularized) least squares regression in this subspace. This note
shows that ... | computer science |
21,584 | Closed-form EM for Sparse Coding and its Application to Source
Separation | stat.ML | We define and discuss the first sparse coding algorithm based on closed-form
EM updates and continuous latent variables. The underlying generative model
consists of a standard `spike-and-slab' prior and a Gaussian noise model.
Closed-form solutions for E- and M-step equations are derived by generalizing
probabilistic P... | computer science |
21,585 | Independent screening for single-index hazard rate models with
ultra-high dimensional features | stat.ML | In data sets with many more features than observations, independent screening
based on all univariate regression models leads to a computationally convenient
variable selection method. Recent efforts have shown that in the case of
generalized linear models, independent screening may suffice to capture all
relevant feat... | computer science |
21,586 | Minimax Policies for Combinatorial Prediction Games | stat.ML | We address the online linear optimization problem when the actions of the
forecaster are represented by binary vectors. Our goal is to understand the
magnitude of the minimax regret for the worst possible set of actions. We study
the problem under three different assumptions for the feedback: full
information, and the ... | computer science |
21,587 | PAC learnability under non-atomic measures: a problem by Vidyasagar | stat.ML | In response to a 1997 problem of M. Vidyasagar, we state a criterion for PAC
learnability of a concept class $\mathscr C$ under the family of all non-atomic
(diffuse) measures on the domain $\Omega$. The uniform Glivenko--Cantelli
property with respect to non-atomic measures is no longer a necessary
condition, and cons... | computer science |
21,588 | Restricted Collapsed Draw: Accurate Sampling for Hierarchical Chinese
Restaurant Process Hidden Markov Models | stat.ML | We propose a restricted collapsed draw (RCD) sampler, a general Markov chain
Monte Carlo sampler of simultaneous draws from a hierarchical Chinese
restaurant process (HCRP) with restriction. Models that require simultaneous
draws from a hierarchical Dirichlet process with restriction, such as infinite
Hidden markov mod... | computer science |
21,589 | Multi-stage Convex Relaxation for Feature Selection | stat.ML | A number of recent work studied the effectiveness of feature selection using
Lasso. It is known that under the restricted isometry properties (RIP), Lasso
does not generally lead to the exact recovery of the set of nonzero
coefficients, due to the looseness of convex relaxation. This paper considers
the feature selecti... | computer science |
21,590 | Causal Network Inference via Group Sparse Regularization | stat.ML | This paper addresses the problem of inferring sparse causal networks modeled
by multivariate auto-regressive (MAR) processes. Conditions are derived under
which the Group Lasso (gLasso) procedure consistently estimates sparse network
structure. The key condition involves a "false connection score." In
particular, we sh... | computer science |
21,591 | Source Separation and Clustering of Phase-Locked Subspaces: Derivations
and Proofs | stat.ML | Due to space limitations, our submission "Source Separation and Clustering of
Phase-Locked Subspaces", accepted for publication on the IEEE Transactions on
Neural Networks in 2011, presented some results without proof. Those proofs are
provided in this paper. | computer science |
21,592 | Pitman-Yor Diffusion Trees | stat.ML | We introduce the Pitman Yor Diffusion Tree (PYDT) for hierarchical
clustering, a generalization of the Dirichlet Diffusion Tree (Neal, 2001) which
removes the restriction to binary branching structure. The generative process
is described and shown to result in an exchangeable distribution over data
points. We prove som... | computer science |
21,593 | ANOVA kernels and RKHS of zero mean functions for model-based
sensitivity analysis | stat.ML | Given a reproducing kernel Hilbert space H of real-valued functions and a
suitable measure mu over the source space D (subset of R), we decompose H as
the sum of a subspace of centered functions for mu and its orthogonal in H.
This decomposition leads to a special case of ANOVA kernels, for which the
functional ANOVA r... | computer science |
21,594 | Online algorithms for Nonnegative Matrix Factorization with the
Itakura-Saito divergence | stat.ML | Nonnegative matrix factorization (NMF) is now a common tool for audio source
separation. When learning NMF on large audio databases, one major drawback is
that the complexity in time is O(FKN) when updating the dictionary (where (F;N)
is the dimension of the input power spectrograms, and K the number of basis
spectra),... | computer science |
21,595 | Sparse Inverse Covariance Estimation via an Adaptive Gradient-Based
Method | stat.ML | We study the problem of estimating from data, a sparse approximation to the
inverse covariance matrix. Estimating a sparsity constrained inverse covariance
matrix is a key component in Gaussian graphical model learning, but one that is
numerically very challenging. We address this challenge by developing a new
adaptive... | computer science |
21,596 | On the Evaluation Criterions for the Active Learning Processes | stat.ML | In many data mining applications collection of sufficiently large datasets is
the most time consuming and expensive. On the other hand, industrial methods of
data collection create huge databases, and make difficult direct applications
of the advanced machine learning algorithms. To address the above problems, we
consi... | computer science |
21,597 | Algebraic Geometric Comparison of Probability Distributions | stat.ML | We propose a novel algebraic framework for treating probability distributions
represented by their cumulants such as the mean and covariance matrix. As an
example, we consider the unsupervised learning problem of finding the subspace
on which several probability distributions agree. Instead of minimizing an
objective f... | computer science |
21,598 | A consistent adjacency spectral embedding for stochastic blockmodel
graphs | stat.ML | We present a method to estimate block membership of nodes in a random graph
generated by a stochastic blockmodel. We use an embedding procedure motivated
by the random dot product graph model, a particular example of the latent
position model. The embedding associates each node with a vector; these vectors
are clustere... | computer science |
21,599 | Sparse Estimation using Bayesian Hierarchical Prior Modeling for Real
and Complex Linear Models | stat.ML | In sparse Bayesian learning (SBL), Gaussian scale mixtures (GSMs) have been
used to model sparsity-inducing priors that realize a class of concave penalty
functions for the regression task in real-valued signal models. Motivated by
the relative scarcity of formal tools for SBL in complex-valued models, this
paper propo... | computer science |
21,600 | A General Theory of Concave Regularization for High Dimensional Sparse
Estimation Problems | stat.ML | Concave regularization methods provide natural procedures for sparse
recovery. However, they are difficult to analyze in the high dimensional
setting. Only recently a few sparse recovery results have been established for
some specific local solutions obtained via specialized numerical procedures.
Still, the fundamental... | computer science |
21,601 | Bayesian Group Factor Analysis | stat.ML | We introduce a factor analysis model that summarizes the dependencies between
observed variable groups, instead of dependencies between individual variables
as standard factor analysis does. A group may correspond to one view of the
same set of objects, one of many data sets tied by co-occurrence, or a set of
alternati... | computer science |
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