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21,802 | The Matrix Generalized Inverse Gaussian Distribution: Properties and
Applications | stat.ML | While the Matrix Generalized Inverse Gaussian ($\mathcal{MGIG}$) distribution
arises naturally in some settings as a distribution over symmetric positive
semi-definite matrices, certain key properties of the distribution and
effective ways of sampling from the distribution have not been carefully
studied. In this paper... | computer science |
21,803 | Structured Matrix Recovery via the Generalized Dantzig Selector | stat.ML | In recent years, structured matrix recovery problems have gained considerable
attention for its real world applications, such as recommender systems and
computer vision. Much of the existing work has focused on matrices with
low-rank structure, and limited progress has been made matrices with other
types of structure. ... | computer science |
21,804 | Optimal Rates For Regularization Of Statistical Inverse Learning
Problems | stat.ML | We consider a statistical inverse learning problem, where we observe the
image of a function $f$ through a linear operator $A$ at i.i.d. random design
points $X_i$, superposed with an additive noise. The distribution of the design
points is unknown and can be very general. We analyze simultaneously the direct
(estimati... | computer science |
21,805 | 1-bit Matrix Completion: PAC-Bayesian Analysis of a Variational
Approximation | stat.ML | Due to challenging applications such as collaborative filtering, the matrix
completion problem has been widely studied in the past few years. Different
approaches rely on different structure assumptions on the matrix in hand. Here,
we focus on the completion of a (possibly) low-rank matrix with binary entries,
the so-c... | computer science |
21,806 | Estimating parameters of nonlinear systems using the elitist particle
filter based on evolutionary strategies | stat.ML | In this article, we present the elitist particle filter based on evolutionary
strategies (EPFES) as an efficient approach for nonlinear system
identification. The EPFES is derived from the frequently-employed state-space
model, where the relevant information of the nonlinear system is captured by an
unknown state vecto... | computer science |
21,807 | Smoothed Hierarchical Dirichlet Process: A Non-Parametric Approach to
Constraint Measures | stat.ML | Time-varying mixture densities occur in many scenarios, for example, the
distributions of keywords that appear in publications may evolve from year to
year, video frame features associated with multiple targets may evolve in a
sequence. Any models that realistically cater to this phenomenon must exhibit
two important p... | computer science |
21,808 | Random Projection Estimation of Discrete-Choice Models with Large Choice
Sets | stat.ML | We introduce sparse random projection, an important dimension-reduction tool
from machine learning, for the estimation of discrete-choice models with
high-dimensional choice sets. Initially, high-dimensional data are compressed
into a lower-dimensional Euclidean space using random projections.
Subsequently, estimation ... | computer science |
21,809 | Dynamic Pricing with Demand Covariates | stat.ML | We consider a firm that sells products over $T$ periods without knowing the
demand function. The firm sequentially sets prices to earn revenue and to learn
the underlying demand function simultaneously. A natural heuristic for this
problem, commonly used in practice, is greedy iterative least squares (GILS).
At each ti... | computer science |
21,810 | Optimal Transport vs. Fisher-Rao distance between Copulas for Clustering
Multivariate Time Series | stat.ML | We present a methodology for clustering N objects which are described by
multivariate time series, i.e. several sequences of real-valued random
variables. This clustering methodology leverages copulas which are
distributions encoding the dependence structure between several random
variables. To take fully into account ... | computer science |
21,811 | Sparse Generalized Eigenvalue Problem: Optimal Statistical Rates via
Truncated Rayleigh Flow | stat.ML | Sparse generalized eigenvalue problem plays a pivotal role in a large family
of high-dimensional learning tasks, including sparse Fisher's discriminant
analysis, canonical correlation analysis, and sufficient dimension reduction.
However, the theory of sparse generalized eigenvalue problem remains largely
unexplored. I... | computer science |
21,812 | LLE with low-dimensional neighborhood representation | stat.ML | The local linear embedding algorithm (LLE) is a non-linear dimension-reducing
technique, widely used due to its computational simplicity and intuitive
approach. LLE first linearly reconstructs each input point from its nearest
neighbors and then preserves these neighborhood relations in the
low-dimensional embedding. W... | computer science |
21,813 | Persistent Clustering and a Theorem of J. Kleinberg | stat.ML | We construct a framework for studying clustering algorithms, which includes
two key ideas: persistence and functoriality. The first encodes the idea that
the output of a clustering scheme should carry a multiresolution structure, the
second the idea that one should be able to compare the results of clustering
algorithm... | computer science |
21,814 | Decomposable Principal Component Analysis | stat.ML | We consider principal component analysis (PCA) in decomposable Gaussian
graphical models. We exploit the prior information in these models in order to
distribute its computation. For this purpose, we reformulate the problem in the
sparse inverse covariance (concentration) domain and solve the global
eigenvalue problem ... | computer science |
21,815 | Multi-view predictive partitioning in high dimensions | stat.ML | Many modern data mining applications are concerned with the analysis of
datasets in which the observations are described by paired high-dimensional
vectorial representations or "views". Some typical examples can be found in web
mining and genomics applications. In this article we present an algorithm for
data clusterin... | computer science |
21,816 | Greedy Learning of Markov Network Structure | stat.ML | We propose a new yet natural algorithm for learning the graph structure of
general discrete graphical models (a.k.a. Markov random fields) from samples.
Our algorithm finds the neighborhood of a node by sequentially adding nodes
that produce the largest reduction in empirical conditional entropy; it is
greedy in the se... | computer science |
21,817 | High Dimensional Semiparametric Gaussian Copula Graphical Models | stat.ML | In this paper, we propose a semiparametric approach, named nonparanormal
skeptic, for efficiently and robustly estimating high dimensional undirected
graphical models. To achieve modeling flexibility, we consider Gaussian Copula
graphical models (or the nonparanormal) as proposed by Liu et al. (2009). To
achieve estima... | computer science |
21,818 | Regularized Tensor Factorizations and Higher-Order Principal Components
Analysis | stat.ML | High-dimensional tensors or multi-way data are becoming prevalent in areas
such as biomedical imaging, chemometrics, networking and bibliometrics.
Traditional approaches to finding lower dimensional representations of tensor
data include flattening the data and applying matrix factorizations such as
principal component... | computer science |
21,819 | Robust subspace recovery by Tyler's M-estimator | stat.ML | This paper considers the problem of robust subspace recovery: given a set of
$N$ points in $\mathbb{R}^D$, if many lie in a $d$-dimensional subspace, then
can we recover the underlying subspace? We show that Tyler's M-estimator can be
used to recover the underlying subspace, if the percentage of the inliers is
larger t... | computer science |
21,820 | Warped Mixtures for Nonparametric Cluster Shapes | stat.ML | A mixture of Gaussians fit to a single curved or heavy-tailed cluster will
report that the data contains many clusters. To produce more appropriate
clusterings, we introduce a model which warps a latent mixture of Gaussians to
produce nonparametric cluster shapes. The possibly low-dimensional latent
mixture model allow... | computer science |
21,821 | On the probabilistic continuous complexity conjecture | stat.ML | In this paper we prove the probabilistic continuous complexity conjecture. In
continuous complexity theory, this states that the complexity of solving a
continuous problem with probability approaching 1 converges (in this limit) to
the complexity of solving the same problem in its worst case. We prove the
conjecture ho... | computer science |
21,822 | Developments in the theory of randomized shortest paths with a
comparison of graph node distances | stat.ML | There have lately been several suggestions for parametrized distances on a
graph that generalize the shortest path distance and the commute time or
resistance distance. The need for developing such distances has risen from the
observation that the above-mentioned common distances in many situations fail
to take into ac... | computer science |
21,823 | An Empirical Comparison of V-fold Penalisation and Cross Validation for
Model Selection in Distribution-Free Regression | stat.ML | Model selection is a crucial issue in machine-learning and a wide variety of
penalisation methods (with possibly data dependent complexity penalties) have
recently been introduced for this purpose. However their empirical performance
is generally not well documented in the literature. It is the goal of this
paper to in... | computer science |
21,824 | MAD-Bayes: MAP-based Asymptotic Derivations from Bayes | stat.ML | The classical mixture of Gaussians model is related to K-means via
small-variance asymptotics: as the covariances of the Gaussians tend to zero,
the negative log-likelihood of the mixture of Gaussians model approaches the
K-means objective, and the EM algorithm approaches the K-means algorithm. Kulis
& Jordan (2012) us... | computer science |
21,825 | A complexity analysis of statistical learning algorithms | stat.ML | We apply information-based complexity analysis to support vector machine
(SVM) algorithms, with the goal of a comprehensive continuous algorithmic
analysis of such algorithms. This involves complexity measures in which some
higher order operations (e.g., certain optimizations) are considered primitive
for the purposes ... | computer science |
21,826 | Feature vector regularization in machine learning | stat.ML | Problems in machine learning (ML) can involve noisy input data, and ML
classification methods have reached limiting accuracies when based on standard
ML data sets consisting of feature vectors and their classes. Greater accuracy
will require incorporation of prior structural information on data into
learning. We study ... | computer science |
21,827 | Blind Analysis of EGM Signals: Sparsity-Aware Formulation | stat.ML | This technical note considers the problems of blind sparse learning and
inference of electrogram (EGM) signals under atrial fibrillation (AF)
conditions. First of all we introduce a mathematical model for the observed
signals that takes into account the multiple foci typically appearing inside
the heart during AF. Then... | computer science |
21,828 | Regression shrinkage and grouping of highly correlated predictors with
HORSES | stat.ML | Identifying homogeneous subgroups of variables can be challenging in high
dimensional data analysis with highly correlated predictors. We propose a new
method called Hexagonal Operator for Regression with Shrinkage and Equality
Selection, HORSES for short, that simultaneously selects positively correlated
variables and... | computer science |
21,829 | Efficiency for Regularization Parameter Selection in Penalized
Likelihood Estimation of Misspecified Models | stat.ML | It has been shown that AIC-type criteria are asymptotically efficient
selectors of the tuning parameter in non-concave penalized regression methods
under the assumption that the population variance is known or that a consistent
estimator is available. We relax this assumption to prove that AIC itself is
asymptotically ... | computer science |
21,830 | Towards Identification of Relevant Variables in the observed Aerosol
Optical Depth Bias between MODIS and AERONET observations | stat.ML | Measurements made by satellite remote sensing, Moderate Resolution Imaging
Spectroradiometer (MODIS), and globally distributed Aerosol Robotic Network
(AERONET) are compared. Comparison of the two datasets measurements for aerosol
optical depth values show that there are biases between the two data products.
In this pa... | computer science |
21,831 | Multiclass Data Segmentation using Diffuse Interface Methods on Graphs | stat.ML | We present two graph-based algorithms for multiclass segmentation of
high-dimensional data. The algorithms use a diffuse interface model based on
the Ginzburg-Landau functional, related to total variation compressed sensing
and image processing. A multiclass extension is introduced using the Gibbs
simplex, with the fun... | computer science |
21,832 | Consistency of Online Random Forests | stat.ML | As a testament to their success, the theory of random forests has long been
outpaced by their application in practice. In this paper, we take a step
towards narrowing this gap by providing a consistency result for online random
forests. | computer science |
21,833 | Spectral Clustering with Unbalanced Data | stat.ML | Spectral clustering (SC) and graph-based semi-supervised learning (SSL)
algorithms are sensitive to how graphs are constructed from data. In particular
if the data has proximal and unbalanced clusters these algorithms can lead to
poor performance on well-known graphs such as $k$-NN, full-RBF,
$\epsilon$-graphs. This is... | computer science |
21,834 | A bag-of-paths framework for network data analysis | stat.ML | This work develops a generic framework, called the bag-of-paths (BoP), for
link and network data analysis. The central idea is to assign a probability
distribution on the set of all paths in a network. More precisely, a
Gibbs-Boltzmann distribution is defined over a bag of paths in a network, that
is, on a representati... | computer science |
21,835 | A New Monte Carlo Based Algorithm for the Gaussian Process
Classification Problem | stat.ML | Gaussian process is a very promising novel technology that has been applied
to both the regression problem and the classification problem. While for the
regression problem it yields simple exact solutions, this is not the case for
the classification problem, because we encounter intractable integrals. In this
paper we ... | computer science |
21,836 | Dictionary LASSO: Guaranteed Sparse Recovery under Linear Transformation | stat.ML | We consider the following signal recovery problem: given a measurement matrix
$\Phi\in \mathbb{R}^{n\times p}$ and a noisy observation vector $c\in
\mathbb{R}^{n}$ constructed from $c = \Phi\theta^* + \epsilon$ where
$\epsilon\in \mathbb{R}^{n}$ is the noise vector whose entries follow i.i.d.
centered sub-Gaussian dist... | computer science |
21,837 | Learning Mixtures of Bernoulli Templates by Two-Round EM with
Performance Guarantee | stat.ML | Dasgupta and Shulman showed that a two-round variant of the EM algorithm can
learn mixture of Gaussian distributions with near optimal precision with high
probability if the Gaussian distributions are well separated and if the
dimension is sufficiently high. In this paper, we generalize their theory to
learning mixture... | computer science |
21,838 | Inferring Team Strengths Using a Discrete Markov Random Field | stat.ML | We propose an original model for inferring team strengths using a Markov
Random Field, which can be used to generate historical estimates of the
offensive and defensive strengths of a team over time. This model was designed
to be applied to sports such as soccer or hockey, in which contest outcomes
take value in a limi... | computer science |
21,839 | Sparse Approximate Inference for Spatio-Temporal Point Process Models | stat.ML | Spatio-temporal point process models play a central role in the analysis of
spatially distributed systems in several disciplines. Yet, scalable inference
remains computa- tionally challenging both due to the high resolution modelling
generally required and the analytically intractable likelihood function. Here,
we expl... | computer science |
21,840 | Factored expectation propagation for input-output FHMM models in systems
biology | stat.ML | We consider the problem of joint modelling of metabolic signals and gene
expression in systems biology applications. We propose an approach based on
input-output factorial hidden Markov models and propose a structured
variational inference approach to infer the structure and states of the model.
We start from the class... | computer science |
21,841 | Out-of-sample Extension for Latent Position Graphs | stat.ML | We consider the problem of vertex classification for graphs constructed from
the latent position model. It was shown previously that the approach of
embedding the graphs into some Euclidean space followed by classification in
that space can yields a universally consistent vertex classifier. However, a
major technical d... | computer science |
21,842 | Adaptive estimation of the copula correlation matrix for semiparametric
elliptical copulas | stat.ML | We study the adaptive estimation of copula correlation matrix $\Sigma$ for
the semi-parametric elliptical copula model. In this context, the correlations
are connected to Kendall's tau through a sine function transformation. Hence, a
natural estimate for $\Sigma$ is the plug-in estimator $\hat{\Sigma}$ with
Kendall's t... | computer science |
21,843 | Statistical analysis of latent generalized correlation matrix estimation
in transelliptical distribution | stat.ML | Correlation matrices play a key role in many multivariate methods (e.g.,
graphical model estimation and factor analysis). The current state-of-the-art
in estimating large correlation matrices focuses on the use of Pearson's sample
correlation matrix. Although Pearson's sample correlation matrix enjoys various
good prop... | computer science |
21,844 | Non-linear dimensionality reduction: Riemannian metric estimation and
the problem of geometric discovery | stat.ML | In recent years, manifold learning has become increasingly popular as a tool
for performing non-linear dimensionality reduction. This has led to the
development of numerous algorithms of varying degrees of complexity that aim to
recover man ifold geometry using either local or global features of the data.
Building on... | computer science |
21,845 | Joint Modeling and Registration of Cell Populations in Cohorts of
High-Dimensional Flow Cytometric Data | stat.ML | In systems biomedicine, an experimenter encounters different potential
sources of variation in data such as individual samples, multiple experimental
conditions, and multi-variable network-level responses. In multiparametric
cytometry, which is often used for analyzing patient samples, such issues are
critical. While c... | computer science |
21,846 | Forward-Backward Greedy Algorithms for General Convex Smooth Functions
over A Cardinality Constraint | stat.ML | We consider forward-backward greedy algorithms for solving sparse feature
selection problems with general convex smooth functions. A state-of-the-art
greedy method, the Forward-Backward greedy algorithm (FoBa-obj) requires to
solve a large number of optimization problems, thus it is not scalable for
large-size problems... | computer science |
21,847 | Online Matrix Completion Through Nuclear Norm Regularisation | stat.ML | It is the main goal of this paper to propose a novel method to perform matrix
completion on-line. Motivated by a wide variety of applications, ranging from
the design of recommender systems to sensor network localization through
seismic data reconstruction, we consider the matrix completion problem when
entries of the ... | computer science |
21,848 | Multiscale Shrinkage and Lévy Processes | stat.ML | A new shrinkage-based construction is developed for a compressible vector
$\boldsymbol{x}\in\mathbb{R}^n$, for cases in which the components of $\xv$ are
naturally associated with a tree structure. Important examples are when $\xv$
corresponds to the coefficients of a wavelet or block-DCT representation of
data. The me... | computer science |
21,849 | A variational Bayes framework for sparse adaptive estimation | stat.ML | Recently, a number of mostly $\ell_1$-norm regularized least squares type
deterministic algorithms have been proposed to address the problem of
\emph{sparse} adaptive signal estimation and system identification. From a
Bayesian perspective, this task is equivalent to maximum a posteriori
probability estimation under a ... | computer science |
21,850 | Detection of Anomalous Crowd Behavior Using Spatio-Temporal
Multiresolution Model and Kronecker Sum Decompositions | stat.ML | In this work we consider the problem of detecting anomalous spatio-temporal
behavior in videos. Our approach is to learn the normative multiframe pixel
joint distribution and detect deviations from it using a likelihood based
approach. Due to the extreme lack of available training samples relative to the
dimension of t... | computer science |
21,851 | Survey On The Estimation Of Mutual Information Methods as a Measure of
Dependency Versus Correlation Analysis | stat.ML | In this survey, we present and compare different approaches to estimate
Mutual Information (MI) from data to analyse general dependencies between
variables of interest in a system. We demonstrate the performance difference of
MI versus correlation analysis, which is only optimal in case of linear
dependencies. First, w... | computer science |
21,852 | Nonparametric Latent Tree Graphical Models: Inference, Estimation, and
Structure Learning | stat.ML | Tree structured graphical models are powerful at expressing long range or
hierarchical dependency among many variables, and have been widely applied in
different areas of computer science and statistics. However, existing methods
for parameter estimation, inference, and structure learning mainly rely on the
Gaussian or... | computer science |
21,853 | Embedding Graphs under Centrality Constraints for Network Visualization | stat.ML | Visual rendering of graphs is a key task in the mapping of complex network
data. Although most graph drawing algorithms emphasize aesthetic appeal,
certain applications such as travel-time maps place more importance on
visualization of structural network properties. The present paper advocates two
graph embedding appro... | computer science |
21,854 | Marginal Pseudo-Likelihood Learning of Markov Network structures | stat.ML | Undirected graphical models known as Markov networks are popular for a wide
variety of applications ranging from statistical physics to computational
biology. Traditionally, learning of the network structure has been done under
the assumption of chordality which ensures that efficient scoring methods can
be used. In ge... | computer science |
21,855 | Hilbert Space Methods for Reduced-Rank Gaussian Process Regression | stat.ML | This paper proposes a novel scheme for reduced-rank Gaussian process
regression. The method is based on an approximate series expansion of the
covariance function in terms of an eigenfunction expansion of the Laplace
operator in a compact subset of $\mathbb{R}^d$. On this approximate eigenbasis
the eigenvalues of the c... | computer science |
21,856 | Identifiability of an Integer Modular Acyclic Additive Noise Model and
its Causal Structure Discovery | stat.ML | The notion of causality is used in many situations dealing with uncertainty.
We consider the problem whether causality can be identified given data set
generated by discrete random variables rather than continuous ones. In
particular, for non-binary data, thus far it was only known that causality can
be identified exce... | computer science |
21,857 | The EM algorithm and the Laplace Approximation | stat.ML | The Laplace approximation calls for the computation of second derivatives at
the likelihood maximum. When the maximum is found by the EM-algorithm, there is
a convenient way to compute these derivatives. The likelihood gradient can be
obtained from the EM-auxiliary, while the Hessian can be obtained from this
gradient ... | computer science |
21,858 | Near-Ideal Behavior of Compressed Sensing Algorithms | stat.ML | In a recent paper, it is shown that the LASSO algorithm exhibits "near-ideal
behavior," in the following sense: Suppose $y = Az + \eta$ where $A$ satisfies
the restricted isometry property (RIP) with a sufficiently small constant, and
$\Vert \eta \Vert_2 \leq \epsilon$. Then minimizing $\Vert z \Vert_1$ subject
to $\Ve... | computer science |
21,859 | Safe Sample Screening for Support Vector Machines | stat.ML | Sparse classifiers such as the support vector machines (SVM) are efficient in
test-phases because the classifier is characterized only by a subset of the
samples called support vectors (SVs), and the rest of the samples (non SVs)
have no influence on the classification result. However, the advantage of the
sparsity has... | computer science |
21,860 | Tempering by Subsampling | stat.ML | In this paper we demonstrate that tempering Markov chain Monte Carlo samplers
for Bayesian models by recursively subsampling observations without replacement
can improve the performance of baseline samplers in terms of effective sample
size per computation. We present two tempering by subsampling algorithms,
subsampled... | computer science |
21,861 | Sparse Bayesian Unsupervised Learning | stat.ML | This paper is about variable selection, clustering and estimation in an
unsupervised high-dimensional setting. Our approach is based on fitting
constrained Gaussian mixture models, where we learn the number of clusters $K$
and the set of relevant variables $S$ using a generalized Bayesian posterior
with a sparsity indu... | computer science |
21,862 | A Unifying Framework in Vector-valued Reproducing Kernel Hilbert Spaces
for Manifold Regularization and Co-Regularized Multi-view Learning | stat.ML | This paper presents a general vector-valued reproducing kernel Hilbert spaces
(RKHS) framework for the problem of learning an unknown functional dependency
between a structured input space and a structured output space. Our formulation
encompasses both Vector-valued Manifold Regularization and Co-regularized
Multi-view... | computer science |
21,863 | Marginal and simultaneous predictive classification using stratified
graphical models | stat.ML | An inductive probabilistic classification rule must generally obey the
principles of Bayesian predictive inference, such that all observed and
unobserved stochastic quantities are jointly modeled and the parameter
uncertainty is fully acknowledged through the posterior predictive
distribution. Several such rules have b... | computer science |
21,864 | Variational Inference in Sparse Gaussian Process Regression and Latent
Variable Models - a Gentle Tutorial | stat.ML | In this tutorial we explain the inference procedures developed for the sparse
Gaussian process (GP) regression and Gaussian process latent variable model
(GPLVM). Due to page limit the derivation given in Titsias (2009) and Titsias &
Lawrence (2010) is brief, hence getting a full picture of it requires
collecting resul... | computer science |
21,865 | An Algorithmic Framework for Computing Validation Performance Bounds by
Using Suboptimal Models | stat.ML | Practical model building processes are often time-consuming because many
different models must be trained and validated. In this paper, we introduce a
novel algorithm that can be used for computing the lower and the upper bounds
of model validation errors without actually training the model itself. A key
idea behind ou... | computer science |
21,866 | Justifying Information-Geometric Causal Inference | stat.ML | Information Geometric Causal Inference (IGCI) is a new approach to
distinguish between cause and effect for two variables. It is based on an
independence assumption between input distribution and causal mechanism that
can be phrased in terms of orthogonality in information space. We describe two
intuitive reinterpretat... | computer science |
21,867 | Performance Limits of Dictionary Learning for Sparse Coding | stat.ML | We consider the problem of dictionary learning under the assumption that the
observed signals can be represented as sparse linear combinations of the
columns of a single large dictionary matrix. In particular, we analyze the
minimax risk of the dictionary learning problem which governs the mean squared
error (MSE) perf... | computer science |
21,868 | A Kernel Independence Test for Random Processes | stat.ML | A new non parametric approach to the problem of testing the independence of
two random process is developed. The test statistic is the Hilbert Schmidt
Independence Criterion (HSIC), which was used previously in testing
independence for i.i.d pairs of variables. The asymptotic behaviour of HSIC is
established when compu... | computer science |
21,869 | High Dimensional Semiparametric Scale-Invariant Principal Component
Analysis | stat.ML | We propose a new high dimensional semiparametric principal component analysis
(PCA) method, named Copula Component Analysis (COCA). The semiparametric model
assumes that, after unspecified marginally monotone transformations, the
distributions are multivariate Gaussian. COCA improves upon PCA and sparse PCA
in three as... | computer science |
21,870 | Le Cam meets LeCun: Deficiency and Generic Feature Learning | stat.ML | "Deep Learning" methods attempt to learn generic features in an unsupervised
fashion from a large unlabelled data set. These generic features should perform
as well as the best hand crafted features for any learning problem that makes
use of this data. We provide a definition of generic features, characterize
when it i... | computer science |
21,871 | Novel Deviation Bounds for Mixture of Independent Bernoulli Variables
with Application to the Missing Mass | stat.ML | In this paper, we are concerned with obtaining distribution-free
concentration inequalities for mixture of independent Bernoulli variables that
incorporate a notion of variance. Missing mass is the total probability mass
associated to the outcomes that have not been seen in a given sample which is
an important quantity... | computer science |
21,872 | Addendum on the scoring of Gaussian directed acyclic graphical models | stat.ML | We provide a correction to the expression for scoring Gaussian directed
acyclic graphical models derived in Geiger and Heckerman [Ann. Statist. 30
(2002) 1414-1440] and discuss how to evaluate the score efficiently. | computer science |
21,873 | New Perspectives on k-Support and Cluster Norms | stat.ML | The $k$-support norm is a regularizer which has been successfully applied to
sparse vector prediction problems. We show that it belongs to a general class
of norms which can be formulated as a parameterized infimum over quadratics. We
further extend the $k$-support norm to matrices, and we observe that it is a
special ... | computer science |
21,874 | A reversible infinite HMM using normalised random measures | stat.ML | We present a nonparametric prior over reversible Markov chains. We use
completely random measures, specifically gamma processes, to construct a
countably infinite graph with weighted edges. By enforcing symmetry to make the
edges undirected we define a prior over random walks on graphs that results in
a reversible Mark... | computer science |
21,875 | On the Sensitivity of the Lasso to the Number of Predictor Variables | stat.ML | The Lasso is a computationally efficient regression regularization procedure
that can produce sparse estimators when the number of predictors (p) is large.
Oracle inequalities provide probability loss bounds for the Lasso estimator at
a deterministic choice of the regularization parameter. These bounds tend to
zero if ... | computer science |
21,876 | On The Sample Complexity of Sparse Dictionary Learning | stat.ML | In the synthesis model signals are represented as a sparse combinations of
atoms from a dictionary. Dictionary learning describes the acquisition process
of the underlying dictionary for a given set of training samples. While ideally
this would be achieved by optimizing the expectation of the factors over the
underlyin... | computer science |
21,877 | Sparse Learning over Infinite Subgraph Features | stat.ML | We present a supervised-learning algorithm from graph data (a set of graphs)
for arbitrary twice-differentiable loss functions and sparse linear models over
all possible subgraph features. To date, it has been shown that under all
possible subgraph features, several types of sparse learning, such as Adaboost,
LPBoost, ... | computer science |
21,878 | First Order Methods for Robust Non-negative Matrix Factorization for
Large Scale Noisy Data | stat.ML | Nonnegative matrix factorization (NMF) has been shown to be identifiable
under the separability assumption, under which all the columns(or rows) of the
input data matrix belong to the convex cone generated by only a few of these
columns(or rows) [1]. In real applications, however, such separability
assumption is hard t... | computer science |
21,879 | Optimal Schatten-q and Ky-Fan-k Norm Rate of Low Rank Matrix Estimation | stat.ML | In this paper, we consider low rank matrix estimation using either
matrix-version Dantzig Selector $\hat{A}_{\lambda}^d$ or matrix-version LASSO
estimator $\hat{A}_{\lambda}^L$. We consider sub-Gaussian measurements, $i.e.$,
the measurements $X_1,\ldots,X_n\in\mathbb{R}^{m\times m}$ have $i.i.d.$
sub-Gaussian entries. ... | computer science |
21,880 | Systematic Ensemble Learning for Regression | stat.ML | The motivation of this work is to improve the performance of standard
stacking approaches or ensembles, which are composed of simple, heterogeneous
base models, through the integration of the generation and selection stages for
regression problems. We propose two extensions to the standard stacking
approach. In the fir... | computer science |
21,881 | Characteristic Kernels and Infinitely Divisible Distributions | stat.ML | We connect shift-invariant characteristic kernels to infinitely divisible
distributions on $\mathbb{R}^{d}$. Characteristic kernels play an important
role in machine learning applications with their kernel means to distinguish
any two probability measures. The contribution of this paper is two-fold.
First, we show, usi... | computer science |
21,882 | A Rank-SVM Approach to Anomaly Detection | stat.ML | We propose a novel non-parametric adaptive anomaly detection algorithm for
high dimensional data based on rank-SVM. Data points are first ranked based on
scores derived from nearest neighbor graphs on n-point nominal data. We then
train a rank-SVM using this ranked data. A test-point is declared as an anomaly
at alpha-... | computer science |
21,883 | The Falling Factorial Basis and Its Statistical Applications | stat.ML | We study a novel spline-like basis, which we name the "falling factorial
basis", bearing many similarities to the classic truncated power basis. The
advantage of the falling factorial basis is that it enables rapid, linear-time
computations in basis matrix multiplication and basis matrix inversion. The
falling factoria... | computer science |
21,884 | PAC-Bayes Mini-tutorial: A Continuous Union Bound | stat.ML | When I first encountered PAC-Bayesian concentration inequalities they seemed
to me to be rather disconnected from good old-fashioned results like
Hoeffding's and Bernstein's inequalities. But, at least for one flavour of the
PAC-Bayesian bounds, there is actually a very close relation, and the main
innovation is a cont... | computer science |
21,885 | Learning rates for the risk of kernel based quantile regression
estimators in additive models | stat.ML | Additive models play an important role in semiparametric statistics. This
paper gives learning rates for regularized kernel based methods for additive
models. These learning rates compare favourably in particular in high
dimensions to recent results on optimal learning rates for purely nonparametric
regularized kernel ... | computer science |
21,886 | Fast Ridge Regression with Randomized Principal Component Analysis and
Gradient Descent | stat.ML | We propose a new two stage algorithm LING for large scale regression
problems. LING has the same risk as the well known Ridge Regression under the
fixed design setting and can be computed much faster. Our experiments have
shown that LING performs well in terms of both prediction accuracy and
computational efficiency co... | computer science |
21,887 | A convergence and asymptotic analysis of the generalized symmetric
FastICA algorithm | stat.ML | This contribution deals with the generalized symmetric FastICA algorithm in
the domain of Independent Component Analysis (ICA). The generalized symmetric
version of FastICA has been shown to have the potential to achieve the
Cram\'er-Rao Bound (CRB) by allowing the usage of different nonlinearity
functions in its paral... | computer science |
21,888 | A Bayesian estimation approach to analyze non-Gaussian data-generating
processes with latent classes | stat.ML | A large amount of observational data has been accumulated in various fields
in recent times, and there is a growing need to estimate the generating
processes of these data. A linear non-Gaussian acyclic model (LiNGAM) based on
the non-Gaussianity of external influences has been proposed to estimate the
data-generating ... | computer science |
21,889 | L0 Sparse Inverse Covariance Estimation | stat.ML | Recently, there has been focus on penalized log-likelihood covariance
estimation for sparse inverse covariance (precision) matrices. The penalty is
responsible for inducing sparsity, and a very common choice is the convex $l_1$
norm. However, the best estimator performance is not always achieved with this
penalty. The ... | computer science |
21,890 | On the Generalization of the C-Bound to Structured Output Ensemble
Methods | stat.ML | This paper generalizes an important result from the PAC-Bayesian literature
for binary classification to the case of ensemble methods for structured
outputs. We prove a generic version of the \Cbound, an upper bound over the
risk of models expressed as a weighted majority vote that is based on the first
and second stat... | computer science |
21,891 | Learning From Non-iid Data: Fast Rates for the One-vs-All Multiclass
Plug-in Classifiers | stat.ML | We prove new fast learning rates for the one-vs-all multiclass plug-in
classifiers trained either from exponentially strongly mixing data or from data
generated by a converging drifting distribution. These are two typical
scenarios where training data are not iid. The learning rates are obtained
under a multiclass vers... | computer science |
21,892 | Beta diffusion trees and hierarchical feature allocations | stat.ML | We define the beta diffusion tree, a random tree structure with a set of
leaves that defines a collection of overlapping subsets of objects, known as a
feature allocation. A generative process for the tree structure is defined in
terms of particles (representing the objects) diffusing in some continuous
space, analogou... | computer science |
21,893 | On the Sample Complexity of Subspace Learning | stat.ML | A large number of algorithms in machine learning, from principal component
analysis (PCA), and its non-linear (kernel) extensions, to more recent spectral
embedding and support estimation methods, rely on estimating a linear subspace
from samples. In this paper we introduce a general formulation of this problem
and der... | computer science |
21,894 | A Wild Bootstrap for Degenerate Kernel Tests | stat.ML | A wild bootstrap method for nonparametric hypothesis tests based on kernel
distribution embeddings is proposed. This bootstrap method is used to construct
provably consistent tests that apply to random processes, for which the naive
permutation-based bootstrap fails. It applies to a large group of kernel tests
based on... | computer science |
21,895 | Kernel-based Information Criterion | stat.ML | This paper introduces Kernel-based Information Criterion (KIC) for model
selection in regression analysis. The novel kernel-based complexity measure in
KIC efficiently computes the interdependency between parameters of the model
using a variable-wise variance and yields selection of better, more robust
regressors. Expe... | computer science |
21,896 | A study of the fixed points and spurious solutions of the FastICA
algorithm | stat.ML | The FastICA algorithm is one of the most popular iterative algorithms in the
domain of linear independent component analysis. Despite its success, it is
observed that FastICA occasionally yields outcomes that do not correspond to
any true solutions (known as demixing vectors) of the ICA problem. These
outcomes are comm... | computer science |
21,897 | Laplacian Mixture Modeling for Network Analysis and Unsupervised
Learning on Graphs | stat.ML | Laplacian mixture models identify overlapping regions of influence in
unlabeled graph and network data in a scalable and computationally efficient
way, yielding useful low-dimensional representations. By combining Laplacian
eigenspace and finite mixture modeling methods, they provide probabilistic
dimensionality reduct... | computer science |
21,898 | Learning Planar Ising Models | stat.ML | Inference and learning of graphical models are both well-studied problems in
statistics and machine learning that have found many applications in science
and engineering. However, exact inference is intractable in general graphical
models, which suggests the problem of seeking the best approximation to a
collection of ... | computer science |
21,899 | Sparse Representation Classification Beyond L1 Minimization and the
Subspace Assumption | stat.ML | The sparse representation classifier (SRC) has been utilized in various
classification problems, which makes use of L1 minimization and is shown to
work well for image recognition problems that satisfy a subspace assumption. In
this paper we propose a new implementation of SRC via screening, establish its
equivalence t... | computer science |
21,900 | Provable Sparse Tensor Decomposition | stat.ML | We propose a novel sparse tensor decomposition method, namely Tensor
Truncated Power (TTP) method, that incorporates variable selection into the
estimation of decomposition components. The sparsity is achieved via an
efficient truncation step embedded in the tensor power iteration. Our method
applies to a broad family ... | computer science |
21,901 | Active Function Cross-Entropy Clustering | stat.ML | Gaussian Mixture Models (GMM) have found many applications in density
estimation and data clustering. However, the model does not adapt well to
curved and strongly nonlinear data. Recently there appeared an improvement
called AcaGMM (Active curve axis Gaussian Mixture Model), which fits Gaussians
along curves using an ... | computer science |
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