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22,102 | Robust Kernel Density Estimation by Scaling and Projection in Hilbert
Space | stat.ML | While robust parameter estimation has been well studied in parametric density
estimation, there has been little investigation into robust density estimation
in the nonparametric setting. We present a robust version of the popular kernel
density estimator (KDE). As with other estimators, a robust version of the KDE
is u... | computer science |
22,103 | The NLMS algorithm with time-variant optimum stepsize derived from a
Bayesian network perspective | stat.ML | In this article, we derive a new stepsize adaptation for the normalized least
mean square algorithm (NLMS) by describing the task of linear acoustic echo
cancellation from a Bayesian network perspective. Similar to the well-known
Kalman filter equations, we model the acoustic wave propagation from the
loudspeaker to th... | computer science |
22,104 | Quantifying error in estimates of human brain fiber directions using
Earth Mover's Distance | stat.ML | Diffusion-weighted MR imaging (DWI) is the only method we currently have to
measure connections between different parts of the human brain in vivo. To
elucidate the structure of these connections, algorithms for tracking bundles
of axonal fibers through the subcortical white matter rely on local estimates
of the fiber ... | computer science |
22,105 | Group Factor Analysis | stat.ML | Factor analysis provides linear factors that describe relationships between
individual variables of a data set. We extend this classical formulation into
linear factors that describe relationships between groups of variables, where
each group represents either a set of related variables or a data set. The
model also na... | computer science |
22,106 | Efficient Minimax Signal Detection on Graphs | stat.ML | Several problems such as network intrusion, community detection, and disease
outbreak can be described by observations attributed to nodes or edges of a
graph. In these applications presence of intrusion, community or disease
outbreak is characterized by novel observations on some unknown connected
subgraph. These prob... | computer science |
22,107 | Optimal variable selection in multi-group sparse discriminant analysis | stat.ML | This article considers the problem of multi-group classification in the
setting where the number of variables $p$ is larger than the number of
observations $n$. Several methods have been proposed in the literature that
address this problem, however their variable selection performance is either
unknown or suboptimal to... | computer science |
22,108 | Streaming Variational Inference for Bayesian Nonparametric Mixture
Models | stat.ML | In theory, Bayesian nonparametric (BNP) models are well suited to streaming
data scenarios due to their ability to adapt model complexity with the observed
data. Unfortunately, such benefits have not been fully realized in practice;
existing inference algorithms are either not applicable to streaming
applications or no... | computer science |
22,109 | Nested Variational Compression in Deep Gaussian Processes | stat.ML | Deep Gaussian processes provide a flexible approach to probabilistic
modelling of data using either supervised or unsupervised learning. For
tractable inference approximations to the marginal likelihood of the model must
be made. The original approach to approximate inference in these models used
variational compressio... | computer science |
22,110 | A Likelihood Ratio Framework for High Dimensional Semiparametric
Regression | stat.ML | We propose a likelihood ratio based inferential framework for high
dimensional semiparametric generalized linear models. This framework addresses
a variety of challenging problems in high dimensional data analysis, including
incomplete data, selection bias, and heterogeneous multitask learning. Our work
has three main ... | computer science |
22,111 | Detecting Overlapping Communities in Networks Using Spectral Methods | stat.ML | Community detection is a fundamental problem in network analysis which is
made more challenging by overlaps between communities which often occur in
practice. Here we propose a general, flexible, and interpretable generative
model for overlapping communities, which can be thought of as a generalization
of the degree-co... | computer science |
22,112 | Manifold Matching using Shortest-Path Distance and Joint Neighborhood
Selection | stat.ML | Matching datasets of multiple modalities has become an important task in data
analysis. Existing methods often rely on the embedding and transformation of
each single modality without utilizing any correspondence information, which
often results in sub-optimal matching performance. In this paper, we propose a
nonlinear... | computer science |
22,113 | Bayesian multi-tensor factorization | stat.ML | We introduce Bayesian multi-tensor factorization, a model that is the first
Bayesian formulation for joint factorization of multiple matrices and tensors.
The research problem generalizes the joint matrix-tensor factorization problem
to arbitrary sets of tensors of any depth, including matrices, can be
interpreted as u... | computer science |
22,114 | On distinguishability criteria for estimating generative models | stat.ML | Two recently introduced criteria for estimation of generative models are both
based on a reduction to binary classification. Noise-contrastive estimation
(NCE) is an estimation procedure in which a generative model is trained to be
able to distinguish data samples from noise samples. Generative adversarial
networks (GA... | computer science |
22,115 | Approximate Subspace-Sparse Recovery with Corrupted Data via Constrained
$\ell_1$-Minimization | stat.ML | High-dimensional data often lie in low-dimensional subspaces corresponding to
different classes they belong to. Finding sparse representations of data points
in a dictionary built using the collection of data helps to uncover
low-dimensional subspaces and address problems such as clustering,
classification, subset sele... | computer science |
22,116 | Inference for Sparse Conditional Precision Matrices | stat.ML | Given $n$ i.i.d. observations of a random vector $(X,Z)$, where $X$ is a
high-dimensional vector and $Z$ is a low-dimensional index variable, we study
the problem of estimating the conditional inverse covariance matrix $\Omega(z)
= (E[(X-E[X \mid Z])(X-E[X \mid Z])^T \mid Z=z])^{-1}$ under the assumption
that the set o... | computer science |
22,117 | Exploring Sparsity in Multi-class Linear Discriminant Analysis | stat.ML | Recent studies in the literature have paid much attention to the sparsity in
linear classification tasks. One motivation of imposing sparsity assumption on
the linear discriminant direction is to rule out the noninformative features,
making hardly contribution to the classification problem. Most of those work
were focu... | computer science |
22,118 | On Semiparametric Exponential Family Graphical Models | stat.ML | We propose a new class of semiparametric exponential family graphical models
for the analysis of high dimensional mixed data. Different from the existing
mixed graphical models, we allow the nodewise conditional distributions to be
semiparametric generalized linear models with unspecified base measure
functions. Thus, ... | computer science |
22,119 | A General Framework for Robust Testing and Confidence Regions in
High-Dimensional Quantile Regression | stat.ML | We propose a robust inferential procedure for assessing uncertainties of
parameter estimation in high-dimensional linear models, where the dimension $p$
can grow exponentially fast with the sample size $n$. Our method combines the
de-biasing technique with the composite quantile function to construct an
estimator that ... | computer science |
22,120 | High Dimensional Expectation-Maximization Algorithm: Statistical
Optimization and Asymptotic Normality | stat.ML | We provide a general theory of the expectation-maximization (EM) algorithm
for inferring high dimensional latent variable models. In particular, we make
two contributions: (i) For parameter estimation, we propose a novel high
dimensional EM algorithm which naturally incorporates sparsity structure into
parameter estima... | computer science |
22,121 | A General Theory of Hypothesis Tests and Confidence Regions for Sparse
High Dimensional Models | stat.ML | We consider the problem of uncertainty assessment for low dimensional
components in high dimensional models. Specifically, we propose a decorrelated
score function to handle the impact of high dimensional nuisance parameters. We
consider both hypothesis tests and confidence regions for generic penalized
M-estimators. U... | computer science |
22,122 | Learning Parameters for Weighted Matrix Completion via Empirical
Estimation | stat.ML | Recently theoretical guarantees have been obtained for matrix completion in
the non-uniform sampling regime. In particular, if the sampling distribution
aligns with the underlying matrix's leverage scores, then with high probability
nuclear norm minimization will exactly recover the low rank matrix. In this
article, we... | computer science |
22,123 | A Taxonomy of Big Data for Optimal Predictive Machine Learning and Data
Mining | stat.ML | Big data comes in various ways, types, shapes, forms and sizes. Indeed,
almost all areas of science, technology, medicine, public health, economics,
business, linguistics and social science are bombarded by ever increasing flows
of data begging to analyzed efficiently and effectively. In this paper, we
propose a rough ... | computer science |
22,124 | A generalization error bound for sparse and low-rank multivariate Hawkes
processes | stat.ML | We consider the problem of unveiling the implicit network structure of user
interactions in a social network, based only on high-frequency timestamps. Our
inference is based on the minimization of the least-squares loss associated
with a multivariate Hawkes model, penalized by $\ell_1$ and trace norms. We
provide a fir... | computer science |
22,125 | Innovated interaction screening for high-dimensional nonlinear
classification | stat.ML | This paper is concerned with the problems of interaction screening and
nonlinear classification in a high-dimensional setting. We propose a two-step
procedure, IIS-SQDA, where in the first step an innovated interaction screening
(IIS) approach based on transforming the original $p$-dimensional feature
vector is propose... | computer science |
22,126 | Equitability of Dependence Measure | stat.ML | A measure of dependence is said to be equitable if it gives similar scores to
equally noisy relationship of different types. In practice, we do not know what
kind of functional relationship is underlying two given observations, Hence the
equitability of dependence measure is critical in analysis and by scoring
relation... | computer science |
22,127 | Survey schemes for stochastic gradient descent with applications to
M-estimation | stat.ML | In certain situations that shall be undoubtedly more and more common in the
Big Data era, the datasets available are so massive that computing statistics
over the full sample is hardly feasible, if not unfeasible. A natural approach
in this context consists in using survey schemes and substituting the "full
data" stati... | computer science |
22,128 | Combined modeling of sparse and dense noise for improvement of Relevance
Vector Machine | stat.ML | Using a Bayesian approach, we consider the problem of recovering sparse
signals under additive sparse and dense noise. Typically, sparse noise models
outliers, impulse bursts or data loss. To handle sparse noise, existing methods
simultaneously estimate the sparse signal of interest and the sparse noise of
no interest.... | computer science |
22,129 | SPRITE: A Response Model For Multiple Choice Testing | stat.ML | Item response theory (IRT) models for categorical response data are widely
used in the analysis of educational data, computerized adaptive testing, and
psychological surveys. However, most IRT models rely on both the assumption
that categories are strictly ordered and the assumption that this ordering is
known a priori... | computer science |
22,130 | Bayesian Nonparametrics in Topic Modeling: A Brief Tutorial | stat.ML | Using nonparametric methods has been increasingly explored in Bayesian
hierarchical modeling as a way to increase model flexibility. Although the
field shows a lot of promise, inference in many models, including Hierachical
Dirichlet Processes (HDP), remain prohibitively slow. One promising path
forward is to exploit t... | computer science |
22,131 | Differentially Private Bayesian Optimization | stat.ML | Bayesian optimization is a powerful tool for fine-tuning the hyper-parameters
of a wide variety of machine learning models. The success of machine learning
has led practitioners in diverse real-world settings to learn classifiers for
practical problems. As machine learning becomes commonplace, Bayesian
optimization bec... | computer science |
22,132 | Implementable confidence sets in high dimensional regression | stat.ML | We consider the setting of linear regression in high dimension. We focus on
the problem of constructing adaptive and honest confidence sets for the sparse
parameter \theta, i.e. we want to construct a confidence set for theta that
contains theta with high probability, and that is as small as possible. The l_2
diameter ... | computer science |
22,133 | BDgraph: An R Package for Bayesian Structure Learning in Graphical
Models | stat.ML | Graphical models provide powerful tools to uncover complicated patterns in
multivariate data and are commonly used in Bayesian statistics and machine
learning. In this paper, we introduce an R package BDgraph which performs
Bayesian structure learning for general undirected graphical models with either
continuous or di... | computer science |
22,134 | Minimax Optimal Sparse Signal Recovery with Poisson Statistics | stat.ML | We are motivated by problems that arise in a number of applications such as
Online Marketing and Explosives detection, where the observations are usually
modeled using Poisson statistics. We model each observation as a Poisson random
variable whose mean is a sparse linear superposition of known patterns. Unlike
many co... | computer science |
22,135 | A simpler condition for consistency of a kernel independence test | stat.ML | A statistical test of independence may be constructed using the
Hilbert-Schmidt Independence Criterion (HSIC) as a test statistic. The HSIC is
defined as the distance between the embedding of the joint distribution, and
the embedding of the product of the marginals, in a Reproducing Kernel Hilbert
Space (RKHS). It has ... | computer science |
22,136 | Prediction Error Reduction Function as a Variable Importance Score | stat.ML | This paper introduces and develops a novel variable importance score function
in the context of ensemble learning and demonstrates its appeal both
theoretically and empirically. Our proposed score function is simple and more
straightforward than its counterpart proposed in the context of random forest,
and by avoiding ... | computer science |
22,137 | Confidence intervals for AB-test | stat.ML | AB-testing is a very popular technique in web companies since it makes it
possible to accurately predict the impact of a modification with the simplicity
of a random split across users. One of the critical aspects of an AB-test is
its duration and it is important to reliably compute confidence intervals
associated with... | computer science |
22,138 | Structure Learning of Partitioned Markov Networks | stat.ML | We learn the structure of a Markov Network between two groups of random
variables from joint observations. Since modelling and learning the full MN
structure may be hard, learning the links between two groups directly may be a
preferable option. We introduce a novel concept called the \emph{partitioned
ratio} whose fac... | computer science |
22,139 | Point Localization and Density Estimation from Ordinal kNN graphs using
Synchronization | stat.ML | We consider the problem of embedding unweighted, directed k-nearest neighbor
graphs in low-dimensional Euclidean space. The k-nearest neighbors of each
vertex provides ordinal information on the distances between points, but not
the distances themselves. We use this ordinal information along with the
low-dimensionality... | computer science |
22,140 | A New Approach to Building the Interindustry Input--Output Table | stat.ML | We present a new approach to estimating the interdependence of industries in
an economy by applying data science solutions. By exploiting interfirm
buyer--seller network data, we show that the problem of estimating the
interdependence of industries is similar to the problem of uncovering the
latent block structure in n... | computer science |
22,141 | A closed-form approach to Bayesian inference in tree-structured
graphical models | stat.ML | We consider the inference of the structure of an undirected graphical model
in an exact Bayesian framework. More specifically we aim at achieving the
inference with close-form posteriors, avoiding any sampling step. This task
would be intractable without any restriction on the considered graphs, so we
limit our explora... | computer science |
22,142 | High-Dimensional Classification for Brain Decoding | stat.ML | Brain decoding involves the determination of a subject's cognitive state or
an associated stimulus from functional neuroimaging data measuring brain
activity. In this setting the cognitive state is typically characterized by an
element of a finite set, and the neuroimaging data comprise voluminous amounts
of spatiotemp... | computer science |
22,143 | Partition MCMC for inference on acyclic digraphs | stat.ML | Acyclic digraphs are the underlying representation of Bayesian networks, a
widely used class of probabilistic graphical models. Learning the underlying
graph from data is a way of gaining insights about the structural properties of
a domain. Structure learning forms one of the inference challenges of
statistical graphi... | computer science |
22,144 | Nonparametric Testing for Heterogeneous Correlation | stat.ML | In the presence of weak overall correlation, it may be useful to investigate
if the correlation is significantly and substantially more pronounced over a
subpopulation. Two different testing procedures are compared. Both are based on
the rankings of the values of two variables from a data set with a large number
n of o... | computer science |
22,145 | A local approach to estimation in discrete loglinear models | stat.ML | We consider two connected aspects of maximum likelihood estimation of the
parameter for high-dimensional discrete graphical models: the existence of the
maximum likelihood estimate (mle) and its computation.
When the data is sparse, there are many zeros in the contingency table and
the maximum likelihood estimate of ... | computer science |
22,146 | Graphical Fermat's Principle and Triangle-Free Graph Estimation | stat.ML | We consider the problem of estimating undirected triangle-free graphs of high
dimensional distributions. Triangle-free graphs form a rich graph family which
allows arbitrary loopy structures but 3-cliques. For inferential tractability,
we propose a graphical Fermat's principle to regularize the distribution
family. Suc... | computer science |
22,147 | A Prior Distribution over Directed Acyclic Graphs for Sparse Bayesian
Networks | stat.ML | The main contribution of this article is a new prior distribution over
directed acyclic graphs, which gives larger weight to sparse graphs. This
distribution is intended for structured Bayesian networks, where the structure
is given by an ordered block model. That is, the nodes of the graph are objects
which fall into ... | computer science |
22,148 | On Sparse variational methods and the Kullback-Leibler divergence
between stochastic processes | stat.ML | The variational framework for learning inducing variables (Titsias, 2009a)
has had a large impact on the Gaussian process literature. The framework may be
interpreted as minimizing a rigorously defined Kullback-Leibler divergence
between the approximating and posterior processes. To our knowledge this
connection has th... | computer science |
22,149 | Non-Gaussian Discriminative Factor Models via the Max-Margin
Rank-Likelihood | stat.ML | We consider the problem of discriminative factor analysis for data that are
in general non-Gaussian. A Bayesian model based on the ranks of the data is
proposed. We first introduce a new {\em max-margin} version of the
rank-likelihood. A discriminative factor model is then developed, integrating
the max-margin rank-lik... | computer science |
22,150 | Automatic Inference for Inverting Software Simulators via Probabilistic
Programming | stat.ML | Models of complex systems are often formalized as sequential software
simulators: computationally intensive programs that iteratively build up
probable system configurations given parameters and initial conditions. These
simulators enable modelers to capture effects that are difficult to
characterize analytically or su... | computer science |
22,151 | Bootstrap Bias Corrections for Ensemble Methods | stat.ML | This paper examines the use of a residual bootstrap for bias correction in
machine learning regression methods. Accounting for bias is an important
obstacle in recent efforts to develop statistical inference for machine
learning methods. We demonstrate empirically that the proposed bootstrap bias
correction can lead to... | computer science |
22,152 | Parallel Stochastic Gradient Markov Chain Monte Carlo for Matrix
Factorisation Models | stat.ML | For large matrix factorisation problems, we develop a distributed Markov
Chain Monte Carlo (MCMC) method based on stochastic gradient Langevin dynamics
(SGLD) that we call Parallel SGLD (PSGLD). PSGLD has very favourable scaling
properties with increasing data size and is comparable in terms of
computational requiremen... | computer science |
22,153 | Dropout as a Bayesian Approximation: Appendix | stat.ML | We show that a neural network with arbitrary depth and non-linearities, with
dropout applied before every weight layer, is mathematically equivalent to an
approximation to a well known Bayesian model. This interpretation might offer
an explanation to some of dropout's key properties, such as its robustness to
over-fitt... | computer science |
22,154 | Generalized Spectral Kernels | stat.ML | In this paper we propose a family of tractable kernels that is dense in the
family of bounded positive semi-definite functions (i.e. can approximate any
bounded kernel with arbitrary precision). We start by discussing the case of
stationary kernels, and propose a family of spectral kernels that extends
existing approac... | computer science |
22,155 | String Gaussian Process Kernels | stat.ML | We introduce a new class of nonstationary kernels, which we derive as
covariance functions of a novel family of stochastic processes we refer to as
string Gaussian processes (string GPs). We construct string GPs to allow for
multiple types of local patterns in the data, while ensuring a mild global
regularity condition... | computer science |
22,156 | Interpretable Selection and Visualization of Features and Interactions
Using Bayesian Forests | stat.ML | It is becoming increasingly important for machine learning methods to make
predictions that are interpretable as well as accurate. In many practical
applications, it is of interest which features and feature interactions are
relevant to the prediction task. We present a novel method, Selective Bayesian
Forest Classifie... | computer science |
22,157 | Convex recovery of tensors using nuclear norm penalization | stat.ML | The subdifferential of convex functions of the singular spectrum of real
matrices has been widely studied in matrix analysis, optimization and automatic
control theory. Convex analysis and optimization over spaces of tensors is now
gaining much interest due to its potential applications to signal processing,
statistics... | computer science |
22,158 | Gradient-free Hamiltonian Monte Carlo with Efficient Kernel Exponential
Families | stat.ML | We propose Kernel Hamiltonian Monte Carlo (KMC), a gradient-free adaptive
MCMC algorithm based on Hamiltonian Monte Carlo (HMC). On target densities
where classical HMC is not an option due to intractable gradients, KMC
adaptively learns the target's gradient structure by fitting an exponential
family model in a Reprod... | computer science |
22,159 | Frank-Wolfe Bayesian Quadrature: Probabilistic Integration with
Theoretical Guarantees | stat.ML | There is renewed interest in formulating integration as an inference problem,
motivated by obtaining a full distribution over numerical error that can be
propagated through subsequent computation. Current methods, such as Bayesian
Quadrature, demonstrate impressive empirical performance but lack theoretical
analysis. A... | computer science |
22,160 | Community detection in multi-relational data with restricted multi-layer
stochastic blockmodel | stat.ML | In recent years there has been an increased interest in statistical analysis
of data with multiple types of relations among a set of entities. Such
multi-relational data can be represented as multi-layer graphs where the set of
vertices represents the entities and multiple types of edges represent the
different relatio... | computer science |
22,161 | Parallelizing MCMC with Random Partition Trees | stat.ML | The modern scale of data has brought new challenges to Bayesian inference. In
particular, conventional MCMC algorithms are computationally very expensive for
large data sets. A promising approach to solve this problem is embarrassingly
parallel MCMC (EP-MCMC), which first partitions the data into multiple subsets
and r... | computer science |
22,162 | A Scale Mixture Perspective of Multiplicative Noise in Neural Networks | stat.ML | Corrupting the input and hidden layers of deep neural networks (DNNs) with
multiplicative noise, often drawn from the Bernoulli distribution (or
'dropout'), provides regularization that has significantly contributed to deep
learning's success. However, understanding how multiplicative corruptions
prevent overfitting ha... | computer science |
22,163 | Automatic Variational Inference in Stan | stat.ML | Variational inference is a scalable technique for approximate Bayesian
inference. Deriving variational inference algorithms requires tedious
model-specific calculations; this makes it difficult to automate. We propose an
automatic variational inference algorithm, automatic differentiation
variational inference (ADVI). ... | computer science |
22,164 | Probabilistic Curve Learning: Coulomb Repulsion and the Electrostatic
Gaussian Process | stat.ML | Learning of low dimensional structure in multidimensional data is a canonical
problem in machine learning. One common approach is to suppose that the
observed data are close to a lower-dimensional smooth manifold. There are a
rich variety of manifold learning methods available, which allow mapping of
data points to the... | computer science |
22,165 | Generalized Additive Model Selection | stat.ML | We introduce GAMSEL (Generalized Additive Model Selection), a penalized
likelihood approach for fitting sparse generalized additive models in high
dimension. Our method interpolates between null, linear and additive models by
allowing the effect of each variable to be estimated as being either zero,
linear, or a low-co... | computer science |
22,166 | Robust Structured Low-Rank Approximation on the Grassmannian | stat.ML | Over the past years Robust PCA has been established as a standard tool for
reliable low-rank approximation of matrices in the presence of outliers.
Recently, the Robust PCA approach via nuclear norm minimization has been
extended to matrices with linear structures which appear in applications such
as system identificat... | computer science |
22,167 | MCMC for Variationally Sparse Gaussian Processes | stat.ML | Gaussian process (GP) models form a core part of probabilistic machine
learning. Considerable research effort has been made into attacking three
issues with GP models: how to compute efficiently when the number of data is
large; how to approximate the posterior when the likelihood is not Gaussian and
how to estimate co... | computer science |
22,168 | Linear Response Methods for Accurate Covariance Estimates from Mean
Field Variational Bayes | stat.ML | Mean field variational Bayes (MFVB) is a popular posterior approximation
method due to its fast runtime on large-scale data sets. However, it is well
known that a major failing of MFVB is that it underestimates the uncertainty of
model variables (sometimes severely) and provides no information about model
variable cova... | computer science |
22,169 | Exact ICL maximization in a non-stationary time extension of the latent
block model for dynamic networks | stat.ML | The latent block model (LBM) is a flexible probabilistic tool to describe
interactions between node sets in bipartite networks, but it does not account
for interactions of time varying intensity between nodes in unknown classes. In
this paper we propose a non stationary temporal extension of the LBM that
clusters simul... | computer science |
22,170 | A Spectral Algorithm with Additive Clustering for the Recovery of
Overlapping Communities in Networks | stat.ML | This paper presents a novel spectral algorithm with additive clustering
designed to identify overlapping communities in networks. The algorithm is
based on geometric properties of the spectrum of the expected adjacency matrix
in a random graph model that we call stochastic blockmodel with overlap (SBMO).
An adaptive ve... | computer science |
22,171 | Online Matrix Factorization via Broyden Updates | stat.ML | In this paper, we propose an online algorithm to compute matrix
factorizations. Proposed algorithm updates the dictionary matrix and associated
coefficients using a single observation at each time. The algorithm performs
low-rank updates to dictionary matrix. We derive the algorithm by defining a
simple objective funct... | computer science |
22,172 | Fast Two-Sample Testing with Analytic Representations of Probability
Measures | stat.ML | We propose a class of nonparametric two-sample tests with a cost linear in
the sample size. Two tests are given, both based on an ensemble of distances
between analytic functions representing each of the distributions. The first
test uses smoothed empirical characteristic functions to represent the
distributions, the s... | computer science |
22,173 | Simultaneous Estimation of Non-Gaussian Components and their Correlation
Structure | stat.ML | The statistical dependencies which independent component analysis (ICA)
cannot remove often provide rich information beyond the linear independent
components. It would thus be very useful to estimate the dependency structure
from data. While such models have been proposed, they usually concentrated on
higher-order corr... | computer science |
22,174 | Dependent Multinomial Models Made Easy: Stick Breaking with the
Pólya-Gamma Augmentation | stat.ML | Many practical modeling problems involve discrete data that are best
represented as draws from multinomial or categorical distributions. For
example, nucleotides in a DNA sequence, children's names in a given state and
year, and text documents are all commonly modeled with multinomial
distributions. In all of these cas... | computer science |
22,175 | Doubly Decomposing Nonparametric Tensor Regression | stat.ML | Nonparametric extension of tensor regression is proposed. Nonlinearity in a
high-dimensional tensor space is broken into simple local functions by
incorporating low-rank tensor decomposition. Compared to naive nonparametric
approaches, our formulation considerably improves the convergence rate of
estimation while maint... | computer science |
22,176 | Clustering categorical data via ensembling dissimilarity matrices | stat.ML | We present a technique for clustering categorical data by generating many
dissimilarity matrices and averaging over them. We begin by demonstrating our
technique on low dimensional categorical data and comparing it to several other
techniques that have been proposed. Then we give conditions under which our
method shoul... | computer science |
22,177 | Principal Geodesic Analysis for Probability Measures under the Optimal
Transport Metric | stat.ML | Given a family of probability measures in P(X), the space of probability
measures on a Hilbert space X, our goal in this paper is to highlight one ore
more curves in P(X) that summarize efficiently that family. We propose to study
this problem under the optimal transport (Wasserstein) geometry, using curves
that are re... | computer science |
22,178 | Factorized Asymptotic Bayesian Inference for Factorial Hidden Markov
Models | stat.ML | Factorial hidden Markov models (FHMMs) are powerful tools of modeling
sequential data. Learning FHMMs yields a challenging simultaneous model
selection issue, i.e., selecting the number of multiple Markov chains and the
dimensionality of each chain. Our main contribution is to address this model
selection issue by exte... | computer science |
22,179 | An Efficient Post-Selection Inference on High-Order Interaction Models | stat.ML | Finding statistically significant high-order interaction features in
predictive modeling is important but challenging task. The difficulty lies in
the fact that, for a recent applications with high-dimensional covariates, the
number of possible high-order interaction features would be extremely large.
Identifying stati... | computer science |
22,180 | Safe Feature Pruning for Sparse High-Order Interaction Models | stat.ML | Taking into account high-order interactions among covariates is valuable in
many practical regression problems. This is, however, computationally
challenging task because the number of high-order interaction features to be
considered would be extremely large unless the number of covariates is
sufficiently small. In thi... | computer science |
22,181 | Bayesian Nonparametric Kernel-Learning | stat.ML | Kernel methods are ubiquitous tools in machine learning. However, there is
often little reason for the common practice of selecting a kernel a priori.
Even if a universal approximating kernel is selected, the quality of the finite
sample estimator may be greatly affected by the choice of kernel. Furthermore,
when direc... | computer science |
22,182 | On the Equivalence of Factorized Information Criterion Regularization
and the Chinese Restaurant Process Prior | stat.ML | Factorized Information Criterion (FIC) is a recently developed information
criterion, based on which a novel model selection methodology, namely
Factorized Asymptotic Bayesian (FAB) Inference, has been developed and
successfully applied to various hierarchical Bayesian models. The Dirichlet
Process (DP) prior, and one ... | computer science |
22,183 | Gaussian Process for Noisy Inputs with Ordering Constraints | stat.ML | We study the Gaussian Process regression model in the context of training
data with noise in both input and output. The presence of two sources of noise
makes the task of learning accurate predictive models extremely challenging.
However, in some instances additional constraints may be available that can
reduce the unc... | computer science |
22,184 | Identification of stable models via nonparametric prediction error
methods | stat.ML | A new Bayesian approach to linear system identification has been proposed in
a series of recent papers. The main idea is to frame linear system
identification as predictor estimation in an infinite dimensional space, with
the aid of regularization/Bayesian techniques. This approach guarantees the
identification of stab... | computer science |
22,185 | Classical vs. Bayesian methods for linear system identification: point
estimators and confidence sets | stat.ML | This paper compares classical parametric methods with recently developed
Bayesian methods for system identification. A Full Bayes solution is considered
together with one of the standard approximations based on the Empirical Bayes
paradigm. Results regarding point estimators for the impulse response as well
as for conf... | computer science |
22,186 | Anomaly Detection and Removal Using Non-Stationary Gaussian Processes | stat.ML | This paper proposes a novel Gaussian process approach to fault removal in
time-series data. Fault removal does not delete the faulty signal data but,
instead, massages the fault from the data. We assume that only one fault occurs
at any one time and model the signal by two separate non-parametric Gaussian
process model... | computer science |
22,187 | Remarks on kernel Bayes' rule | stat.ML | Kernel Bayes' rule has been proposed as a nonparametric kernel-based method
to realize Bayesian inference in reproducing kernel Hilbert spaces. However, we
demonstrate both theoretically and experimentally that the prediction result by
kernel Bayes' rule is in some cases unnatural. We consider that this phenomenon
is i... | computer science |
22,188 | Semiblind Hyperspectral Unmixing in the Presence of Spectral Library
Mismatches | stat.ML | The dictionary-aided sparse regression (SR) approach has recently emerged as
a promising alternative to hyperspectral unmixing (HU) in remote sensing. By
using an available spectral library as a dictionary, the SR approach identifies
the underlying materials in a given hyperspectral image by selecting a small
subset of... | computer science |
22,189 | Completely random measures for modelling block-structured networks | stat.ML | Many statistical methods for network data parameterize the edge-probability
by attributing latent traits to the vertices such as block structure and assume
exchangeability in the sense of the Aldous-Hoover representation theorem.
Empirical studies of networks indicate that many real-world networks have a
power-law dist... | computer science |
22,190 | On the use of Harrell's C for clinical risk prediction via random
survival forests | stat.ML | Random survival forests (RSF) are a powerful method for risk prediction of
right-censored outcomes in biomedical research. RSF use the log-rank split
criterion to form an ensemble of survival trees. The most common approach to
evaluate the prediction accuracy of a RSF model is Harrell's concordance index
for survival d... | computer science |
22,191 | Dependent Indian Buffet Process-based Sparse Nonparametric Nonnegative
Matrix Factorization | stat.ML | Nonnegative Matrix Factorization (NMF) aims to factorize a matrix into two
optimized nonnegative matrices appropriate for the intended applications. The
method has been widely used for unsupervised learning tasks, including
recommender systems (rating matrix of users by items) and document clustering
(weighting matrix ... | computer science |
22,192 | Scalable Bayesian Inference for Excitatory Point Process Networks | stat.ML | Networks capture our intuition about relationships in the world. They
describe the friendships between Facebook users, interactions in financial
markets, and synapses connecting neurons in the brain. These networks are
richly structured with cliques of friends, sectors of stocks, and a smorgasbord
of cell types that go... | computer science |
22,193 | Scatter Matrix Concordance: A Diagnostic for Regressions on Subsets of
Data | stat.ML | Linear regression models depend directly on the design matrix and its
properties. Techniques that efficiently estimate model coefficients by
partitioning rows of the design matrix are increasingly popular for large-scale
problems because they fit well with modern parallel computing architectures. We
propose a simple me... | computer science |
22,194 | Joint Tensor Factorization and Outlying Slab Suppression with
Applications | stat.ML | We consider factoring low-rank tensors in the presence of outlying slabs.
This problem is important in practice, because data collected in many
real-world applications, such as speech, fluorescence, and some social network
data, fit this paradigm. Prior work tackles this problem by iteratively
selecting a fixed number ... | computer science |
22,195 | On the Convergence of Stochastic Variational Inference in Bayesian
Networks | stat.ML | We highlight a pitfall when applying stochastic variational inference to
general Bayesian networks. For global random variables approximated by an
exponential family distribution, natural gradient steps, commonly starting from
a unit length step size, are averaged to convergence. This useful insight into
the scaling of... | computer science |
22,196 | Scalable Gaussian Process Classification via Expectation Propagation | stat.ML | Variational methods have been recently considered for scaling the training
process of Gaussian process classifiers to large datasets. As an alternative,
we describe here how to train these classifiers efficiently using expectation
propagation. The proposed method allows for handling datasets with millions of
data insta... | computer science |
22,197 | Incremental Variational Inference for Latent Dirichlet Allocation | stat.ML | We introduce incremental variational inference and apply it to latent
Dirichlet allocation (LDA). Incremental variational inference is inspired by
incremental EM and provides an alternative to stochastic variational inference.
Incremental LDA can process massive document collections, does not require to
set a learning ... | computer science |
22,198 | Fast Approximate Bayesian Computation for Estimating Parameters in
Differential Equations | stat.ML | Approximate Bayesian computation (ABC) using a sequential Monte Carlo method
provides a comprehensive platform for parameter estimation, model selection and
sensitivity analysis in differential equations. However, this method, like
other Monte Carlo methods, incurs a significant computational cost as it
requires explic... | computer science |
22,199 | Optimal Estimation of Low Rank Density Matrices | stat.ML | The density matrices are positively semi-definite Hermitian matrices of unit
trace that describe the state of a quantum system. The goal of the paper is to
develop minimax lower bounds on error rates of estimation of low rank density
matrices in trace regression models used in quantum state tomography (in
particular, i... | computer science |
22,200 | The Population Posterior and Bayesian Inference on Streams | stat.ML | Many modern data analysis problems involve inferences from streaming data.
However, streaming data is not easily amenable to the standard probabilistic
modeling approaches, which assume that we condition on finite data. We develop
population variational Bayes, a new approach for using Bayesian modeling to
analyze strea... | computer science |
22,201 | Causal Transfer in Machine Learning | stat.ML | Methods of transfer learning try to combine knowledge from several related
tasks (or domains) to improve performance on a test task. Inspired by causal
methodology, we relax the usual covariate shift assumption and assume that it
holds true for a subset of predictor variables: the conditional distribution of
the target... | computer science |
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