54 research outputs found
Graph-based Estimation of Information Divergence Functions
abstract: Information divergence functions, such as the Kullback-Leibler divergence or the Hellinger distance, play a critical role in statistical signal processing and information theory; however estimating them can be challenge. Most often, parametric assumptions are made about the two distributions to estimate the divergence of interest. In cases where no parametric model fits the data, non-parametric density estimation is used. In statistical signal processing applications, Gaussianity is usually assumed since closed-form expressions for common divergence measures have been derived for this family of distributions. Parametric assumptions are preferred when it is known that the data follows the model, however this is rarely the case in real-word scenarios. Non-parametric density estimators are characterized by a very large number of parameters that have to be tuned with costly cross-validation. In this dissertation we focus on a specific family of non-parametric estimators, called direct estimators, that bypass density estimation completely and directly estimate the quantity of interest from the data. We introduce a new divergence measure, the -divergence, that can be estimated directly from samples without parametric assumptions on the distribution. We show that the -divergence bounds the binary, cross-domain, and multi-class Bayes error rates and, in certain cases, provides provably tighter bounds than the Hellinger divergence. In addition, we also propose a new methodology that allows the experimenter to construct direct estimators for existing divergence measures or to construct new divergence measures with custom properties that are tailored to the application. To examine the practical efficacy of these new methods, we evaluate them in a statistical learning framework on a series of real-world data science problems involving speech-based monitoring of neuro-motor disorders.Dissertation/ThesisDoctoral Dissertation Electrical Engineering 201
A generalized risk approach to path inference based on hidden Markov models
Motivated by the unceasing interest in hidden Markov models (HMMs), this
paper re-examines hidden path inference in these models, using primarily a
risk-based framework. While the most common maximum a posteriori (MAP), or
Viterbi, path estimator and the minimum error, or Posterior Decoder (PD), have
long been around, other path estimators, or decoders, have been either only
hinted at or applied more recently and in dedicated applications generally
unfamiliar to the statistical learning community. Over a decade ago, however, a
family of algorithmically defined decoders aiming to hybridize the two standard
ones was proposed (Brushe et al., 1998). The present paper gives a careful
analysis of this hybridization approach, identifies several problems and issues
with it and other previously proposed approaches, and proposes practical
resolutions of those. Furthermore, simple modifications of the classical
criteria for hidden path recognition are shown to lead to a new class of
decoders. Dynamic programming algorithms to compute these decoders in the usual
forward-backward manner are presented. A particularly interesting subclass of
such estimators can be also viewed as hybrids of the MAP and PD estimators.
Similar to previously proposed MAP-PD hybrids, the new class is parameterized
by a small number of tunable parameters. Unlike their algorithmic predecessors,
the new risk-based decoders are more clearly interpretable, and, most
importantly, work "out of the box" in practice, which is demonstrated on some
real bioinformatics tasks and data. Some further generalizations and
applications are discussed in conclusion.Comment: Section 5: corrected denominators of the scaled beta variables (pp.
27-30), => corrections in claims 1, 3, Prop. 12, bottom of Table 1. Decoder
(49), Corol. 14 are generalized to handle 0 probabilities. Notation is more
closely aligned with (Bishop, 2006). Details are inserted in eqn-s (43); the
positivity assumption in Prop. 11 is explicit. Fixed typing errors in
equation (41), Example
Sparse Modeling for Image and Vision Processing
In recent years, a large amount of multi-disciplinary research has been
conducted on sparse models and their applications. In statistics and machine
learning, the sparsity principle is used to perform model selection---that is,
automatically selecting a simple model among a large collection of them. In
signal processing, sparse coding consists of representing data with linear
combinations of a few dictionary elements. Subsequently, the corresponding
tools have been widely adopted by several scientific communities such as
neuroscience, bioinformatics, or computer vision. The goal of this monograph is
to offer a self-contained view of sparse modeling for visual recognition and
image processing. More specifically, we focus on applications where the
dictionary is learned and adapted to data, yielding a compact representation
that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics
and Visio
Advances in Data Mining Knowledge Discovery and Applications
Advances in Data Mining Knowledge Discovery and Applications aims to help data miners, researchers, scholars, and PhD students who wish to apply data mining techniques. The primary contribution of this book is highlighting frontier fields and implementations of the knowledge discovery and data mining. It seems to be same things are repeated again. But in general, same approach and techniques may help us in different fields and expertise areas. This book presents knowledge discovery and data mining applications in two different sections. As known that, data mining covers areas of statistics, machine learning, data management and databases, pattern recognition, artificial intelligence, and other areas. In this book, most of the areas are covered with different data mining applications. The eighteen chapters have been classified in two parts: Knowledge Discovery and Data Mining Applications
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