201,314 research outputs found
Data selection in binary hypothesis testing
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, February 2004.Includes bibliographical references (p. 119-123).This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Traditionally, statistical signal processing algorithms are developed from probabilistic models for data. The design of the algorithms and their ultimate performance depend upon these assumed models. In certain situations, collecting or processing all available measurements may be inefficient or prohibitively costly. A potential technique to cope with such situations is data selection, where a subset of the measurements that can be collected and processed in a cost-effective manner is used as input to the signal processing algorithm. Careful evaluation of the selection procedure is important, since the probabilistic description of distinct data subsets can vary significantly. An algorithm designed for the probabilistic description of a poorly chosen data subset can lose much of the potential performance available to a well-chosen subset. This thesis considers algorithms for data selection combined with binary hypothesis testing. We develop models for data selection in several cases, considering both random and deterministic approaches. Our considerations are divided into two classes depending upon the amount of information available about the competing hypotheses. In the first class, the target signal is precisely known, and data selection is done deterministically. In the second class, the target signal belongs to a large class of random signals, selection is performed randomly, and semi-parametric detectors are developed.by Charles K. Sestok, IV.Ph.D
Toward Optimal Feature Selection in Naive Bayes for Text Categorization
Automated feature selection is important for text categorization to reduce
the feature size and to speed up the learning process of classifiers. In this
paper, we present a novel and efficient feature selection framework based on
the Information Theory, which aims to rank the features with their
discriminative capacity for classification. We first revisit two information
measures: Kullback-Leibler divergence and Jeffreys divergence for binary
hypothesis testing, and analyze their asymptotic properties relating to type I
and type II errors of a Bayesian classifier. We then introduce a new divergence
measure, called Jeffreys-Multi-Hypothesis (JMH) divergence, to measure
multi-distribution divergence for multi-class classification. Based on the
JMH-divergence, we develop two efficient feature selection methods, termed
maximum discrimination () and methods, for text categorization.
The promising results of extensive experiments demonstrate the effectiveness of
the proposed approaches.Comment: This paper has been submitted to the IEEE Trans. Knowledge and Data
Engineering. 14 pages, 5 figure
Maximally selected chi-square statistics and binary splits of nominal variables
We address the problem of maximally selected chi-square statistics in the case of a binary Y variable and a nominal X variable with several categories. The distribution of the maximally selected chi-square statistic has already been derived when the best cutpoint is chosen from a continuous or an ordinal X, but not when the best split is chosen from a nominal X. In this paper, we derive the exact distribution of the maximally selected chi-square statistic in this case using a combinatorial approach. Applications of the derived distribution to variable selection and hypothesis testing are discussed based on simulations. As an illustration, our method is applied to a pregnancy and birth data set
Active Classification: Theory and Application to Underwater Inspection
We discuss the problem in which an autonomous vehicle must classify an object
based on multiple views. We focus on the active classification setting, where
the vehicle controls which views to select to best perform the classification.
The problem is formulated as an extension to Bayesian active learning, and we
show connections to recent theoretical guarantees in this area. We formally
analyze the benefit of acting adaptively as new information becomes available.
The analysis leads to a probabilistic algorithm for determining the best views
to observe based on information theoretic costs. We validate our approach in
two ways, both related to underwater inspection: 3D polyhedra recognition in
synthetic depth maps and ship hull inspection with imaging sonar. These tasks
encompass both the planning and recognition aspects of the active
classification problem. The results demonstrate that actively planning for
informative views can reduce the number of necessary views by up to 80% when
compared to passive methods.Comment: 16 page
Random-set methods identify distinct aspects of the enrichment signal in gene-set analysis
A prespecified set of genes may be enriched, to varying degrees, for genes
that have altered expression levels relative to two or more states of a cell.
Knowing the enrichment of gene sets defined by functional categories, such as
gene ontology (GO) annotations, is valuable for analyzing the biological
signals in microarray expression data. A common approach to measuring
enrichment is by cross-classifying genes according to membership in a
functional category and membership on a selected list of significantly altered
genes. A small Fisher's exact test -value, for example, in this
table is indicative of enrichment. Other category analysis methods retain the
quantitative gene-level scores and measure significance by referring a
category-level statistic to a permutation distribution associated with the
original differential expression problem. We describe a class of random-set
scoring methods that measure distinct components of the enrichment signal. The
class includes Fisher's test based on selected genes and also tests that
average gene-level evidence across the category. Averaging and selection
methods are compared empirically using Affymetrix data on expression in
nasopharyngeal cancer tissue, and theoretically using a location model of
differential expression. We find that each method has a domain of superiority
in the state space of enrichment problems, and that both methods have benefits
in practice. Our analysis also addresses two problems related to
multiple-category inference, namely, that equally enriched categories are not
detected with equal probability if they are of different sizes, and also that
there is dependence among category statistics owing to shared genes. Random-set
enrichment calculations do not require Monte Carlo for implementation. They are
made available in the R package allez.Comment: Published at http://dx.doi.org/10.1214/07-AOAS104 in the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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