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272
Survey over image thresholding techniques and quatitative performance evaluation
 Journal of Electronic Imaging
, 2004
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Deterministic Annealing for Clustering, Compression, Classification, Regression, and Related Optimization Problems
 Proceedings of the IEEE
, 1998
"... this paper. Let us place it within the neural network perspective, and particularly that of learning. The area of neural networks has greatly benefited from its unique position at the crossroads of several diverse scientific and engineering disciplines including statistics and probability theory, ph ..."
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Cited by 318 (20 self)
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this paper. Let us place it within the neural network perspective, and particularly that of learning. The area of neural networks has greatly benefited from its unique position at the crossroads of several diverse scientific and engineering disciplines including statistics and probability theory, physics, biology, control and signal processing, information theory, complexity theory, and psychology (see [45]). Neural networks have provided a fertile soil for the infusion (and occasionally confusion) of ideas, as well as a meeting ground for comparing viewpoints, sharing tools, and renovating approaches. It is within the illdefined boundaries of the field of neural networks that researchers in traditionally distant fields have come to the realization that they have been attacking fundamentally similar optimization problems.
Hidden Markov processes
 IEEE Trans. Inform. Theory
, 2002
"... Abstract—An overview of statistical and informationtheoretic aspects of hidden Markov processes (HMPs) is presented. An HMP is a discretetime finitestate homogeneous Markov chain observed through a discretetime memoryless invariant channel. In recent years, the work of Baum and Petrie on finite ..."
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Cited by 258 (5 self)
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Abstract—An overview of statistical and informationtheoretic aspects of hidden Markov processes (HMPs) is presented. An HMP is a discretetime finitestate homogeneous Markov chain observed through a discretetime memoryless invariant channel. In recent years, the work of Baum and Petrie on finitestate finitealphabet HMPs was expanded to HMPs with finite as well as continuous state spaces and a general alphabet. In particular, statistical properties and ergodic theorems for relative entropy densities of HMPs were developed. Consistency and asymptotic normality of the maximumlikelihood (ML) parameter estimator were proved under some mild conditions. Similar results were established for switching autoregressive processes. These processes generalize HMPs. New algorithms were developed for estimating the state, parameter, and order of an HMP, for universal coding and classification of HMPs, and for universal decoding of hidden Markov channels. These and other related topics are reviewed in this paper. Index Terms—Baum–Petrie algorithm, entropy ergodic theorems, finitestate channels, hidden Markov models, identifiability, Kalman filter, maximumlikelihood (ML) estimation, order estimation, recursive parameter estimation, switching autoregressive processes, Ziv inequality. I.
Maximum entropy modeling of short sequence motifs with applications to RNA splicing signals
 J. Comput. Biol
, 2004
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A Generalized Maximum Entropy Approach to Bregman Coclustering and Matrix Approximation
 In KDD
, 2004
"... Coclustering is a powerful data mining technique with varied applications such as text clustering, microarray analysis and recommender systems. Recently, an informationtheoretic coclustering approach applicable to empirical joint probability distributions was proposed. In many situations, coclust ..."
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Cited by 133 (29 self)
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Coclustering is a powerful data mining technique with varied applications such as text clustering, microarray analysis and recommender systems. Recently, an informationtheoretic coclustering approach applicable to empirical joint probability distributions was proposed. In many situations, coclustering of more general matrices is desired. In this paper, we present a substantially generalized coclustering framework wherein any Bregman divergence can be used in the objective function, and various conditional expectation based constraints can be considered based on the statistics that need to be preserved. Analysis of the coclustering problem leads to the minimum Bregman information principle, which generalizes the maximum entropy principle, and yields an elegant meta algorithm that is guaranteed to achieve local optimality. Our methodology yields new algorithms and also encompasses several previously known clustering and coclustering algorithms based on alternate minimization.
Comparing Dynamic Equilibrium Models to Data: A Bayesian Approach
, 2002
"... This paper studies the properties of the Bayesian approach to estimation and comparison of dynamic equilibrium economies. Both tasks can be performed even if the models are nonnested, misspecified, and nonlinear. First, we show that Bayesian methods have a classical interpretation: asymptotically ..."
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Cited by 91 (13 self)
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This paper studies the properties of the Bayesian approach to estimation and comparison of dynamic equilibrium economies. Both tasks can be performed even if the models are nonnested, misspecified, and nonlinear. First, we show that Bayesian methods have a classical interpretation: asymptotically, the parameter point estimates converge to their pseudotrue values, and the best model under the KullbackLeibler distance will have the highest posterior probability. Second, we illustrate the strong small sample behavior of the approach using a wellknown application: the U.S. cattle cycle. Bayesian estimates outperform maximum likelihood results, and the proposed model is easily compared with a set of BVARs.
Updating Probabilities
, 2002
"... As examples such as the Monty Hall puzzle show, applying conditioning to update a probability distribution on a "naive space", which does not take into account the protocol used, can often lead to counterintuitive results. Here we examine why. A criterion known as CAR ("coarsening a ..."
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Cited by 69 (4 self)
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As examples such as the Monty Hall puzzle show, applying conditioning to update a probability distribution on a "naive space", which does not take into account the protocol used, can often lead to counterintuitive results. Here we examine why. A criterion known as CAR ("coarsening at random") in the statistical literature characterizes when "naive" conditioning in a naive space works. We show that the CAR condition holds rather infrequently, and we provide a procedural characterization of it, by giving a randomized algorithm that generates all and only distributions for which CAR holds. This substantially extends previous characterizations of CAR. We also consider more generalized notions of update such as Jeffrey conditioning and minimizing relative entropy (MRE). We give a generalization of the CAR condition that characterizes when Jeffrey conditioning leads to appropriate answers, and show that there exist some very simple settings in which MRE essentially never gives the right results. This generalizes and interconnects previous results obtained in the literature on CAR and MRE.
From Laplace To Supernova Sn 1987a: Bayesian Inference In Astrophysics
, 1990
"... . The Bayesian approach to probability theory is presented as an alternative to the currently used longrun relative frequency approach, which does not offer clear, compelling criteria for the design of statistical methods. Bayesian probability theory offers unique and demonstrably optimal solutions ..."
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Cited by 68 (2 self)
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. The Bayesian approach to probability theory is presented as an alternative to the currently used longrun relative frequency approach, which does not offer clear, compelling criteria for the design of statistical methods. Bayesian probability theory offers unique and demonstrably optimal solutions to wellposed statistical problems, and is historically the original approach to statistics. The reasons for earlier rejection of Bayesian methods are discussed, and it is noted that the work of Cox, Jaynes, and others answers earlier objections, giving Bayesian inference a firm logical and mathematical foundation as the correct mathematical language for quantifying uncertainty. The Bayesian approaches to parameter estimation and model comparison are outlined and illustrated by application to a simple problem based on the gaussian distribution. As further illustrations of the Bayesian paradigm, Bayesian solutions to two interesting astrophysical problems are outlined: the measurement of wea...