Journal ArticleDOI
Parameter estimation of dependence tree models using the EM algorithm
TLDR
The authors address the problem of maximum likelihood estimation of dependence tree models with missing observations, using the expectation-maximization algorithm, which involves computing observation probabilities with an iterative "upward-downward" algorithm.Abstract:
A dependence tree is a model for the joint probability distribution of an n-dimensional random vector, which requires a relatively small number of free parameters by making Markov-like assumptions on the tree. The authors address the problem of maximum likelihood estimation of dependence tree models with missing observations, using the expectation-maximization algorithm. The solution involves computing observation probabilities with an iterative "upward-downward" algorithm, which is similar to an algorithm proposed for belief propagation in causal trees, a special case of Bayesian networks. >read more
Citations
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Journal ArticleDOI
Wavelet-based statistical signal processing using hidden Markov models
TL;DR: A new framework for statistical signal processing based on wavelet-domain hidden Markov models (HMMs) that concisely models the statistical dependencies and non-Gaussian statistics encountered in real-world signals is developed.
Journal ArticleDOI
Bayesian tree-structured image modeling using wavelet-domain hidden Markov models
TL;DR: This work greatly simplify the HMT model by exploiting the inherent self-similarity of real-world images, and introduces a Bayesian universal HMT (uHMT) that fixes these nine parameters.
Journal ArticleDOI
Multiresolution Markov models for signal and image processing
TL;DR: This presentation reviews a significant component of the rich field of statistical multiresolution (MR) modeling and processing, and shows how a variety of methods and models relate to this framework including models for self-similar and 1/f processes.
Directional multiresolution image representations
TL;DR: This thesis focuses on the development of new "true" two-dimensional representations for images using a discrete framework that can lead to algorithmic implementations and a new family of block directional and orthonormal transforms based on the ridgelet idea.
Journal ArticleDOI
Fast approximation of Kullback-Leibler distance for dependence trees and hidden Markov models
TL;DR: A fast algorithm to approximate the Kullback-Leibler distance (KLD) between two dependence tree models is presented, which offers a saving of hundreds of times in computational complexity compared to the commonly used Monte Carlo method.
References
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Journal ArticleDOI
A tutorial on hidden Markov models and selected applications in speech recognition
TL;DR: In this paper, the authors provide an overview of the basic theory of hidden Markov models (HMMs) as originated by L.E. Baum and T. Petrie (1966) and give practical details on methods of implementation of the theory along with a description of selected applications of HMMs to distinct problems in speech recognition.
Book
Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference
TL;DR: Probabilistic Reasoning in Intelligent Systems as mentioned in this paper is a complete and accessible account of the theoretical foundations and computational methods that underlie plausible reasoning under uncertainty, and provides a coherent explication of probability as a language for reasoning with partial belief.
Journal ArticleDOI
Approximating discrete probability distributions with dependence trees
TL;DR: It is shown that the procedure derived in this paper yields an approximation of a minimum difference in information when applied to empirical observations from an unknown distribution of tree dependence, and the procedure is the maximum-likelihood estimate of the distribution.
Journal ArticleDOI
Applications of stochastic context-free grammars using the Inside-Outside algorithm
K. Lari,Steve Young +1 more
TL;DR: Two applications in speech recognition of the use of stochastic context-free grammars trained automatically via the Inside-Outside Algorithm, used to model VQ encoded speech for isolated word recognition and compared directly to HMMs used for the same task are described.