Abstract/Details

Identification and universal data compression of hidden Markov processes

Liu, Chuang-Chun. 
 University of Maryland, College Park ProQuest Dissertations Publishing,  1991. 9133119.

Abstract (summary)

Statistical modeling entails the inference of the behavior of a physical phenomenon or a mechanism from the data it generates. A model or a class of models must serve as a means of capturing succinctly and completely the properties of the observed data. An approach to modeling data is via a shortest universal data-compression code which describes it exactly and invertibly. The length of such a code for a given model is often closely related to the number of parameters needed to specify the models of a given class. We address the problems of "order" (in terms of the number of parameters) estimation and universal data-compression for independent and identically distributed processes, Markov processes and hidden Markov processes.

In estimating the "order" of a process, one technique often used is Rissanen's minimum description length (MDL) principle, which typically involves penalized maximum likelihood functions. In certain cases, the MDL of a given family, though cumbersome to compute, can be approximated by the length of a universal code corresponding to a mixture distribution associated with the family. For a Markov family and a hidden Markov family, the mixture distribution can be computed sequentially as more data samples are received. We show that the estimate of the order defined in terms of the index of the family which achieves the minimum length universal code is strongly consistent. Furthermore, the convergence rates of the error probabilities of the estimates are fast enough to allow sequential coding.

The problem of estimating the order of a Markov process, possibly real-valued, is also approached from the point of view of empirical conditional probabilities, and consistent estimate is obtained.

Indexing (details)


Subject
Electrical engineering
Classification
0544: Electrical engineering
Identifier / keyword
Applied sciences; Markov processes; data compression
Title
Identification and universal data compression of hidden Markov processes
Author
Liu, Chuang-Chun
Number of pages
76
Degree date
1991
School code
0117
Source
DAI-B 52/06, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
979-8-207-77549-4
Advisor
Narayan, Prakash
University/institution
University of Maryland, College Park
University location
United States -- Maryland
Degree
Ph.D.
Source type
Dissertation or Thesis
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
9133119
ProQuest document ID
303967206
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
https://www.proquest.com/docview/303967206