Files in this item



application/pdf3362927.pdf (2MB)Restricted to U of Illinois
(no description provided)PDF


Title:Exact Solution of Bayes and Minimax Change-Detection Problems
Author(s):Isom, Joshua D.
Doctoral Committee Chair(s):Braatz, Richard D.
Department / Program:Chemical and Biomolecular Engineering
Discipline:Chemical Engineering
Degree Granting Institution:University of Illinois at Urbana-Champaign
Engineering, General
Abstract:The challenge of detecting a change in the distribution of data is a sequential decision problem that is relevant to many engineering solutions, including quality control and machine and process monitoring. This dissertation develops techniques for exact solution of change-detection problems with discrete time and discrete observations.
Change-detection problems are classified as Bayes or minimax based on the availability of information on the change-time distribution. A Bayes optimal solution uses prior information about the distribution of the change time to minimize the expected cost, whereas a minimax optimal solution minimizes the cost under the worst-case change-time distribution. Both types of problems are addressed.
The most important result of the dissertation is the development of a polynomial-time algorithm for the solution of important classes of Markov Bayes change-detection problems. Existing techniques for epsilon-exact solution of partially observable Markov decision processes have complexity exponential in the number of observation symbols. A new algorithm, called constellation induction, exploits the concavity and Lipschitz continuity of the value function, and has complexity polynomial in the number of observation symbols. It is shown that change-detection problems with a geometric change-time distribution and identically- and independently-distributed observations before and after the change are solvable in polynomial time. Also, change-detection problems on hidden Markov models with a fixed number of recurrent states are solvable in polynomial time. A detailed implementation and analysis of the constellation-induction algorithm are provided.
Exact solution methods are also established for several types of minimax change-detection problems. Finite-horizon problems with arbitrary observation distributions are modeled as extensive-form games and solved using linear programs. Infinite-horizon problems with linear penalty for detection delay and identically- and independently-distributed observations can be solved in polynomial time via epsilon-optimal parameterization of a cumulative-sum procedure.
Finally, the properties of policies for change-detection problems are described and analyzed. Simple classes of formal languages are shown to be sufficient for epsilon-exact solution of change-detection problems, and methods for finding minimally sized policy representations are described.
Issue Date:2009
Description:240 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2009.
Other Identifier(s):(UMI)AAI3362927
Date Available in IDEALS:2014-12-17
Date Deposited:2009

This item appears in the following Collection(s)

Item Statistics