Yuan, Changhe
(2006)
Importance Sampling for Bayesian Networks: Principles, Algorithms, and Performance.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
Bayesian networks (BNs) offer a compact, intuitive, and efficient graphical representation of uncertain relationships among the variables in a domain and have proven their value in many disciplines over the last two decades. However, two challenges become increasingly critical in practical applications of Bayesian networks. First, real models are reaching the size of hundreds or even thousands of nodes. Second, some decision problems are more naturally represented by hybrid models which contain mixtures ofdiscrete and continuous variables and may represent linear or nonlinear equations and arbitrary probability distributions. Both challenges make building Bayesian network models and reasoning withthem more and more difficult.In this dissertation, I address the challenges by developing representational and computational solutions based on importance sampling. I First develop a more solid understanding of the properties of importance sampling in the context of Bayesian networks. Then, I address a fundamental question of importance sampling in Bayesian networks, the representation of the importance function. I derive an exact representation for the optimal importance function and propose an approximation strategy for therepresentation when it is too complex. Based on these theoretical analysis, I propose a suite of importance sampling-based algorithms for (hybrid) Bayesian networks. I believe the new algorithmssignificantly extend the efficiency, applicability, and scalability of approximate inference methods for Bayesian networks. The ultimate goal of this research is to help users to solve difficult reasoning problems emerging from complex decision problems in the most general settings.
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Details
| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
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| Date: |
2 October 2006 |
| Date Type: |
Completion |
| Defense Date: |
25 May 2006 |
| Approval Date: |
2 October 2006 |
| Submission Date: |
15 July 2006 |
| Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
Dietrich School of Arts and Sciences > Intelligent Systems |
| Degree: |
PhD - Doctor of Philosophy |
| Thesis Type: |
Doctoral Dissertation |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
belief updating; evidence pre-propagation; hybrid Bayesian networks; importance function; LBP; loopy belief propagation; mixture of Gaussian; thick tail; epsilon-cutoff; lazy LBP |
| Other ID: |
http://etd.library.pitt.edu/ETD/available/etd-07152006-172002/, etd-07152006-172002 |
| Date Deposited: |
10 Nov 2011 19:51 |
| Last Modified: |
15 Nov 2016 13:45 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/8383 |
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