Importance Sampling in Bayesian Networks: An Influence-Based Approximation Strategy for Importance Functions

One of the main problems of importance sampling in Bayesian networks is representation of the importance function, which should ideally be as close as possible to the posterior joint distribution. Typically, we represent an importance function as a factorization, i.e., product of conditional probability tables (CPTs). Given diagnostic evidence, we do not have explicit forms for the CPTs in the networks. We first derive the exact form for the CPTs of the optimal importance function. Since the calculation is hard, we usually only use their approximations. We review several popular strategies and point out their limitations. Based on an analysis of the influence of evidence, we propose a method for approximating the exact form of importance function by explicitly modeling the most important additional dependence relations introduced by evidence. Our experimental results show that the new approximation strategy offers an immediate improvement in the quality of the importance function.

[1]  Ross D. Shachter,et al.  Symbolic Probabilistic Inference in Belief Networks , 1990, AAAI.

[2]  Kuo-Chu Chang,et al.  Weighing and Integrating Evidence for Stochastic Simulation in Bayesian Networks , 2013, UAI.

[3]  David Heckerman,et al.  Probabilistic similarity networks , 1991, Networks.

[4]  Max Henrion,et al.  Some Practical Issues in Constructing Belief Networks , 1987, UAI.

[5]  Michael I. Jordan,et al.  Loopy Belief Propagation for Approximate Inference: An Empirical Study , 1999, UAI.

[6]  Nevin L. Zhang,et al.  A simple approach to Bayesian network computations , 1994 .

[7]  Changhe Yuan,et al.  An Importance Sampling Algorithm Based on Evidence Pre-propagation , 2002, UAI.

[8]  Serafín Moral,et al.  A Monte Carlo algorithm for probabilistic propagation in belief networks based on importance sampling and stratified simulation techniques , 1998, Int. J. Approx. Reason..

[9]  Luis E. Ortiz,et al.  Selecting approximately-optimal actions in complex structured domains , 2002 .

[10]  J. Geweke,et al.  Bayesian Inference in Econometric Models Using Monte Carlo Integration , 1989 .

[11]  Ross D. Shachter,et al.  Simulation Approaches to General Probabilistic Inference on Belief Networks , 2013, UAI.

[12]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[13]  Cristina Conati,et al.  On-Line Student Modeling for Coached Problem Solving Using Bayesian Networks , 1997 .

[14]  Scott M. Olmsted.  On representing and solving decision problems , 1983 .

[15]  Leslie Pack Kaelbling,et al.  Adaptive Importance Sampling for Estimation in Structured Domains , 2000, UAI.

[16]  Jian Cheng,et al.  AIS-BN: An Adaptive Importance Sampling Algorithm for Evidential Reasoning in Large Bayesian Networks , 2000, J. Artif. Intell. Res..

[17]  Gregory M. Provan,et al.  Knowledge Engineering for Large Belief Networks , 1994, UAI.

[18]  A. Salmerón,et al.  Importance sampling in Bayesian networks using probability trees , 2000 .

[19]  Max Henrion,et al.  Propagating uncertainty in bayesian networks by probabilistic logic sampling , 1986, UAI.

[20]  Reuven Y. Rubinstein,et al.  Simulation and the Monte Carlo method , 1981, Wiley series in probability and mathematical statistics.