Weighing and Integrating Evidence for Stochastic Simulation in Bayesian Networks

Abstract

Stochastic simulation approaches perform probabilistic inference in Bayesian networks by estimating the probability of an event based on the frequency that that· event occurs in a set of simulation trials. This paper describes the evidence weighting mechanism, for augmenting the lo � ic sampling stochastic simulation algo rithm l5]. Evidence weighting modifies the logic sampling algorithm by weighting each simula tion trial by the likelihood of a network's evi dence given the sampled state node values for that trial. We also describe an enhancement to the basic algorithm which uses the eviden tial integration technique [2]. A comparison of the basic evidence weighting mechanism with the Markov blanket algorithm [8], the logic sampling algorithm, and the evidence integra tion algorithm is presented. The comparison is aided by analyzing the performance of the algorithms in a simple example network.

Probabilistic logic programming for hybrid relational domains

“…Likelihood weighting is a type of importance sampling that forces variables to be consistent with the evidence by using an adapted proposal distribution g. It has been shown (Fung and Chang 1989) that LW reduces the variance of the estimator with respect to the naive Monte-Carlo estimator. In this paper LW is also used to force variables to be consistent with the query.…”

“…The key question is thus how to sample one such partial world x P(i) q for a generic call of EvalSampleQuery (q, x P(i) ). To realize this, we combine likelihood weighting (LW) (Fung and Chang 1989;Koller and Friedman 2009) with a variant of SLD-resolution in the EvalSampleQuery algorithm that we describe below. (Apt 1997;Lloyd 1987;Nilsson and Małiszyński 1995) is an inference procedure to prove a query q, used in logic programming, that focuses the proof on the relevant part of the program P. The basic idea is replacing an atom with its definition.…”

Parallel Importance Sampling in Conditional Linear Gaussian Networks

“…A simple procedure for selecting the sampling distribution is the so-called evidence weighting (EW) [5]. In EW, each variable is sampled from a conditional density given its parents in the network.…”

Automatically Building Diagnostic Bayesian Networks from On-line Data Sources and the SMILE Web-based Interface

“…Section 4 describes the design and implementation of a practical framework for automating the building of diagnostic BN models from online Automatically Building Diagnostic Bayesian Networks from On-line Data Sources and the SMILE Web-based Interface 323 sampling have been developed. Of these, best known are probabilistic logic sampling (Henrion, 1988), likelihood sampling (Shachter & Peot, 1989: Fung & Chang, 1989, and backward sampling (Fung & del Favero, 1994), Adaptive Importance Sampling (AISBN) (Cheng & Druzdzel, 2000), and Approximate Posterior Importance Sampling (APIS-BN) (Yuan & Druzdzel, 2003). Approximate belief updating in Bayesian networks has also been shown to be worst case NP-hard (Dagum & Luby, 1993).…”