Simulation Approaches to General Probabilistic Inference on Belief Networks

Abstract

Although a number of algorithms have been developed to solve probabilistic inference problems on belief networks, they can be divided into two main groups: exact techniques which exploit the conditional independence revealed when the graph structure is relatively sparse, and probabilistic sampling techniques which exploit the "conductance" of an embedded Markov chain when the conditional probabilities have non extreme values. In this paper, we investigate a family of Monte Carlo sampling techniques similar to Logic Sampling [Henrion, 1988] which appear to perform well even in some multiply-connected networks with extreme conditional probabilities, and thus would be generally applicable. We consider several enhancements which reduce the posterior variance using this approach and propose a framework and criteria for choosing when to use those enhancements.

Dynamic Data Feed to Bayesian Network Model and SMILE Web Application

“…Several approximate algorithms based on stochastic 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, www.intechopen.com 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).…”

Embedded Probabilistic Programming

“…2. We develop importance sampling [15,44] with look-ahead, a new, general algorithm for approximate inference. 3.…”

“…If we assert such an observation and wish to estimate its probability, the rejection sampling of fun () -> dcoin_and 10 || fail () offers little help: even with 10,000 attempts, all samples are unsuccessful. Importance sampling [15,44] is an approximate inference strategy that improves upon rejection sampling by assigning weights to each sample. For example, because assigning true to the variable lost leads to failure, the sampler should not pick a value for lost randomly; instead, it should force lost to be false, but scale the weight of the resulting sample by 0.1 to compensate for this artificially induced success.…”

Untitled

“…Such algorithms, particularly stochastic simulation techniques such as likelihood weighting (Shachter & Peot, 1989;Fung & Chang, 1989), provide "anytime" estimates of the required probabilities. This suits our needs very well: Early in the gradient descent process, we need only very rough estimates of the gradient; the use of an anytime algorithm allows these to be generated very quickly.…”