Fine-Tuning the Odds in Bayesian Networks

TL;DR

This paper introduces scalable analysis techniques for Bayesian networks with symbolic CPTs, enabling handling of many dependent parameters and improving upon previous restrictions in parametric Bayesian network analysis.

Contribution

It presents novel methods based on parametric Markov chain synthesis techniques that significantly relax parameter restrictions in Bayesian network analysis.

Findings

Handles hundreds of parameters in benchmarks

Supports various sensitivity and tuning problems

Built on top of Storm probabilistic model checker

Abstract

This paper proposes various new analysis techniques for Bayes networks in which conditional probability tables (CPTs) may contain symbolic variables. The key idea is to exploit scalable and powerful techniques for synthesis problems in parametric Markov chains. Our techniques are applicable to arbitrarily many, possibly dependent parameters that may occur in various CPTs. This lifts the severe restrictions on parameters, e.g., by restricting the number of parametrized CPTs to one or two, or by avoiding parameter dependencies between several CPTs, in existing works for parametric Bayes networks (pBNs). We describe how our techniques can be used for various pBN synthesis problems studied in the literature such as computing sensitivity functions (and values), simple and difference parameter tuning, ratio parameter tuning, and minimal change tuning. Experiments on several benchmarks show that our prototypical tool built on top of the probabilistic model checker Storm can handle several hundreds of parameters.