Updating Probabilistic Knowledge on Condition/Event Nets using Bayesian Networks

TL;DR

This paper introduces a method for updating probabilistic knowledge in condition/event nets using an extended Bayesian network framework, enabling efficient dynamic probability adjustments through a modular algebraic structure.

Contribution

It develops a modular, algebraic approach for dynamic updates of Bayesian networks applied to condition/event nets, enhancing efficiency and structural clarity.

Findings

Provides a compositional semantics for probabilistic updates

Enables structural modifications of Bayesian networks

Improves efficiency of dynamic probability adjustments

Abstract

The paper extends Bayesian networks (BNs) by a mechanism for dynamic changes to the probability distributions represented by BNs. One application scenario is the process of knowledge acquisition of an observer interacting with a system. In particular, the paper considers condition/event nets where the observer's knowledge about the current marking is a probability distribution over markings. The observer can interact with the net to deduce information about the marking by requesting certain transitions to fire and observing their success or failure. Aiming for an efficient implementation of dynamic changes to probability distributions of BNs, we consider a modular form of networks that form the arrows of a free PROP with a commutative comonoid structure, also known as term graphs. The algebraic structure of such PROPs supplies us with a compositional semantics that functorially maps BNs to their underlying probability distribution and, in particular, it provides a convenient means to describe structural updates of networks.