Monotonicity in Bayesian Networks

TL;DR

This paper explores the concept of monotonicity in Bayesian networks, defining two types and analyzing their computational complexity, while providing an approximate method for practical assessment, demonstrated on an oncology network.

Contribution

It introduces two formal notions of monotonicity in Bayesian networks and analyzes their computational complexity, along with an approximate algorithm for practical detection.

Findings

Deciding monotonicity is coNPPP-complete in general

Deciding monotonicity is coNP-complete for polytrees

An approximate algorithm can effectively assess monotonicity in real-world networks

Abstract

For many real-life Bayesian networks, common knowledge dictates that the output established for the main variable of interest increases with higher values for the observable variables. We define two concepts of monotonicity to capture this type of knowledge. We say that a network is isotone in distribution if the probability distribution computed for the output variable given specific observations is stochastically dominated by any such distribution given higher-ordered observations; a network is isotone in mode if a probability distribution given higher observations has a higher mode. We show that establishing whether a network exhibits any of these properties of monotonicity is coNPPP-complete in general, and remains coNP-complete for polytrees. We present an approximate algorithm for deciding whether a network is monotone in distribution and illustrate its application to a real-life network in oncology.