The Impact of Variable Ordering on Bayesian Network Structure Learning

TL;DR

This paper demonstrates that the order of variables significantly affects the accuracy of Bayesian network structure learning algorithms, raising concerns about their reliability and the need for order-invariant methods.

Contribution

It reveals the substantial impact of variable ordering on structure learning accuracy, highlighting a previously underexplored factor affecting algorithm validity.

Findings

Variable order greatly influences learned Bayesian network accuracy.

Sensitivity to variable order surpasses effects of sample size and hyper-parameters.

Raises questions about the validity of existing structure learning algorithms.

Abstract

Causal Bayesian Networks provide an important tool for reasoning under uncertainty with potential application to many complex causal systems. Structure learning algorithms that can tell us something about the causal structure of these systems are becoming increasingly important. In the literature, the validity of these algorithms is often tested for sensitivity over varying sample sizes, hyper-parameters, and occasionally objective functions. In this paper, we show that the order in which the variables are read from data can have much greater impact on the accuracy of the algorithm than these factors. Because the variable ordering is arbitrary, any significant effect it has on learnt graph accuracy is concerning, and this raises questions about the validity of the results produced by algorithms that are sensitive to, but have not been assessed against, different variable orderings.