Analyzing Markov Boundary Discovery Algorithms in Ideal Conditions Using the d-Separation Criterion

Abstract

This article proposes the usage of the d-separation criterion in Markov Boundary Discovery algorithms, instead of or alongside the statistical tests of conditional independence these algorithms usually rely on. This is a methodological improvement applicable when designing, studying or improving such algorithms, but it is not applicable for productive use, because computing the d-separation criterion requires complete knowledge of a Bayesian network. Yet Bayesian networks can be made available to the algorithms when studied in controlled conditions. This approach has the effect of removing sources of suboptimal behavior, allowing the algorithms to perform at their theoretical best and providing insights about their properties. The article also discusses an extension of this approach, namely to use d-separation as a complement to the usual statistical tests performed on synthetic datasets in order to ascertain the overall accuracy of the tests chosen by the algorithms, for further insights into their behavior. To exemplify these two approaches, two Markov Boundary Discovery algorithms were used, namely the Incremental Association Markov Blanket algorithm and the Iterative Parent–Child-Based Search of Markov Blanket algorithm. Firstly, these algorithms were configured to use d-separation alone as their conditional independence test, computed on known Bayesian networks. Subsequently, the algorithms were configured to use the statistical G-test complemented by d-separation to evaluate their behavior on synthetic data.