Who learns better Bayesian network structures: Accuracy and speed of structure learning algorithms

Abstract

Three classes of algorithms to learn the structure of Bayesian networks from data are common in the literature: constraint-based algorithms, which use conditional independence tests to learn the dependence structure of the data; score-based algorithms, which use goodness-of-fit scores as objective functions to maximise; and hybrid algorithms that combine both approaches. Constraint-based and score-based algorithms have been shown to learn the same structures when conditional independence and goodness of fit are both assessed using entropy and the topological ordering of the network is known [1].In this paper, we investigate how these three classes of algorithms perform outside the assumptions above in terms of speed and accuracy of network reconstruction for both discrete and Gaussian Bayesian networks. We approach this question by recognising that structure learning is defined by the combination of a statistical criterion and an algorithm that determines how the criterion is applied to the data. Removing the confounding effect of different choices for the statistical criterion, we find using both simulated and realworld complex data that constraint-based algorithms are often less accurate than score-based algorithms, but are seldom faster (even at large sample sizes); and that hybrid algorithms are neither faster nor more accurate than constraint-based algorithms. This suggests that commonly held beliefs on structure learning in the literature are strongly influenced by the choice of particular statistical criteria rather than just by the properties of the algorithms themselves.

Uncertainties in conditional probability tables of discrete Bayesian Belief Networks: A comprehensive review

“…The current work has focused on CPT derivation for discrete BBN development. The second key ingredient of BBNs is the DAG specification, whose learning from data has been investigated in numerous studies (e.g., Heinze-Deml et al (2018), Scutari et al (2018), Beretta et al (2018, etc.). To address the whole spectrum of uncertainties in BBN building, studies both covering DAG and CPT learning would be beneficial.…”

bAIcis: A Novel Bayesian Network Structural Learning Algorithm and Its Comprehensive Performance Evaluation Against Open-Source Software

“…Score-based algorithms assign a score to each candidate BN on measuring goodness of fit and attempt to return a causal structure that maximizes the score, for example, Bayesian information criterion (BIC) (Chickering, 2002;Tsamardinos et al, 2006;Carvalho, 2009); whereas constraint-based algorithms learn the BN structure based on Markov condition by a series of local conditional independence constraints and construct a graph that meets the independent relationships (Spirtes and Glymour, 1991;Pearl and Verma, 1995;Claassen and Heskes, 2012). The advantages and disadvantages of the two algorithms were discussed elsewhere (Spirtes, 2010;Triantafillou and Tsamardinos, 2016;Scutari et al, 2018).…”

Comparing basal dendrite branches in human and mouse hippocampal CA1 pyramidal neurons with Bayesian networks

“…There are two main approaches to learning G from D 16 : (a) by testing for conditional independence among triplets of sets of variables (the constraint-based approach); and (b) by searching the space of DAGs in order to optimize a score such as penalized likelihood (the score-based approach). While seemingly very different, conditional independence tests and network scores are related statistical criteria 20 . For example, when considering whether to include the arc Y → X into a graph G , the likelihood-ratio test of conditional independence of X and Y given Pa G (X) and the Bayesian information criterion 21 (BIC) score are both functions of log P(X|Pa G (X),Y ) P(X|Pa G (X)) .…”