A Review of Bayesian Networks and Structure Learning

John Noble, Timo J.T. Koski
2012 Mathematica Applicanda  
This article reviews the topic of Bayesian networks. A Bayesian network is a factorisation of a probability distribution along a directed acyclic graph. The relation between graphical d-separation and independence is described. A short article from 1853 by Arthur Cayley [8] is discussed, which contains several ideas later used in Bayesian networks: factorisation, the noisy 'or' gate, applications of algebraic geometry to Bayesian networks. The ideas behind Pearl's intervention calculus when the
more » ... n calculus when the DAG represents a causal dependence structure and the relation between the work of Cayley and Pearl is commented on. Most of the discussion is about structure learning, outlining the two main approaches, search and score versus constraint based. Constraint based algorithms often rely on the assumption of faithfulness, that the data to which the algorithm is applied is generated from distributions satisfying a faithfulness assumption where graphical dseparation and independence are equivalent. The article presents some considerations for constraint based algorithms based on recent data analysis, indicating a variety of situations where the faithfulness assumption does not hold. There is a short discussion about the causal discovery controversy, the idea that causal relations may be learned from data. 2010 Mathematics Subject Classification: 62H05; 68T37; 65S05.
doi:10.14708/ma.v40i1.278 fatcat:xftrlk4azvg3viilrzuikg5o7q