Learning the Structure of Bayesian Networks Dissertation Proposal

Bayesian networks (BNs) are an efficient way of representing joint probability distributions over sets of random variables; they are commonly employed in AI for reasoning under uncertainty.1 A BN is made up of two components: a directed acyclic graph (DAG), whose nodes represent random variables, and a set of conditional probability tables (CPTs), specifying the conditional probability distribution of each variable given the values of its parents in the DAG—figure 1 provides an example. The link between a BN and a joint probability distribution is provided by the Markov assumption, according to which each variable is independent of its non-descendants (in the DAG) given the values of its parents; given the Markov assumption, a joint probability distribution can be easily derived from a BN. While several algorithms are known for doing probabilistic inference with BNs, an open problem in the field of machine learning is that of learning BNs from data. Here, what needs to be automated is not simply the task of computing the CPTs for a fixed DAG, called ‘parameter learning’, but in particular the task of constructing the DAG (and then computing the relevant CPTs) from a dataset. My work is currently focusing on the latter task, called ‘structure learning’.