Computational Intelligence 2008–2009 Practical Assignment II

Search-and-score algorithms search for a Bayesian network structure that fits the data best (in some sense). They start with an initial network structure (often a graph without arcs or a complete graph), and then traverse the search space of network structures by in each step either removing an arc, adding an arc, or reversing an arc. Read again the paper by Castello and Kočka [1] for a good overview of the principles and difficulties associated with this learning method. Recent search-and-score-algorithms take Markov equivalence into account, i.e., they search in the space of equivalence classes of Bayesian networks and the scoring method they use give the same score for equivalent networks. Bayesian networks with different graph topologies that are included in the same Markov equivalence class represent exactly the same conditionalindependence information by d-separation. Examples of search-and-score algorithms are K2 and inclusion-driven learning. They usually are based on hill-climbing (greedy) search. Constraint-based algorithms carry out a conditional (in)dependence analysis on the data. Based on this analysis an undirected graph is generated (to be interpreted as a Markov network). Using additional independence tests, this network is converted into a Bayesian network. Constraint-based learning algorithms allow for the easy incorporation of background knowledge, i.e., prior knowledge on dependences or independences that hold for the domain under consideration. Examples of constraint-based learning algorithms are PC, NPC, growshrink, and incremental association. A good paper discussing the difficulties with constraintbased methods is the paper by Chickering and Meek [2]. For the underlying theory, consult the book “Bayesian Artificial Intelligence” [3] and the two paper referred to above, which can be downloaded from the CI seminar website. Also consult more specialised books and papers if required. Below, you will find descriptions of a number of tasks that you need to perform. You are free to do something different in the context of Bayesian-network structure learning, e.g., to investigate learning dynamic Bayesian networks from temporal data, but it is required to obtain approval from the lecturer in that case.