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Many real world sequences such as protein secondary structures or shell logsexhibit a rich internal structures. Traditional probabilistic models ofsequences, however, consider sequences of flat symbols only. Logical hiddenMarkov models have been proposed as one solution. They deal with logicalsequences, i.e., sequences over an alphabet of logical atoms. This comes at theexpense of a more complex model selection problem. Indeed, differentabstraction levels have to be explored. In this paper, we propose a novelmethod for selecting logical hidden Markov models from data called SAGEM. SAGEMcombines generalized expectation maximization, which optimizes parameters, withstructure search for model selection using inductive logic programmingrefinement operators. We provide convergence and experimental results that showSAGEM's effectiveness.

'Say EM' for Selecting Probabilistic Models for Logical Sequences