'Say EM' for Selecting Probabilistic Models for Logical Sequences

TL;DR

This paper introduces SAGEM, a novel method combining generalized expectation maximization and logic-based structure search to select logical hidden Markov models from data, improving modeling of complex logical sequences.

Contribution

SAGEM is the first method to integrate EM optimization with ILP-based structure search for logical HMM model selection.

Findings

SAGEM effectively selects models with better data fit.

Experimental results demonstrate SAGEM's convergence and efficiency.

SAGEM outperforms existing approaches in modeling logical sequences.

Abstract

Many real world sequences such as protein secondary structures or shell logs exhibit a rich internal structures. Traditional probabilistic models of sequences, however, consider sequences of flat symbols only. Logical hidden Markov models have been proposed as one solution. They deal with logical sequences, i.e., sequences over an alphabet of logical atoms. This comes at the expense of a more complex model selection problem. Indeed, different abstraction levels have to be explored. In this paper, we propose a novel method for selecting logical hidden Markov models from data called SAGEM. SAGEM combines generalized expectation maximization, which optimizes parameters, with structure search for model selection using inductive logic programming refinement operators. We provide convergence and experimental results that show SAGEM's effectiveness.