Graphical Local Genetic Algorithm for High-Dimensional Log-Linear Models

Abstract

Graphical log-linear models are effective for representing complex structures that emerge from high-dimensional data. It is challenging to fit an appropriate model in the high-dimensional setting and many existing methods rely on a convenient class of models, called decomposable models, which lend well to a stepwise approach. However, these methods restrict the pool of candidate models from which they can search, and these methods are difficult to scale. It can be shown that a non-decomposable model can be approximated by the decomposable model which is its minimal triangulation, thus extending the convenient computational properties of decomposable models to any model. In this paper, we propose a local genetic algorithm with a crossover-hill-climbing operator, adapted for log-linear graphical models. We show that the graphical local genetic algorithm can be used successfully to fit non-decomposable models for both a low number of variables and a high number of variables. We use the posterior probability as a measure of fitness and parallel computing to decrease the computation time.