Discrete Graphic Markov Model Selection by Multiobjective Genetic Algorithm (GMS-MGA)

The problem of graphic Markov model selection (GMS) is considered as a multiobjective one, where the objectives are: (1) best fitting of the model to the sample data and, (2) least possible number of edges, and the fitting criteria function is the Kullback-Leibler. The multiobjective strategy is to obtain an approximate Pareto front using a multi-starting multiobjective genetic algorithm (MGA). To test the performance of the algorithm, 48 samples of 6 different model complexities are generated using a Markov model random sampler (MMRS) and used as benchmarks. The performance is assessed through the times that the Pareto front contains the true model. As results the algorithm obtains the true models in 93% of the cases, the complexity of the model made a difference in the performance of the algorithm. The mean time of execution is least or equal to 2 minutes for 10 binary variables in a PC