Parameter estimation in mixture models using evolutive algorithms (2015)
The mixture models are widely used in cases when there are elements that come from diverse populations, mixed in a superpopulation. i.e. the proportions of expresed genes, and the weight of colombian $100 coins, year 1994. There are two main approaches for the modelling of mixture models: the bayesian and the clasical method. In the bayesian approach, the data are modelated and fitted to a given distribution, for example, the Dirichlet distribution. Further, the data are clustered for the posterior analysis. The classical method is the maximum likelihood estimation, using the Expectation-Maximization (EM) algorithm. This last method needs, as initial data, the amount of populations and their proportions in the superpopulation. Often, these data are very difficult to know or measure, because of the unknown nature of the problem. For that reason, in this work we propose the use of evolutive algorithms, such as genetic algorithms, simulated annealing and taboo search, to estimate the parameters of the mixture models. We propose an algorithm for the comparison of evolutive and traditional methods, and we illustrate the use of this algorithm with a real application. We found that the evolutive algorithms are a competitive option to estimate the parameters in mixture models in the cases when the populations in the mixture follows a gamma distribution, the weights of the populations in the mixture are even and the sample size is bigger than 100 items. For the mixture of normal distributions and the estimation of the number of populations in a mixture, the traditional method is a better option than the genetic algorithm.