Inferência variacional aplicada à análise de agrupamentos via modelos de mistura de normais multivariadas

Abstract

We apply the Variational Inference (IV) method to adjust Multivariate Normal Mixture Models, in the context of unsupervised learning, aiming at grouping observation vectors. We use IV methods seeking to gain computational efficiency and scalability in the approximation of posteriori distributions for inference on unknown quantities, when such distributions are intractable. Another approach to intractable density problems are in Markov Chain Monte Carlo (MCMC) methods. However, in several contexts, the computational cost of MCMC can be prohibitive. We apply the IV methodology in three databases: first in a simulated study with a mixture of bivariate normals (dimension D = 2), allowing us a better comparison between IV and MCMC; real data aiming at the grouping of images, through mixtures of multivariate normals color red (of dimension D = 786); and, finally, to time series data, satellite image data (D = 46), where their groupings are sought by pattern similarity. We evaluated both the accuracy and performance of the aforementioned methods.