MATHEMATICAL MODELING

Bayesian identification of a Gaussian mixture model

Yu. A. Dubnov^abc, A. V. Boulytchev<sup>ab

a</sup> Institute for Systems Analysis (ISA), FRC CSC RAS
^b Higher School of Economics (HSE)
^c MIPT

Abstract: We consider a problem of parameters estimation for gaussian mixture models widely used in data analysis and unsupervised machine learning. A new model identification method based on Bayesian aproach and the principle of maximum posterior distribution is proposed. In the article we describe the method of multiextremum density function maximum definition using sampling by Metropolis-Hastings algorithm. The proposed method is compared with the traditional expectation maximization algorithm by computational experiments both on a sample synthetic data and the real one from «fisheriris» dataset.

Keywords: Gaussian mixture model, Bayesian approach, Metropolis-Hastings algorithm, classification problem.