A Mean Field Games model for finite mixtures of Bernoulli and categorical distributions

Finite mixture models are an important tool in the statistical analysis of data, for example data clustering. The optimal parameters a model usually computed by maximizing log-likelihood functional via Expectation-Maximization algorithm. We propose alternative approach based on theory Mean Field Games, class differential games with infinite number agents. show that solution finite state space multi-population Games system characterizes critical points Bernoulli mixture. is then generalized to categorical distributions. Hence, provides method compute model, and we its application some standard examples cluster analysis.