A Mean Field Games model for finite mixtures of Bernoulli and Categorical distributions
This provides a novel computational method for mixture models in statistical data analysis, though it appears incremental as it offers an alternative to existing techniques without claiming broad performance gains.
The authors tackled the problem of estimating parameters in finite mixture models, such as Bernoulli and categorical mixtures, by proposing a Mean Field Games approach as an alternative to the Expectation-Maximization algorithm, showing that it characterizes critical points of the log-likelihood functional and applying it to standard clustering examples.
Finite mixture models are an important tool in the statistical analysis of data, for example in data clustering. The optimal parameters of a mixture model are usually computed by maximizing the log-likelihood functional via the Expectation-Maximization algorithm. We propose an alternative approach based on the theory of Mean Field Games, a class of differential games with an infinite number of agents. We show that the solution of a finite state space multi-population Mean Field Games system characterizes the critical points of the log-likelihood functional for a Bernoulli mixture. The approach is then generalized to mixture models of categorical distributions. Hence, the Mean Field Games approach provides a method to compute the parameters of the mixture model, and we show its application to some standard examples in cluster analysis.