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.
翻译:极量混合物模型是数据统计分析的重要工具,例如数据集群。混合物模型的最佳参数通常通过通过预期-最大化算法最大限度地发挥日志相似性功能来计算。我们建议了一种基于 " 平极场运动会 " 理论的替代方法,这是一种具有无限代理人的差别游戏类别。我们表明,有限空间空间-多人口中度场运动系统的解决方案是伯努利混合物日志相似性功能的临界点。这种方法随后被普遍推广到绝对分布的混合物模型中。因此, " 平极场运动 " 方法提供了一种计算混合模型参数的方法,我们展示了其在群集分析中某些标准例子中的应用情况。