论文标题
伯努利和分配分布有限混合物的平均现场游戏模型
A Mean Field Games model for finite mixtures of Bernoulli and Categorical distributions
论文作者
论文摘要
有限混合模型是数据统计分析的重要工具，例如在数据聚类中。混合模型的最佳参数通常是通过通过期望最大化算法最大化对数可能性功能的来计算的。我们根据平均野外游戏理论，一类具有无限数量的代理商的差异游戏提出了一种替代方法。我们表明，有限状态空间多人群的解决方案均值野外游戏系统表征了Bernoulli混合物的对数可能点功能的临界点。然后将该方法推广到分类分布的混合模型。因此，平均现场游戏方法提供了一种计算混合模型参数的方法，我们将其应用于集群分析中的一些标准示例。
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.
