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

IF 1.1 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Laura Aquilanti, S. Cacace, F. Camilli, Raul De Maio
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引用次数: 1

Abstract

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.
伯努利分布与分类分布有限混合的平均场博弈模型
有限混合模型是数据统计分析的重要工具,例如数据聚类。混合模型的最优参数通常是通过期望最大化算法最大化对数似然函数来计算的。我们提出了一种基于平均场博弈理论的替代方法,平均场博弈是一类具有无限数量代理的微分博弈。我们证明了有限状态空间多种群平均场博弈系统的解具有伯努利混合的对数似然泛函的临界点。然后将该方法推广到分类分布的混合模型。因此,平均场博弈方法提供了一种计算混合模型参数的方法,并展示了它在聚类分析中的一些标准示例中的应用。
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来源期刊
Journal of Dynamics and Games
Journal of Dynamics and Games MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-
CiteScore
2.00
自引率
0.00%
发文量
26
期刊介绍: The Journal of Dynamics and Games (JDG) is a pure and applied mathematical journal that publishes high quality peer-review and expository papers in all research areas of expertise of its editors. The main focus of JDG is in the interface of Dynamical Systems and Game Theory.
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