The Expectation--Maximization (EM) algorithm is a simple meta-algorithm that has been used for many years as a methodology for statistical inference when there are missing measurements in the observed data or when the data is composed of observables and unobservables. Its general properties are well studied, and also, there are countless ways to apply it to individual problems. In this paper, we introduce the $em$ algorithm, an information geometric formulation of the EM algorithm, and its extensions and applications to various problems. Specifically, we will see that it is possible to formulate an outlier-robust inference algorithm, an algorithm for calculating channel capacity, parameter estimation methods on probability simplex, particular multivariate analysis methods such as principal component analysis in a space of probability models and modal regression, matrix factorization, and learning generative models, which have recently attracted attention in deep learning, from the geometric perspective.

翻译：期望- 最大化算法(EM) 是一种简单的元值算法,多年来一直用来作为统计推断方法,当观测数据缺少测量数据时,或当数据由可观测和不可观测数据组成时,这种算法是一种统计推论方法。它的一般特性经过了仔细研究,并且有无数方法将其应用于个别问题。在本文中,我们引入了美元算法,一种EM算法的信息几何配方,以及其延伸和应用于各种问题。具体地说,我们将看到有可能制定一种外部- 紫外推推算法,一种计算频道能力的算法,对概率简单x的参数估计方法,特别是多变量分析方法,例如概率模型和模式回归空间的主要组成部分分析,矩阵因子化,以及学习基因化模型,这些模型最近从几何角度的深层学习中引起了注意。