Mixtures and products in two graphical models semi-algebraic statistics restricted Boltzmann machine mixture model maximum likelihood estimation We compare two statistical models of three binary random variables. One is a mixture model and the other is a product of mixtures model called a restricted Boltzmann machine. Although the two models we study look different from their parametrizations, we show that they represent the same set of distributions on the interior of the probability simplex, and are equal up to closure. We give a semi-algebraic description of the model in terms of six binomial inequalities and obtain closed form expressions for the maximum likelihood estimates. We briefly discuss extensions to larger models. Seigal,Anna Montufar, Guido 2018 2018-09-24 Article application/pdf islandora:1007797 http://hdl.handle.net/10560/islandora:1007797 MATH / Applied Mathematics Illinois Institute of Technology Journal of Algebraic Statistics en Open Access