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Tutorial on Estimation and Multivariate Gaussians

Tutorial on Estimation and MultivariateGaussiansSTAT 27725/CMSC 25400: Machine LearningShubhendu Trivedi - Technological InstituteOctober 2015 Tutorial on Estimation and Multivariate GaussiansSTAT 27725/CMSC 25400 Things we will look at today Maximum Likelihood Estimation ML for Bernoulli Random Variables Maximizing a Multinomial Likelihood: LagrangeMultipliers Multivariate Gaussians Properties of Multivariate Gaussians Maximum Likelihood for Multivariate Gaussians (Time permitting) Mixture ModelsTutorial on Estimation and Multivariate GaussiansSTAT 27725/CMSC 25400 The Principle of Maximum LikelihoodSuppose we haveNdata pointsX={x1,x2,..,xN}(or{(x1,y1),(x2,y2) ,..,(xN,yN)})Suppose we know the probability distribution function thatdescribes the datap(x; )(orp(y|x; ))Suppose we want to determine the parameter(s) Pick so as toexplainyour data bestWhat does this mean?

Tutorial on Estimation and Multivariate Gaussians STAT 27725/CMSC 25400: Machine Learning Shubhendu Trivedi - shubhendu@uchicago.edu Toyota Technological Institute October 2015 Tutorial on Estimation and Multivariate GaussiansSTAT 27725/CMSC 25400

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