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I am taking two courses where I learn GMM and MNL separately. However, I do see some similarities between they two: like we need indicator variable for discrete choice modeling when using the MLE, while we also need the categorical variable for estimation mean/variance/weight for GMM using the E-M algorithm. My problem is how to intuitively understand why we cannot only use MLE to estimate the parameters of GMM? Like MLE is a method of finding the set of population parameters that produce observed sample most often. Some tutorials that I am referring to are : (1) discrete choice model http://www.tcd.ie/civileng/Staff/Brian.Caulfield/T2%20-%20Transport%20Modelling/Discrete%20Choice%20Modelling.pdf (2)GMM http://www.idiap.ch/~fleuret/files/EE613/EE613-slides-4.pdf

Thanks in advance!

DQ_happy
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  • I find the first answer of this question useful to my question. (http://math.stackexchange.com/questions/377576/how-gaussian-mixture-models-work?rq=1)we cannot estimate all the parameters of GMM since we have weight.EM works by replacing this maximization problem with maximizing an "expected" log-likelihood. However, I kind of still do not get the intuition of why this works here just by using maximizing the "expected" log-likelihood. Also, I am wondering in which case can we apply the E-M algorithm? like when we get conjugate prior? what is the relationship between MLE and bayesian estimation – DQ_happy Mar 25 '15 at 02:21

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