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I have fitted a Gaussian Mixture Model to the multiple joint probability density functions. How can I obtain the conditional probability density function (i.e.,p(x|y)) from this mixture model (NXN matrix) in Matlab?

user3087937
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Based on Bayes rule, you can write down formula p(x|y)=p(x,y)/p(y). If you are able to obtain probability value p(y) for some given y, you can plug it in directly into Bayes formula. Otherwise you can go on and express each gaussian of the mixture as conditional gaussian with parameters (P stands for covariance matrices, mu stands for means):

mu_x|y = mu_x + P_xy P_yy^-1 (y - mu_y)

P_x|y = P_xx + P_xy P_yy^-1 P_yx

Gawl
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