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The Naive Bayes assumption for estimation assumes that the dimensions in a given estimation problem are (conditionally) independent. For classification we used this to dramatically

The Naive Bayes assumption for estimation assumes that the dimensions in a given estimation problem are (conditionally) independent. For classification we used this to dramatically reduce the number of parameters that we needed to estimate. The Naive Bayes assumption can also be used for continuous distributions. AssumexRD is distributed according to a multivariate Gaussian distribution, i.e., p(x)=N(x,), where N(x,)=(2)2d(det)21exp(21(x)T1(x)), and =E[x],Cov[x]=E[(x)(x)T]=. Given a set of samples D={x(1),...,x(n)}, derive the Maximum Likelihood estimate ofML=N1i=1Nxi andML=N1i=1N(xiML)(xiML)T under the Naive Bayes assumption (i.e., that p(x)=i=1Np(xi)). Be sure to show your derivation in detail. What specific structure does have and why?

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