1 6 Examples MULTIVARIATE GAUSSIAN MLE | Machine Learning

So if we have data x1; : : : ; xn in Rd that we hypothesize is i.i.d. Gaussian, the
maximum likelihood values of the mean and covariance matrix are
µ^ML = 1
n
nXi=1
xi; Σ^ML = 1
n
nXi=1
(xi − µ^ML)(xi − µ^ML)T:
Are we done? There are many assumptions/issues with this approach that
makes finding the “best” parameter values not a complete victory.
I We made a model assumption (multivariate Gaussian).
I We made an i.i.d. assumption.
I We assumed that maximizing the likelihood is the best thing to do.
Comment: We often use θML to make predictions about xnew (Block #4).
How does θML generalize to xnew?
If x1:n don’t “capture the space” well, θML can overfit the data.
#multivariable #gaussian #linear #regression #maximum #maximumlikelihood
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