Question

1. In the derivation of the maximum likelihood estimate, probability distribution for a random vector y: we factorize the following conditional , y(m)|e(1) p(y(2()(y(2) lz(2)...py(m)(m) , x(m)) P(y X) p(y() m IIP(y)) i=1 What assumptions justify this factorization? If we had not made any assumptions what would be a valid way to factorize the conditional distribution? 2. In the derivation of the maximum likelihood estimate, why is it okay to minimize the negative log likelihood instead of maximize the likelihood? 3. Is mean squared error identical to the cost function derived by maximum likelihood? If there differences, are they important to the optimization problem? are 4. In the mean squared error, which of the depend on wj? m 2 (w0)-go) MSE m 2=1 5. What is the partial derivative of MSE with respect to Συ'-1) 2 MSE m i=1 ()fe 6. What is the partial derivative of with respect to w,? i) k 1 (e)e

need some help on this homework involving likelihood e sd tinations.

any help would be greatly appreciated!

Answer 1

The assumption is that all features are independent of each other and there is no Correlation between them.

If we don't assume features to be independent, then we need to apply the 'Chain Rule of Probability' which would be very very lengthy procedure.

For A,B are two random variables.

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