Description
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Written Problems (6 points)
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MLE minimizes KL divergence to the empirical distribution (Exercise 2.15 of Murphy’s book) (1 point)
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Centering and ridge regression (Exercise 7.3 of Murphy’s book) (1 point)
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Symmetric version of ‘2 regularized multinomial logistic regression (Ex-ercise 8.5 of Murphy’s book) (1 point)
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Elementary properties of ‘2 regularized logistic regression (Exercise 8.6 of Murphy’s book) (1 point)
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Given the following denominator layout derivatives, (2 points)
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Di erentiation of a scalar function w.r.t. a vector: If f(w) is a scalar function of d variables, w is a d 1 vector, then di erentiation of f(w) w.r.t. w results in a d 1 vector
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2 @f 3
@w1
df(w) .
dw = 6 .. 7
4 5
@f
@wd
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Di erentiation of a vector function w.r.t. a vector: If f(w) is a vector function of size h 1 and w is a d 1 vector, then di erentiation of f(w) w.r.t. w results in a d h vector
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2
@f1
:.:..:
@fh
3
df(w)
=
@x...1
@w...1
dw
6
@wd
: : :
@wd
7
4
@f1
@fh
5
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Please prove the following derivatives, and X and y are not functions of w:
d(X>w)
2
