Description
1. (20 pts.) Let ~x = (x1, . . . , xd)
t be a d-dimensional binary (0 or 1) vector with a multivariate
Bernoulli distribution
P(~x|
~θ) = Y
d
i=1
θ
xi
i
(1 − θi)
1−xi
,
where ~θ = (θ1, . . . , θd)
t
is an unknown parameter vector, θi being the probability that xi = 1.
Given i.i.d. data set D = {~x1, . . . , ~xn}, derive the maximum-likelihood estimate for ~θ.
2. (10 pts.) Assume that a classifier correctly classifies 900 of the 1000 examples in the test set.
What is the estimated accuracy of the classifier? Give 95% confidence interval.
