B555 - Machine Learning - Homework 1
Enrique Areyan
February 07, 2015
Problem 1: Let (, F, P ) be a probability space. Using only the set operations and axioms of probability, show that for
any two sets, not necessarily disjoint, A and B
P (A B) = P (A)

B555 - Machine Learning - Homework 2
Enrique Areyan
March 05, 2015
Problem 1: Suppose that the number of accidents occurring daily in a certain plant has a Poisson distribution with an
unknown mean . Based on previous experience in similar industrial plan

B555 - Machine Learning - Homework 4
Enrique Areyan
April 28, 2015
Problem 1: Give decision trees to represent the following Boolean functions
a) A B
b) A [B C]
c) A B
d) [A B] [C D]
B
e) [A B] [C D]
where A is a negation of A and is an exclusive OR oper

B555 - Machine Learning - Homework 3
Enrique Areyan
April 13, 2015
Problem 1: Consider a logistic regression problem where X = Rk and Y = cfw_1, +1.
Derive the weight update rule that maximizes the likelihood.
Solution: By definition, for this logistic re