# INTRODUCTION TO MACHINE LEARNING Week 11

Session: JAN-APR 2023

Course Name: Introduction to Machine Learning

#### Q1. Given n samples x1,x2,…,xN drawn independently from an Exponential distribution unknown parameter λ, find the MLE of λ.a. λMLE=∑ni=1xib. λMLE=n∑ni=1xic. λMLE=n∑ni=1xid. λMLE=∑ni=1xi/ne. λMLE=n−1/∑ni=1xif. λMLE=∑ni=1xi/n−1

Q2. Given n samples x1,x2,…,xn drawn independently from an Geometric distribution unknown parameter p given by pdf Pr(X=k)=(1−p)k−1p for k=1,2,3,⋅⋅⋅ , find the MLE of p.
a. pMLE=∑ni=1xi
b. pMLE=n∑ni=1xi
c. pMLE=n/∑ni=1xi
d. pMLE=∑ni=1xi/n
e. pMLE=n−1/∑ni=1xi
f. pMLE=∑ni=1xi/n−1

These are Introduction to Machine Learning Week 11 Assignment 11 Answers

Q3. Suppose we are trying to model a p dimensional Gaussian distribution. What is the actual number of independent parameters that need to be estimated in mean and covariance matrix respectively?
a. 1,1
b. p−1,1
c. p,p
d. p,p(p+1)
e. p,p(p+1)/2
f. p,(p+3)/2
g. p−1,p(p+1)
h. p−1,p(p+1)/2+1
i. p−1,(p+3)/2
j. p,p(p+1)−1
k. p,p(p+1)/2−1
l. p,(p+3)/2−1
m. p,p2
n. p,p2/2
o. None of these

Q4. Given n samples x1,x2,…,xN drawn independently from a Poisson distribution unknown parameter λ, find the MLE of λ.
a. λMLE=∑ni=1xi
b. λMLE=n∑ni=1xi
c. λMLE=n/∑ni=1xi
d. λMLE=∑ni=1xi/n
e. λMLE=n−1/∑ni=1xi
f. λMLE=∑ni=1xi/n−1

These are Introduction to Machine Learning Week 11 Assignment 11 Answers

Q5. In Gaussian Mixture Models, πi are the mixing coefficients. Select the correct conditions that the mixing coefficients need to satisfy for a valid GMM model.
a. −1≤πi≤1,∀i
b. 0≤πi≤1,∀i
c. ∑iπi=1
d. ∑iπi need not be bounded

Q6. Expectation-Maximization, or the EM algorithm, consists of two steps – E step and the M-step. Using the following notation, select the correct set of equations used at each step of the algorithm.
Notation.
X: Known/Given variables/data
Z: Hidden/Unknown variables
θ: Total set of parameters to be learned
θk: Values of all the parameters after stage k
Q(,): The Q-function as described in the lectures

a. E-step: EZ|X,θ[log(Pr(X,Z|θm))]
b. E-step: EZ|X,θm−1[log(Pr(X,Z|θ))]
c. M-step: argmaxθ∑ZPr(Z|X,θm−2)⋅log(Pr(X,Z|θ))
d. M-step: argmaxθQ(θ,θm−1)
e. M-step: argmaxθQ(θ,θm−2)