INTRODUCTION TO MACHINE LEARNING Week 11
Session: JAN-APR 2023
Course Name: Introduction to Machine Learning
Course Link: Click Here
These are Introduction to Machine Learning Week 11 Assignment 11 Answers
Q1. Given n samples x1,x2,…,xN drawn independently from an Exponential 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
Answer: c. λMLE=n∑ni=1xi
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
Answer: c. pMLE=n/∑ni=1xi
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
Answer: e. p,p(p+1)/2
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
Answer: d. λMLE=∑ni=1xi/n
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
Answer: b, c
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)
Answer: b, d
These are Introduction to Machine Learning Week 11 Assignment 11 Answers
More Weeks of Introduction to Machine Learning: Click Here
More Nptel courses: https://progiez.com/nptel
