Introduction to Machine Learning: Assignment 5

1. Which of the following are false?

a. If a linear separable decision boundary exists for a classification problem, the perceptron model
is capable of finding it
b. One perceptron can be trained with zero training error for an XOR function
c. The backpropagation algorithm updates the parameters using gradient descent rule
d. While training a neural network for binary classification task, an ideal choice for the initialization
of parameters should be large random numbers so that the gradient is higher

Ans: b and d

2. For training a binary classification model with three independent variables, you choose to
use neural networks. You apply one hidden layer with four neurons. What are the number of parameters to be estimated? (Consider the bias term as a parameter)

a. 16
b. 21
c. 3^4 = 81
d. 4^3 = 64
e. 12
f. 4
g. None of these

Ans: e

3. Consider the following function f(x) = exp(x)/(1+exp(x))
The derivative f '(x) will be:

Ans: f(x).ln(1-f(x))

4. Suppose the marks obtained by randomly sampled students follow a normal distribution with
unknown . A random sample of 5 marks are 30, 50, 69, 23 and 99. Using the given samples find the maximum likelihood estimate for the mean

a. 54.2
b. 67.75
c. 50
d. Information not sufficient for estimation

Ans: b

5. Some points are sampled from a Probability distribution following the given probability
distribution function Gaussian with variance x
where x > 0 and m > 0. The collected points are 10, 12, 16, 14 and 15. Give the maximum
likelihood estimate for m.
a. 13.4
b. 13.02
c. 14
d. 20
e. None of these

Ans: b

6. We have a function which takes a two-dimensional input x=(x1,x2) and has two parameters w=(w1,w2) given by f(x)=                      where sigma(x)1 /(1+exp(-x)). We use back propagation to
estimate the right parameter values.
We start by setting both the parameters to 1. Assume that we are given a training point . Given this information answer the next two questions. What is the value of  derivative of f w.r.t w2?

a. 0.098
b. 0.693
c. 0.143
d. -0.367

Ans: b

7. In the previous question, if the learning rate is 0.5, what will be the value of after one
update using backpropagation algorithm?

a. -0.4423
b. 0.4423
c. 1.62
d. 0.381

Ans: b

8. Which of the following is NOT a valid conjugate prior?

a. Gaussian - Gaussian
b. Beta - Binomial
c. Binomial - Bernoulli
d. Beta - Bernoulli

Ans: c