STATS202 Homework4 Solved

Description

Homework problems are selected from the course textbook: An Introduction to Statistical Learning.

Problem 1 

Chapter 8, Exercise 4 (p. 332).

Problem 2 

Chapter 8, Exercise 8 (p. 333).

Problem 3 

Chapter 8, Exercise 10 (p. 334).

Problem 4 

Chapter 8, Exercise 11 (p. 335).

Problem 5

Let x_i : i = 1,…,p be the input predictor values andbe the K-dimensional output from a 2-layer and M-hidden unit neural network with sigmoid activation σ(a) = {1 + e^−a}⁻¹ such that

Show that there exists an equivalent network that computes exactly the same output values, but with hidden unit activation functions given by, i.e.

Hint: first derive the relation between σ(a) and tanh(a). Then show that the parameters of the two networks differ by linear transformations.