[Solved] STATS202 Homework4

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 (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 (a) and tanh(a). Then show that the parameters of the two networks differ by linear transformations.