Introduction
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 (10 points)
Let xi : i = 1,...,p be the input predictor values and be 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.
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