## Description

Problem Statement Consider a set of examples with two classes and distributions as

in Figure 1. Given the vector x ∈ R

2

infer its target class t ∈ {0, 1}. As a model

use a multi-layer perceptron f which returns an estimate for the conditional

density p(t = 1 | x):

f : R

2 → [0, 1] (1)

parametrisized by some set of values θ. All of the examples in the training set

should be classified correctedly (i.e. p(t = 1 | x) > 0.5 if and only if t = 1).

Impose an L

2 penalty on the set of parameters. Produce one plot. Show the

examples and the boundary corresponding to p(t = 1 | x) = 0.5. The plot must be

of suitable visual quality. It may be difficult to to find an appropriate functional

form for f, write a few sentences discussing your various attempts.

−10 −5 0 5 10

−15

−10

−5

0

5

10

15

Spirals

Figure 1: Sample spiral data.