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.
