Problem Statement Consider a set of examples with two classes and distributions as
009010 in Figure 1. Given the vector x ∈ R2 infer its target class t ∈ {0,1}. As a model 011 use a multi-layer perceptron f which returns an estimate for the conditional 012 density p(t = 1 | x):
013 2
014 f : R → [0,1] (1)
015 parametrisized by some set of values θ. All of the examples in the training set
016
should be classified correctedly (i.e. p(t = 1 x) 0.5 if and only if t = 1).
017 |
018 Impose an L2 penalty on the set of parameters. Produce one plot. Show the
019 examples and the boundary corresponding to p(t = 1 | x) = 0.5. The plot must be
020
021 of suitable visual quality. It may be difficult to to find an appropriate functional 022 form for f, write a few sentences discussing your various attempts.
023
024
025 15
026
027
028 10
029
030
031 5
032
033
034 0
035
036
037 −5
038
039
040 −10
041
042
043 −15
044 −10 −5 0 5 10
045
046 Figure 1: Sample spiral data.
047
