ECE 4332 Project 3 Solved

1.      Generate the data set D as follows:

a.       𝐷𝐷 = 100

b.      𝑁𝑁 = 25

c.       𝑋𝑋 contains samples from a uniform distribution U(0,1).

d.      𝑡𝑡 = sin(2𝜋𝜋𝑋𝑋) + 𝜀𝜀, where 𝜀𝜀 contains samples from a Gaussian distribution N(0, 𝜎𝜎 =0.3).

2.      Select a set of permissible values for the regularization parameter 𝜆𝜆.

3.      For each value of 𝜆𝜆, use the method of “linear regression with non-linear models” to fit Gaussian basis functions to each of the datasets. Use 𝑠𝑠 = 0.1.

4.      Produce the plot as shown below, where

𝐷𝐷

1

𝑓𝑓(̅ 𝑥𝑥) = 𝑓𝑓(𝑑𝑑)(𝑥𝑥)

𝐷𝐷

𝑑𝑑=1

𝑁𝑁

1

                                                            (𝑏𝑏𝑏𝑏𝑏𝑏𝑠𝑠)2 = 𝑓𝑓𝑥𝑥̅ (𝑛𝑛)− ℎ𝑥𝑥(𝑛𝑛)2

𝑁𝑁

𝑛𝑛=1

                                                                                     𝑁𝑁            𝐷𝐷

                                                                                1        1

                                      𝑣𝑣𝑏𝑏𝑣𝑣𝑏𝑏𝑏𝑏𝑣𝑣𝑣𝑣𝑣𝑣 =                            𝑓𝑓(𝑑𝑑)𝑥𝑥(𝑛𝑛)− 𝑓𝑓𝑥𝑥̅   (𝑛𝑛)2

𝑁𝑁       𝐷𝐷 𝑛𝑛=1 𝑑𝑑=1

5. The test error curve is the average error for a test data set of 1000 points.