[SOLVED] ECE 4332/5332  Project 3

1. Generate the data set _D as follows:
   1. 𝐷𝐷 = 100
   2. 𝑁𝑁 = 25
   3. 𝑋𝑋 contains samples from a uniform distribution _U(0,1).
   4. 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.