Machine Learning ECE 4332 / ECE 5332 Project 3

Description

1. Generate the data set D as follows:
a. 𝐿𝐿 = 100
b. 𝑁𝑁 = 25
c. 𝑋𝑋 contains samples from a uniform distribution U(0,1).
d. 𝑡𝑡 = sin(2𝜋𝜋𝜋𝜋) + 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
𝑓𝑓(̅𝑥𝑥) = 1
𝐿𝐿�𝑓𝑓(𝑙𝑙)
(𝑥𝑥)
𝐿𝐿
𝑙𝑙=1
(𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏)2 = 1
𝑁𝑁 ��𝑓𝑓̅
�𝑥𝑥(𝑛𝑛)
� − ℎ�𝑥𝑥(𝑛𝑛)
��
2
𝑁𝑁
𝑛𝑛=1
𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣 = 1
𝑁𝑁 �1
𝐿𝐿��𝑓𝑓(𝑙𝑙)
�𝑥𝑥(𝑛𝑛)
� − 𝑓𝑓̅
�𝑥𝑥(𝑛𝑛)
��
2
𝐿𝐿
𝑙𝑙=1
𝑁𝑁
𝑛𝑛=1
5. The test error curve is the average error for a test data set of 1000 points.
Upload your .m or .py file to Blackboard prior to the deadline.
Name your files as Lastname_Firstname_Project3.*