Description
Hand in a report that contains both the computer code and the result of the below
question.
1. Generate a training sample of size 1000 from the model
2
1 2 ( ) ( ) 0.3 , T T Y aX aX Z = ++ σ × where σ is the sigmoid function, Z is
standard normal, X=(X1,X2), each Xj being independent standard normal, and
a1=(2,2), a2=(3,-3). Further, generate a test sample of size 1000 from the
same model. Note that this exercise is a regression problem.
a. Plot the surface of responses using function 2
1 2 ( )( ) T T Y aX aX = + σ ,
b. Perform a neural network analysis using both R and Python. Fix the
number of hidden layer as one. Use other options as default.
c. Vary the number of hidden nodes in the hidden layer from 2 up to 10.
d. Plot the training and test error curves as a function of the number of
hidden nodes.
e. Determine the minimum number of hidden nodes needed to perform well
for this task.
f. Are the results of (d) the same for R and Python?
