a) Write a program to fit a single hidden layer neural network via back-propagation and weight decay.

b) Apply your program in part a) to the data . Chose Ion.test as the test set, and Ion.trin as the training set. Plot the training and test error curves as a function of the number of epochs for four different values of the weight decay parameter.Discuss the overfitting behavior in each case.

c) Set the value of weight decay equal to zero, then vary the number of hidden units in the network (starting from 1 unit, and determine the minimum number needed to perform well for this task. Plot the training and test error curves as a function of the number of hidden units.

d) Select the best model (the optimum number of hidden nodes or the best value for weight decay) and classify the test data using the network and report the observed misclassification error rate. Construct a 2 by 2 table of the form h_hat(x)=0 h_hat(x)=1y=0 ? ?y=1 ?