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yaser · #2 02-15-2015, 07:52 PM

Here are the old homework problems (not required in this course, and there is no technical support).

$\bullet$ Backpropagation:

Following the class notes, implement the backpropagation algorithm
that takes as input a network architecture ( $d^{(0)} = d , d^{(1)} , d^{(2)} , ... , d^{(L)} =1$ )
and a set of examples $({\bf x}_1 , y_1) , ... , ({\bf x}_N , y_N)$ where
${\bf x}_n \in {\mathbb R}^d$ and $y \in {\mathbb R}$ , and produces as output the network weights.
The algorithm should perform gradient descent on one example at a time,
but should also keep track of the average error for all the examples in
each epoch. Try your algorithm on the data set in

http://work.caltech.edu/train.dat

(the first two columns are the input and the third column is the output).
Test the convergence behavior for architectures with one hidden layer
(

) and 1 to 5 neurons ( $d^{(1)}=1,2,3,4,5$ ), with combinations of the following
parameters:

(i) The initial weight values chosen independently and randomly
from the range (-0.02,0.02), the range (-0.2,0.2), or the range (-2,2).

(ii) The learning rate $\eta$ fixed at

,

or

.

(iii) Sufficient number of epochs to get the training error
to converge (within reason).

Turn in your code and a single parameter combination that resulted
in good convergence for the above architectures.

$\bullet$ Generalization:

Using your backpropagation program and data from the above problem, train different
neural networks with

(an input layer, one `hidden' layer, and an
output layer) where the number of neurons in the hidden layer is 1, 2, 3, 4, or 5.
Use the following out-of-sample data to test your networks:

http://work.caltech.edu/test.dat

Plot the training and test errors for each network as a function of
the epoch number (hence the `intermediate' networks are evaluated using the
test data, but the test data is not used in the backpropagation).
Repeat the experiment by reversing the roles of the training and test
sets (you may need to readjust the parameter combination from the previous problem), and plot
the training and test errors again. Briefly analyze the results you get.