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# Homework 3: Using Backprop for a regression task

[Points: 10; Issued: 2003/03/14; Deadline: 2003/04/04; Tutor: Martin Ebner; Infohour: 2003/04/02, 14:00-15:00, Seminarraum IGI; Einsichtnahme: 2003/05/14, 14:00-15:00, Seminarraum IGI; Download: pdf; ps.gz]

This homework assignment asks you to apply backprop to a regression problem: the Boston Housing data set. The file housing.zip contains the data as the file `housing.mat`. See the file `housing-description.txt` which is also contained in `housing.zip` for more information on the data set.

1. Initialize the random number generator using the Matlab commands `rand('state',<MatrNmr>);` and `randn('state',<MatrNmr>);`.
2. Split the data randomly into a training set (2/3) and a test set (1/3) (use the function `randperm`).
3. Normalize the data such that each attribute has a zero mean and a variance of 1 (use the function `prestd`).
4. Train a 2 layer feed forward network with 2 hidden units and one output unit on the training set (use proper activation functions at each layer) for `net.trainParam.epochs`=150 epochs and the training function `trainbfg`1 with standard parameters. Describe how the error on the training and on the test set changes with the number of epochs.
5. Investigate how the error on the test set changes if one uses only the first 10%, 20%, 50%, or 75% of the set for training (same network as in 3). In particular create a plot which shows how the error on the test set after 150 epochs depends on the size (10%, ..., 100%) of the training set. Interpret the resulting plot.
6. Repeat step 5) but with a network with 20 hidden units.
7. Compare the results obtained in 5) and 6).

### Remarks

• Present your results clearly, structured and legible. Document them in such a way that anybody can reproduce them effortless.
• Please hand in the print out of the Matlab program you have used.

#### Fußnoten

... `trainbfg`1
trainbfg is an enhanced gradient descent method which usually converges faster than the default backprop algorithm.