Module 12 (Neural Network Learning)

The following is the same data from assignment 11:

We want to use this data to learn the value of

Example boughtedufirstvisitedmore_infoe_{1}false true false false true e_{2}true false true false false e_{3}false false true true true e_{4}false false true false false e_{5}false false false true false e_{6}true false false true true e_{7}true false false false true e_{8}false true true true false e_{9}false true true false false e_{10}true true true false true e_{11}true true false true true e_{12}false false false false true

In this assignment we will consider neural network learning for this data. We have a Java applet and a CILog program that can be used to answer this assignment.

- Consider neural network learning with no hidden layers. After the network has converged, what are the parameter values? What is the Boolean function that the network represents? Are all the training examples classified correctly (if not, which aren't)? Give two examples, not in the training set, and specify what the predicted values is.
- Consider neural network learning with one hidden layer containing two variables. After the network has converged, what are the parameter values? What is the Boolean function that the network represents? Are all the training examples classified correctly (if not, which aren't)? Give two examples, not in the training set, and specify what the predicted values is.
- For the network with a hidden layer what is a local minima of
the learning rate (within one decimal point)? The value to minimize is
the number of steps before the error gets below 1.0. Hint: there is a local
minima in the range
*[0.3,7.0]*.

- Consider neural network learning with no hidden layers.
- After
the network has converged, what are the parameter values?
After 200 iterations with a learning rate of 0.5 the parameter values are:

Parameter Parent Value *w*_{0}1.58 *w*_{4}bought 3.96 *w*_{3}edu 3.52 *w*_{2}first *-7.42**w*_{1}visited *-3.40* - What is the
Boolean function that the network represents?
When

*first*is true, the value of the linear expression is negative unless*bought*and*edu*are true and*visited*is false.When

*first*is false, the value of the linear expression is positive unless*bought*and*edu*are false and*visited*is true.This can be written as the decision tree:

So the boolean expression is:

*(first &bought &edu ¬ visited) or**(not first &bought) or**(not first &edu) or**(not first ¬ visited)*. - Are all the training
examples classified correctly (if not, which aren't)?
No.

*e3*is misclassified. The neural network classifies it as false. - Give two
examples, not in the training set, and specify what the predicted
values is.
The following

*bought**edu**first**visited**more_info*true true true true false true true false false true true false true true false false true false true true

- After
the network has converged, what are the parameter values?
- Consider neural network learning with one hidden layer
containing two variables.
- After
the network has converged, what are the parameter values?
run the applet....

- What is the
Boolean function that the network represents?
After 200 iterations with learning rate of 0.5, we can have the following table:

*bought**edu**first**visited**more_info*true true true true false true true true false true true true false true true true true false false true true

false true true false true false true false false true false false true true true false false false true false

true true true false false true true false false false true false true true false true false false true false

false true true false false false true false false false false false true false false false false false true This represents the same Boolean function as part (a).

- Are all the training
examples classified correctly (if not, which aren't)?
Again e3 is misclassified.

- Give two examples, not in the training set, and specify what the predicted values is.

- After
the network has converged, what are the parameter values?
- For the network with a hidden layer what is a local minima of
the learning rate (within one decimal point)? The value to minimize is
the number of steps before the error gets below 1.0. Hint: there is a local
minima in the range
*[0.3,7.0]*.There is local minimum at 1.7 or 1.8 (with 42 iterations), another at 2.7 (with 33 iterations) and another at 3.0 (with 34 iterations).

David Poole