For this homework, do the following things:

1. Compute the following values using the restaurant example.

   1. The *information gain* provided by using the price attribute as the root of the decision tree. Is it more or less valuable than the type or patrons attributes computed in class?

2. In class, we attempted to create by hand a neural network that computes the XOR function. If this was possible, see if you can simplify the network we built. Consider relaxing the conventions of densely-connected, sequential layers. If it was not possible, give a full explanation why it can’t be done.

3. Use Python/NumPy/Pandas/Keras to load and manipulate the Boston Housing Dataset as follows.

   1. Compute the dimensions of the data structures. Include code to print these values.
   2. Construct a suitable testing set, training set, and validation set for this data. Submit code to create these datasets but do not include the datasets themselves.
   3. Create one new synthetic feature that could be useful for machine learning in this domain. Explain what it is and why it might be useful, and submit code to add it to the dataset.

   These homework exercises are rather open-ended. See the guide exercises for examples of what can be done.

Checking in

Submit a Jupyter notebook (homework3.ipynb). We will grade your work according to the following criteria:

• 30% — Information Gain
• 30% — XOR
• 40% — Pandas

See the policies page for homework due-dates and times.