# CS322 Fall 1999Module 11 (Decision Tree Learning)

## Question 1

In electronic commerce applications we want to make predictions about what a user will do. Consider the following made-up data used to predict whether someone will ask for more information (more_info) based on whether they accessed from an educational domain (edu), whether this is a first visit (first), whether they have bought goods from an affiliated company (bought), and whether they have visited a famous online information store (visited).
 Example bought edu first visited more_info e1 false true false false true e2 true false true false false e3 false false true true true e4 false false true false false e5 false false false true false e6 true false false true true e7 true false false false true e8 false true true true false e9 false true true false false e10 true true true false true e11 true true false true true e12 false false false false true
We want to use this data to learn the value of more_info as a function of the values of the other variables.

Suppose we measure the error of a decision tree as the number of misclassified examples. The optimal decision tree from a class of decision trees is an element of the class with minimal error.

1. Give the optimal decision tree with only one node. What is the error of this tree?
2. Give the optimal decision tree of depth 2 (i.e., the root node is the only node with children). For each node in the tree give the examples that are filtered to that node. What is the error of this tree?
3. Give the decision tree that is produced by the top-down induction algorithm run to completion, where we split on the attribute that reduces the error the most. For each node in the tree specify which examples are filtered to that node. As well as drawing the tree, give the tree in the format of question 2 of assignment 7 (i.e., in terms of if(Att,Then,Else)).
4. Give two instances that don't appear in the examples above and show how they are classified. Use this to explain the bias inherent in the tree (how does the bias give you these particular predications?).
5. How can overfitting occur in the learned network? Explain in terms of this example.

## Question 2

For each question in this assignment, say how long you spent on it. Was this reasonable? What did you learn?

David Poole