Sample Assignment on  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 DT algorithm discussed in class, 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 growing the tree, give a logical representation of the tree using the prop predicate, as we did in class.
  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
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