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This exercise considers $\chi^2$ pruning of decision trees (Section chi-squared-section
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  1. Create a data set with two input attributes, such that the information gain at the root of the tree for both attributes is zero, but there is a decision tree of depth 2 that is consistent with all the data. What would $\chi^2$ pruning do on this data set if applied bottom up? If applied top down?

  2. Modify DECISION-TREE-LEARNING to include $\chi^2$-pruning. You might wish to consult Quinlan [Quinlan:1986] or [Kearns+Mansour:1998] for details.