8. The decision tree learning algorithm of Figure 7.7 has to stop if it runs out of features and not all examples agree.

Suppose that you are building a decision tree for a Boolean target feature and you have come to the stage where there are no remaining input features to split on and there are examples in the training set, n1 of which are positive and n0 of which are negative. Consider the strategies

(a) Return whichever value has the most examples – return true if n1 > n0, false if n1 < n0, and either if n1 = n0.

(b) Return the empirical frequency, n1/(n0 + n1).

(c) Return (n1 + 1)/(n0 + n1 + 2).
For each of the following objectives predict which of the strategies will have the smallest error on a test set.

(a) Minimize the sum of the absolute differences between the value of the example (
1 = true and 0 = false) and the predicted values in the tree (either 1 = true and 0 = false or the probability).

(b) Minimize the sum of the squares of the differences in values.

(c) Maximize the log-likelihood of the data.
Explain your predictions, test it on some data sets, and report as to whether your prediction holds.