In the recursive construction of
decision trees, it sometimes happens that a mixed set of positive and
negative examples remains at a leaf node, even after all the attributes
have been used. Suppose that we have $p$ positive examples and $n$
negative examples.
1. Show that the solution used by DECISION-TREE-LEARNING, which picks the majority classification, minimizes the absolute error over the set of examples at the leaf.
2. Show that the class probability $p/(p+n)$ minimizes the sum of squared errors.
1. Show that the solution used by DECISION-TREE-LEARNING, which picks the majority classification, minimizes the absolute error over the set of examples at the leaf.
2. Show that the class probability $p/(p+n)$ minimizes the sum of squared errors.
In the recursive construction of
decision trees, it sometimes happens that a mixed set of positive and
negative examples remains at a leaf node, even after all the attributes
have been used. Suppose that we have $p$ positive examples and $n$
negative examples.
1. Show that the solution used by DECISION-TREE-LEARNING, which picks the majority
classification, minimizes the absolute error over the set of
examples at the leaf.
2. Show that the class probability $p/(p+n)$ minimizes the sum of squared errors.