Errata

This submission is to correct/clarify the errata submission by Adler Santos on Oct 25, 2015. The reader proposed a correction to the information gain equation, which was adopted by the author, but the original equation is correct.

When calculating information gain, each "probability" is the proportion of instances belonging to each child. There are 13 instances in the child "Balance < 50K" and 30 instances in the parent, so p(Balance < 50K) = 13/30 = 0.43. There are 17 instances in the other child, so p(Balance >= 50K) = 17/30 = 0.57.

On the left side of the tree (after the OVERAGE attribute test), the attribute LEFTOVER appears twice as an interior node. On the right side of the tree (after the INCOME attribute test), the attribute OVERAGE appears twice as an interior node. Are these repeated attributes supposed to be other attributes?

On a different note: In Figure 3-10 and Figure 3-15, the interior nodes are rectangular and the terminal nodes are oval, while in Figure 3-18 and Figure 4-12, it is the opposite. I don't know if there is a standard in the industry, but it would be nice to see consistency in the tree representations to help with learning the basic concepts.

Hi,

"Overall, the (b) tree will have a total expected error rate of 30%..."

The accuracy of the tree in (b) appears to be 5/8, so the error rate should be 3/8=37.5%. To see this, the possible correct classifications and their probabilities are:

(C1,p,r) = 1/2 x 3/4 x 1/2 = 3/16 (correct C1 classification)
(C2,p,s) = 1/2 x 1/4 x 1/2 = 1/16 (correct C2 classification)
(C2,q, r or s) = 1/2 x 3/4 = 6/16 (correct C2 classification)

So the accuracy is 10/16, i.e., the error rate is 6/16=3/8=37.5%.

The previous statement about the spurious branch causing "one in eight errors made by the tree" also appears to be incorrect. The spurious branch causes an error when (C1,p,s) occurs, which happens with probability 3/16. So one out of two errors made by the tree are caused by the spurious branch.

The expected profit calculation assumes that we do not send the offer if the prediction is "No" (figure 7-4). However, the 99-1 payoff ratio is so great that it is optimal to send the offer to everybody for an expected value of 54.4. I recommend the use of a decision tree to explain this example.