PAC Learning Decision Lists Step by step Solution with Explanation

Your question:

We want to PAC-learn a variant of decision lists formed by a set of if-then-rules as follows: " (if l₁ then (2) else (if 13 then (4) else (if 15 then (6)... else (if lk then (k+1)"

Assume literals of each variable appear in the formula at most once. For example, the following is a hypothesis that is consistent with the following table:

PAC Learning Decision Lists Answers and Explanation

Here's a polynomial-time algorithm that either returns a consistent hypothesis or guarantees no such hypothesis exists:

1. Initialize:
2. • • Iterate through the hypotheses h in H:

       • If h(x) doesn't match y, remove h from H.

• In the worst case, the algorithm iterates through all training samples and all possible hypotheses.

• The number of training samples is denoted by |S|.

(b) Counting the number of possible hypotheses is crucial to determine the sample complexity for PAC learning.

1. Number of possible single rules:

2. • Each hypothesis is a sequence of at most k single rules (one for each variable).

   • For the first rule, we have 2 * k choices.

Sample Complexity Bound

Given sample complexity:

m>ln+2kln(2k)−2k

Therefore, the updated sample complexity expression, changing nnn to kkk, would be: