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We want to PAC-learn a variant of decision lists formed by a set of if-then-rules as follows: " (if ₁ then (2) else (if (3 then (4) else (if (5 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: V1 V2 V3 V4 V5 y x1: 1 1 1 0 0 1 ¬01 V2 03 x2: 0 10 10 1 x3: 1 0 1 1 0 1 x4: 10000 0 04 ¬05 X5: x5 0 100 1 0 11000 1 (a) Describe a polynomial-time algorithm that either returns a consistent hypothesis or guarantees no such hypothesis exists. Explain the run-time of the algorithm. (b) Count the number of possible hypotheses and use your result to find an upper bound for the sample complexity for PAC-learning the formula with parameters € and 8.

We want to PAC-learn a variant of decision lists formed by a set of if-then-rules as follows: " (if ₁ then (2) else (if (3 then (4) else (if (5 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: V1 V2 V3 V4 V5 y x1: 1 1 1 0 0 1 ¬01 V2 03 x2: 0 10 10 1 x3: 1 0 1 1 0 1 x4: 10000 0 04 ¬05 X5: x5 0 100 1 0 11000 1 (a) Describe a polynomial-time algorithm that either returns a consistent hypothesis or guarantees no such hypothesis exists. Explain the run-time of the algorithm. (b) Count the number of possible hypotheses and use your result to find an upper bound for the sample complexity for PAC-learning the formula with parameters € and 8.

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We want to PAC-learn a variant of decision lists formed by a set of if-then-rules as follows: " (if ₁ then (2) else (if (3 then (4) else (if (5 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: V1 V2 V3 V4 V5 y x1: 1 1 1 0 0 1 ¬01 V2 03 x2: 0 10 10 1 x3: 1 0 1 1 0 1 x4: 10000 0 04 ¬05 X5: x5 0 100 1 0 11000 1 (a) Describe a polynomial-time algorithm that either returns a consistent hypothesis or guarantees no such hypothesis exists. Explain the run-time of the algorithm. (b) Count the number of possible hypotheses and use your result to find an upper bound for the sample complexity for PAC-learning the formula with parameters € and 8.
Transcribed Image Text:We want to PAC-learn a variant of decision lists formed by a set of if-then-rules as follows: " (if ₁ then (2) else (if (3 then (4) else (if (5 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: V1 V2 V3 V4 V5 y x1: 1 1 1 0 0 1 ¬01 V2 03 x2: 0 10 10 1 x3: 1 0 1 1 0 1 x4: 10000 0 04 ¬05 X5: x5 0 100 1 0 11000 1 (a) Describe a polynomial-time algorithm that either returns a consistent hypothesis or guarantees no such hypothesis exists. Explain the run-time of the algorithm. (b) Count the number of possible hypotheses and use your result to find an upper bound for the sample complexity for PAC-learning the formula with parameters € and 8.
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