Probably Approximately Correct Learning Yongsub Lim Applied Algorithm Laboratory KAIST

Definition A class is PAC learnable by a hypothesis class if  there is an algorithm such that  over , # of i.i.d. training examples sampled from, such that where is an output of Probably Approximately Correct Learning2

Example Consider the class space which is the set of all positive half-lines An example is any real number Eg) Probably Approximately Correct Learning 1 0 3

Proof. is PAC learnable is PAC learnable by Probably Approximately Correct Learning4

Proof. is PAC learnable Our algorithm outputs a hypothesis such that Suppose  for a positive example  for a negative example Probably Approximately Correct Learning5

Proof. is PAC learnable Suppose, and it called  only occurs if no training example     Probably Approximately Correct Learning6

Proof. is PAC learnable Probably Approximately Correct Learning7

Proof. is PAC learnable Probably Approximately Correct Learning8

Proof. is PAC learnable The class is PAC learnable by itself with at least training examples Probably Approximately Correct Learning9

A More General Theorem Probably Approximately Correct Learning10

Thanks Probably Approximately Correct Learning 11