JUST C

Agnostic learning of conjunctions first cut. In lecture, we saw the Elimination Al- gorithm for learning conjunctions in the standard (realizable) PAC-learning model. In this problem, we will develop and analyze an algorithm for learning conjunctions in the agnostic learning model with some limited tolerance to adversarial noise. Specifically, we will develop a polynomial-time algorithm such that if there is some conjunction c* such that for the target concept c, Prepc(x) = c*(z)] 1-e, then our algorithm produces a conjunction h such that PrreD()h(x)] 2 1 - O(ne) with confidence 1 - 6 where there are n attributes t consider the following "tolerant" version of the Elimination Algorithm deletes a Use the multiplicative fo determine how many examples we m h if E(z) 0 and c(2) e Chernoff of the m examples earns & Vazirani, Theorem 9.2) to hat with probability 1-, 1 is deleted 1 on more ess (c) Specify values of and m and prove that the tolerant Elimination Algorithm produces a final hypothesis with error at most O(ne) with confidence 1- for these parameters given only that some c* achieves an error rate of at most E. (Hint. To choose consider the following. Suppose that we now say that a literal is "bad" if Pr|EDIE(x) = 0 and c(x)-1] > 2. What is the error if no literals are "bad?" When is it safe to eliminate a literal?) Agnostic learning of conjunctions first cut. In lecture, we saw the Elimination Al- gorithm for learning conjunctions in the standard (realizable) PAC-learning model. In this problem, we will develop and analyze an algorithm for learning conjunctions in the agnostic learning model with some limited tolerance to adversarial noise. Specifically, we will develop a polynomial-time algorithm such that if there is some conjunction c* such that for the target concept c, Prepc(x) = c*(z)] 1-e, then our algorithm produces a conjunction h such that PrreD()h(x)] 2 1 - O(ne) with confidence 1 - 6 where there are n attributes t consider the following "tolerant" version of the Elimination Algorithm deletes a Use the multiplicative fo determine how many examples we m h if E(z) 0 and c(2) e Chernoff of the m examples earns & Vazirani, Theorem 9.2) to hat with probability 1-, 1 is deleted 1 on more ess (c) Specify values of and m and prove that the tolerant Elimination Algorithm produces a final hypothesis with error at most O(ne) with confidence 1- for these parameters given only that some c* achieves an error rate of at most E. (Hint. To choose consider the following. Suppose that we now say that a literal is "bad" if Pr|EDIE(x) = 0 and c(x)-1] > 2. What is the error if no literals are "bad?" When is it safe to eliminate a literal?)