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This lecture presents a polynomial-time algorithm based on boosting for learning DNF formulas to arbitrary precision. The algorithm is due to Jackson [1]. 14.1 Preliminaries Let f = T1 ∨ T2 ∨ · · · ∨ Ts be a Boolean function in DNF on n variables. One of T1, T2,..., Ts must be true on at least 1/s of the satisfying assignments to f; denote some such term by T. The analysis below treats f and T as Boolean functions from {−1, 1} n to {−1, 1}; we denote by f {0,1} and T {0,1} their counterparts from {−1, 1} n to {0, 1}. Let D be an arbitrary distribution over {−1, 1} n. We start by relating E D [f] and E D Thus, E [f] = −1 · Pr[f = −1] + 1 · Pr[

Year: 2009

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