On Learning Ring-Sum-Expansions

What Can We Learn Privately?

“…In this section, we present an efficient private PAC learning algorithm for PARITY. The standard (non-private) PAC learner for PARITY [24,21] looks for the hidden vector r by solving a system of linear equations imposed by examples (x i , c r (x i )) that the algorithm sees. It outputs an arbitrary vector consistent with the examples, i.e., in the solution space of the system of linear equations.…”

On Exact Learning from Random Walk

“…developed efficient algorithms for exact learning boolean threshold functions, 2-term RSE, and 2-term DNF in the RWOnline model. Those classes are already known to be learnable in the Online model [L87,FS92], but the algorithms in [BFH95] achieve a better mistake bound (for threshold functions).…”

“…developed efficient algorithms for exact learning boolean threshold functions, 2-term Ring-Sum Expansion (parity of 2 monotone terms) and 2-term DNF in the RWOnline model. Those classes are already known to be learnable in the Online model [L87,FS92] (and therefore in the RWOnline model), but the algorithm in [BFH95] for boolean threshold functions achieves a better mistake bound. They show that this class can be learned by making no more than n + 1 mistakes in the RWOnline model, improving on the O(n log n) bound for the Online model proven by Littlestone in [L87].…”

Untitled

“…This algorithm is composed of an algorithm for learning parity functions (Fischer & Simon, 1992;Helmbold, Sloan, & Warmuth, 1992) by solving a system of linear equations over the field of integers modulo 2, and a self-correcting algorithm (Blum, Luby, & Rubinfeld, 1993;Lipton, 1991) for the same family of functions. We do not know of any other self-correcting algorithm that has been directly applied to a related learning problem, but the possibility exists that techniques used in one field may be useful in the other.…”