We show that for low-density parity-check (LDPC) codes whose Tanner graphs have sufficient expansion, the linear programming (LP) decoder of Feldman, Karger, and Wainwright can correct a constantâ€¦ (More)

A broad class of boosting algorithms can be interpreted as performing coordinate-wise gradient descent to minimize some potential function of the margins of a data set. This class includes AdaBoost,â€¦ (More)

We propose and analyze a new vantage point for the learning of mixtures of Gaussians: namely, the PAC-style model of learning probability distributions introduced by Kearns et al. [12]. Here the taskâ€¦ (More)

2009 50th Annual IEEE Symposium on Foundations ofâ€¦

2009

We show that any distribution on $\pmo^n$ that is $k$-wise independent fools any halfspace (a.k.a.~threshold) $h : \pmo^n \to \pmo$, i.e., any function of the form $h(x) = \sign(\sum_{i = 1}^n w_iâ€¦ (More)

In this article we develop quantum algorithms for learning and testing juntas, i.e. Boolean functions which depend only on an unknown set of k out of n input variables. Our aim is to developâ€¦ (More)

We describe a general method for testing whether a function on n input variables has a concise representation. The approach combines ideas from the junta test of Fischer et al. 16 with ideas fromâ€¦ (More)