Boolean functions are perhaps the most basic objects of study in theoretical computer
science. They also arise in other areas of mathematics, including combinatorics, statistical …

In a sparse-representation-based face recognition scheme, the desired dictionary should
have good representational power (ie, being able to span the subspace of all faces) while …

We show that any distribution on {-1,+1\}^n that is k-wise independent fools any halfspace
(or linear threshold function) h:{-1,+1\}^n→{-1,+1\}, ie, any function of the form …

We revisit the fundamental problem of learning with distribution shift, in which a learner is
given labeled samples from training distribution D, unlabeled samples from test distribution …

A function f:D→R is Lipschitz if d_R(f(x),f(y))≦d_D(x,y) for all x,y in D, where d_R and d_D
denote the distance metrics on the range and domain of f, respectively. We initiate the study …

We study the natural question of constructing pseudorandom generators (PRGs) for low-
degree polynomial threshold functions (PTFs). We give a PRG with seed-length log n/εO (d) …

We consider the problem of testing whether an unknown Boolean function f:{-1, 1} n→{-1, 1}
is monotone versus ε-far from every monotone function. The two main results of this paper …

For an n-variate degree-2 real polynomial p, we prove that E x~ D [sig (p (x))] Is determined
up to an additive ε as long as D is a k-wise Independent distribution over {-1, 1} n for k= poly …

We prove a lower bound of Ω (n1/2-c), for all c> 0, on the query complexity of (two-sided
error) non-adaptive algorithms for testing whether an n-variable Boolean function is …

We consider the problem of testing whether an unknown and arbitrary set S⊆ ℝ n (given as
a black-box membership oracle) is convex, versus ε-far from every convex set, under the …