We show a directed and robust analogue of a boolean isoperimetric-type theorem of
Talagrand Geom. Funct. Anal., 3 (1993), pp. 295--314. As an application, we give a …

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 …

We prove a lower bound of Ω (n 1/3) for the query complexity of any two-sided and adaptive
algorithm that tests whether an unknown Boolean function f:{0, 1} n→{0, 1} is monotone …

The problem of monotonicity testing over the hypergrid and its special case, the hypercube,
is a classic question in property testing. We are given query access to f:[k] n-> R (for some …

We show that every algorithm for testing n-variate Boolean functions for monotonicityhas
query complexity Ω (n 1/4). All previous lower bounds for this problem were designed for …

We give a 2^̃O(n/ε)-time algorithm for properly learning monotone Boolean functions under
the uniform distribution over {0,1\}^n. Our algorithm is robust to adversarial label noise and …

We initiate a systematic study of sublinear algorithms for approximately testing properties of
real-valued data with respect to L p distances for p= 1, 2. Such algorithms distinguish …

We design a nonadaptive algorithm that, given oracle access to a function which is‐far from
monotone, makes poly queries and returns an estimate that, with high probability, is an …

The problem of testing monotonicity for Boolean functions on the hypergrid, f:[n] d→{0, 1} is a
classic topic in property testing. When n= 2, the domain is the hypercube. For the hypercube …

We show how the communication complexity method introduced in (Blais, Brody, Matulef
2012) can be used to prove lower bounds on the number of queries required to test …