In this expository note, we give a modern proof of Hanson-Wright inequality for quadratic
forms in sub-gaussian random variables. We deduce a useful concentration inequality for …

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 give two different and simple constructions for dimensionality reduction in ℓ 2 via linear
mappings that are sparse: only an O (ε)-fraction of entries in each column of our embedding …

We study the task of agnostically learning halfspaces under the Gaussian distribution.
Specifically, given labeled examples $(\\mathbf {x}, y) $ from an unknown distribution on …

We give the first dimension-efficient algorithms for learning Rectified Linear Units (ReLUs),
which are functions of the form $\mathbf {x}\mapsto\mathsf {max}(0,\mathbf {w}⋅\mathbf {x}) …

We study the fundamental problems of agnostically learning halfspaces and ReLUs under
Gaussian marginals. In the former problem, given labeled examples $(\bx, y) $ from an …

We study the problem of agnostic learning under the Gaussian distribution in the Statistical
Query (SQ) model. We develop a method for finding hard families of examples for a wide …

We give the first statistical-query lower bounds for agnostically learning any non-polynomial
activation with respect to Gaussian marginals (eg, ReLU, sigmoid, sign). For the specific …

We give the first polynomial-time algorithm for the testable learning of halfspaces in the
presence of adversarial label noise under the Gaussian distribution. In the recently …

A remarkable recent paper by Rubinfeld and Vasilyan (2022) initiated the study of testable
learning, where the goal is to replace hard-to-verify distributional assumptions (such as …