Single-index models are a class of functions given by an unknown univariate``link''function
applied to an unknown one-dimensional projection of the input. These models are …

We consider neural networks with a single hidden layer and non-decreasing positively
homogeneous activation functions like the rectified linear units. By letting the number of …

We propose a new and simple framework for dimension reduction in the large p, small n
setting. The framework decomposes the data into pieces, thereby enabling existing …

Single-Index Models are high-dimensional regression problems with planted structure,
whereby labels depend on an unknown one-dimensional projection of the input via a …

Let (X, Y) be a random pair taking values in Rp× R. In the so-called single-index model, one
has Y= f⋆(θ⋆ TX)+ W, where f⋆ is an unknown univariate measurable function, θ⋆ is an …

We study active learning methods for single index models of the form $ F ({\bm x})= f (⟨{\bm
w},{\bm x}⟩) $, where $ f:\mathbb {R}\to\mathbb {R} $ and ${\bx,\bm w}\in\mathbb {R}^ d $. In …

Polynomial regression is a basic primitive in learning and statistics. In its most basic form the
goal is to fit a degree $ d $ polynomial to a response variable $ y $ in terms of an $ n …

We consider regression problems where the response is a smooth but non-linear function of
a $ k $-dimensional projection of $ p $ normally-distributed covariates, contaminated with …

We investigate the distributional extension of the-plane transform in and of related operators.
We parameterize the-plane domain as the Cartesian product of the Stiefel manifold of …

We study the power of query access for the task of agnostic learning under the Gaussian
distribution. In the agnostic model, no assumptions are made on the labels and the goal is to …