In this paper we study the problem of learning Rectified Linear Units (ReLUs) which are
functions of the form $\vct {x}\mapsto\max (0,\langle\vct {w},\vct {x}\rangle) $ with $\vct …

This paper explores the implicit bias of overparameterized neural networks of depth greater
than two layers. Our framework considers a family of networks of varying depths that all have …

We consider a non-linear generalization of low-rank matrix completion to the case where the
data belongs to an algebraic variety, ie, each data point is a solution to a system of …

In this paper, we aim to estimate the direction of an underlying signal from its nonlinear
observations following the semi-parametric single index model (SIM). Unlike for …

We study the monotone single index model where a real response variable $ Y $ is linked to
a $ d $-dimensional covariate $ X $ through the relationship $ E [Y| X]=\Psi_ {0}(\alpha^{T} …

We consider the problem of active learning for single neuron models, also sometimes called
“ridge functions”, in the agnostic setting (under adversarial label noise). Such models have …

The problem of statistical inference for regression coefficients in a high-dimensional single-
index model is considered. Under elliptical symmetry, the single index model can be …

We consider estimation and inference in a single-index regression model with an unknown
convex link function. We introduce a convex and Lipschitz constrained least-square …

We study the problem of demixing a pair of sparse signals from noisy, nonlinear
observations of their superposition. Mathematically, we consider a nonlinear signal …

In this paper, we study phase retrieval under model misspecification and generative priors.
In particular, we aim to estimate an $ n $-dimensional signal $\mathbf {x} $ from $ m $ iid …