Consider estimating an unknown, but structured (eg sparse, low-rank, etc.), signal $ x_0\in
R^ n $ from a vector $ y\in R^ m $ of measurements of the form $ y_i= g_i (a_i^ Tx_0) …

It is known that for a certain class of single index models (SIMs) Y= f (X p× 1T β0, ε), support
recovery is impossible when X∼ N (0; I p× p) and a model complexity adjusted sample size …

We study the problem of recovering an unknown signal x given measurements obtained
from a generalized linear model with a Gaussian sensing matrix. Two popular solutions are …

We study high-dimensional signal recovery from non-linear measurements with design
vectors having elliptically symmetric distribution. Special attention is devoted to the situation …

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

Existing nonconvex statistical optimization theory and methods crucially rely on the correct
specification of the underlying “true” statistical models. To address this issue, we take a first …

We consider estimating the parametric components of semiparametric multi-index models in
high dimensions. To bypass the requirements of Gaussianity or elliptical symmetry of …

We develop adaptive estimation and inference methods for high-dimensional Gaussian
copula regression that achieve the same optimality without the knowledge of the marginal …

A single-index model is given by y= g*(< x, θ*>)+ ε: The scalar response y depends on the
covariate vector x both through an unknown (vector) parameter θ* as well as an unknown …

We consider high dimensional $ M $-estimation in settings where the response $ Y $ is
possibly missing at random and the covariates $\mathbf {X}\in\mathbb {R}^ p $ can be high …