Related papers: Adaptive exact recovery in sparse nonparametric mo…

Conformal prediction is a distribution-free framework for uncertainty quantification that replaces point predictions with sets, offering marginal coverage guarantees (i.e., ensuring that the prediction sets contain the true label with a…

We investigate function estimation in nonparametric regression models with random design and heteroscedastic correlated noise. Adaptive properties of warped wavelet nonlinear approximations are studied over a wide range of Besov scales,…

Performing statistical inference in high-dimension is an outstanding challenge. A major source of difficulty is the absence of precise information on the distribution of high-dimensional estimators. Here, we consider linear regression in…

Sparse recovery is one of the most fundamental and well-studied inverse problems. Standard statistical formulations of the problem are provably solved by general convex programming techniques and more practical, fast (nearly-linear time)…

We consider a nonparametric model $\mathcal{E}^{n},$ generated by independent observations $X_{i},$ $i=1,...,n,$ with densities $p(x,\theta_{i}),$ $i=1,...,n,$ the parameters of which $\theta _{i}=f(i/n)\in \Theta $ are driven by the values…

We study the problem of recovering the underlining sparse signals from clean or noisy phaseless measurements. Due to the sparse prior of signals, we adopt an L0regularized variational model to ensure only a small number of nonzero elements…

This paper focuses on detection tasks in information extraction, where positive instances are sparsely distributed and models are usually evaluated using F-measure on positive classes. These characteristics often result in deficient…

We analyze a practical algorithm for sparse PCA on incomplete and noisy data under a general non-random sampling scheme. The algorithm is based on a semidefinite relaxation of the $\ell_1$-regularized PCA problem. We provide theoretical…

Restoring images degraded by spatially varying blur is a problem encountered in many disciplines such as astrophysics, computer vision or biomedical imaging. One of the main challenges to perform this task is to design efficient numerical…

In many applications sampled data are collected in irregular fashion or are partly lost or unavailable. In these cases it is required to convert irregularly sampled signals to regularly sampled ones or to restore missing data. In this…

In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric…

In this paper we consider the task of estimating the non-zero pattern of the sparse inverse covariance matrix of a zero-mean Gaussian random vector from a set of iid samples. Note that this is also equivalent to recovering the underlying…

In this paper we theoretically study exact recovery of sparse vectors from compressed measurements by minimizing a general nonconvex function that can be decomposed into the sum of single variable functions belonging to a class of smooth…

Given a sample covariance matrix, we examine the problem of maximizing the variance explained by a linear combination of the input variables while constraining the number of nonzero coefficients in this combination. This is known as sparse…

Robots that are trained to perform a task in a fixed environment often fail when facing unexpected changes to the environment due to a lack of exploration. We propose a principled way to adapt the policy for better exploration in changing…

We provide adaptive inference methods, based on $\ell_1$ regularization, for regular (semi-parametric) and non-regular (nonparametric) linear functionals of the conditional expectation function. Examples of regular functionals include…

For consistency (even oracle properties) of estimation and model prediction, almost all existing methods of variable/feature selection critically depend on sparsity of models. However, for ``large $p$ and small $n$" models sparsity…

The estimation of causal treatment effects from observational data is a fundamental problem in causal inference. To avoid bias, the effect estimator must control for all confounders. Hence practitioners often collect data for as many…

Signals sparse in a transformation domain can be recovered from a reduced set of randomly positioned samples by using compressive sensing algorithms. Simple re- construction algorithms are presented in the first part of the paper. The…

We consider a $l_1$-penalization procedure in the non-parametric Gaussian regression model. In many concrete examples, the dimension $d$ of the input variable $X$ is very large (sometimes depending on the number of observations). Estimation…