相关论文: Generalized Dantzig Selector: Application to the k…

We propose a generalized debiased Lasso estimator based on a stability principle. When a single column of the design matrix is perturbed, the estimator admits a simple update formula that can be computed from the original solution. Under…

This paper aims to present a fairly accessible generalization of several symmetric Gauss-Seidel decomposition based multi-block proximal alternating direction methods of multipliers (ADMMs) for convex composite optimization problems. The…

We analyze the sample complexity of full-batch Gradient Descent (GD) in the setup of non-smooth Stochastic Convex Optimization. We show that the generalization error of GD, with common choice of hyper-parameters, can be $\tilde \Theta(d/m +…

Generalized compressed sensing (GCS) is a paradigm in which a structured high-dimensional signal may be recovered from random, under-determined, and corrupted linear measurements. Generalized Lasso (GL) programs are effective for solving…

The $k$-dimensional coding schemes refer to a collection of methods that attempt to represent data using a set of representative $k$-dimensional vectors, and include non-negative matrix factorization, dictionary learning, sparse coding,…

This paper introduces a novel error estimator for the Proper Generalized Decomposition (PGD) approximation of parametrized equations. The estimator is intrinsically random: It builds on concentration inequalities of Gaussian maps and an…

We consider linear prediction with a convex Lipschitz loss, or more generally, stochastic convex optimization problems of generalized linear form, i.e.~where each instantaneous loss is a scalar convex function of a linear function. We show…

The generalised linear model (GLM) is a very important tool for analysing real data in biology, sociology, agriculture, engineering and many other application domain where the relationship between the response and explanatory variables may…

This paper proposes a desparsified GMM estimator for estimating high-dimensional regression models allowing for, but not requiring, many more endogenous regressors than observations. We provide finite sample upper bounds on the estimation…

The scalar-on-image regression model examines the association between a scalar response and a bivariate function (e.g., images) through the estimation of a bivariate coefficient function. Existing approaches often impose smoothness…

Recent advances in quantized compressed sensing and high-dimensional estimation have shown that signal recovery is even feasible under strong non-linear distortions in the observation process. An important characteristic of associated…

Gaussian smoothing (GS) is a derivative-free optimization (DFO) algorithm that estimates the gradient of an objective using perturbations of the current parameters sampled from a standard normal distribution. We generalize it to sampling…

The random dot product graph is a popular model for network data with extensions that accommodate dynamic (time-varying) networks. However, two significant deficiencies exist in the dynamic random dot product graph literature: (1) no…

A new, very general, robust procedure for combining estimators in metric spaces is introduced GROS. The method is reminiscent of the well-known median of means, as described in \cite{devroye2016sub}. Initially, the sample is divided into…

Generalized sampling consists in the recovery of a function $f$, from the samples of the responses of a collection of linear shift-invariant systems to the input $f$. The reconstructed function is typically a member of a finitely generated…

We consider learning high-dimensional multi-response linear models with structured parameters. By exploiting the noise correlations among responses, we propose an alternating estimation (AltEst) procedure to estimate the model parameters…

In applications involving ordinal predictors, common approaches to reduce dimensionality are either extensions of unsupervised techniques such as principal component analysis, or variable selection procedures that rely on modeling the…

We provide faster algorithms for the problem of Gaussian summation, which occurs in many machine learning methods. We develop two new extensions - an O(Dp) Taylor expansion for the Gaussian kernel with rigorous error bounds and a new error…

In this manuscript we consider the problem of generalized linear estimation on Gaussian mixture data with labels given by a single-index model. Our first result is a sharp asymptotic expression for the test and training errors in the…

This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…