Related papers: Statistical Multiresolution Dantzig Estimation in …
A popular class of problem in statistics deals with estimating the support of a density from $n$ observations drawn at random from a $d$-dimensional distribution. The one-dimensional case reduces to estimating the end points of a univariate…
Additive regression models have a long history in multivariate nonparametric regression. They provide a model in which each regression function depends only on a single explanatory variable allowing to obtain estimators at the optimal…
Because of the advance in technologies, modern statistical studies often encounter linear models with the number of explanatory variables much larger than the sample size. Estimation and variable selection in these high-dimensional problems…
We develop a finite-sample optimal estimator for regression discontinuity design when the outcomes are bounded, including binary outcomes as the leading case. Our estimator achieves minimax mean squared error among linear shrinkage…
We propose a formulation for nonlinear recurrent models that includes simple parametric models of recurrent neural networks as a special case. The proposed formulation leads to a natural estimator in the form of a convex program. We provide…
This paper introduces a novel framework for estimation and inference in penalized M-estimators applied to robust high-dimensional linear regression models. Traditional methods for high-dimensional statistical inference, which predominantly…
In this paper, we study the issue of estimating a structured signal $x_0 \in \mathbb{R}^n$ from non-linear and noisy Gaussian observations. Supposing that $x_0$ is contained in a certain convex subset $K \subset \mathbb{R}^n$, we prove that…
This paper studies a Dantzig-selector type regularized estimator for linear functionals of high-dimensional linear processes. Explicit rates of convergence of the proposed estimator are obtained and they cover the broad regime from i.i.d.…
Convex optimization models find interesting applications, especially in signal/image processing and compressive sensing. We study some augmented convex models, which are perturbed by strongly convex functions, and propose a dual gradient…
In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…
This note addresses the question of optimally estimating a linear functional of an object acquired through linear observations corrupted by random noise, where optimality pertains to a worst-case setting tied to a symmetric, convex, and…
In this paper, we consider the problem of identifying a linear map from measurements which are subject to intermittent and arbitarily large errors. This is a fundamental problem in many estimation-related applications such as fault…
We propose a flexible convex relaxation for the phase retrieval problem that operates in the natural domain of the signal. Therefore, we avoid the prohibitive computational cost associated with "lifting" and semidefinite programming (SDP)…
We study the unconstrained minimization of a smooth and strongly convex population loss function under a stochastic oracle that introduces both additive and multiplicative noise; this is a canonical and widely-studied setting that arises…
We investigate the problem of estimating the 3D shape of an object defined by a set of 3D landmarks, given their 2D correspondences in a single image. A successful approach to alleviating the reconstruction ambiguity is the 3D deformable…
Diffractive lenses have recently been applied to the domain of multispectral imaging in the X-ray and UV regimes where they can achieve very high resolution as compared to reflective and refractive optics. Conventionally, spectral…
We propose a novel high-dimensional linear regression estimator: the Discrete Dantzig Selector, which minimizes the number of nonzero regression coefficients subject to a budget on the maximal absolute correlation between the features and…
Compressed Sensing suggests that the required number of samples for reconstructing a signal can be greatly reduced if it is sparse in a known discrete basis, yet many real-world signals are sparse in a continuous dictionary. One example is…
The paper provides global optimization algorithms for two particularly difficult nonconvex problems raised by hybrid system identification: switching linear regression and bounded-error estimation. While most works focus on local…
Multidimensional imaging, capturing image data in more than two dimensions, has been an emerging field with diverse applications. Due to the limitation of two-dimensional detectors in obtaining the high-dimensional image data, computational…