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Line spectral estimation is the problem of recovering the frequencies and amplitudes of a mixture of a few sinusoids from equispaced samples. However, in a variety of signal processing problems arising in imaging, radar, and localization we…
This paper is concerned with inference on the regression function of a high-dimensional linear model when outcomes are missing at random. We propose an estimator which combines a Lasso pilot estimate of the regression function with a bias…
We revisit the classical problem of estimating an unknown distribution from its samples by fitting a mixture model that minimizes cross-entropy loss. Framing the task as a stochastic convex optimization problem over the space of $ M…
A considerable amount of research in harmonic analysis has been devoted to non-linear estimators of signals contaminated by additive Gaussian noise. They are implemented by thresholding coefficients in a frame, which provide a sparse signal…
A challenge in high-dimensional inverse problems is developing iterative solvers to find the accurate solution of regularized optimization problems with low computational cost. An important example is computed tomography (CT) where both…
We introduce a general framework for the reconstruction of periodic multivariate functions from finitely many and possibly noisy linear measurements. The reconstruction task is formulated as a penalized convex optimization problem, taking…
In practice, data often contain discrete variables. But most of the popular nonparametric estimation methods have been developed in a purely continuous framework. A common trick among practitioners is to make discrete variables continuous…
In this paper, we consider an unknown functional estimation problem in a general nonparametric regression model with the feature of having both multiplicative and additive noise.We propose two new wavelet estimators in this general context.…
Multichannel frequency estimation with incomplete data and miscellaneous noises arises in array signal processing, modal analysis, wireless communications, and so on. In this paper, we consider maximum-likelihood(-like) optimization methods…
We consider the linear regression problem, where the number $p$ of covariates is possibly larger than the number $n$ of observations $(x_{i},y_{i})_{i\leq i \leq n}$, under sparsity assumptions. On the one hand, several methods have been…
In this paper, we introduce various mechanisms to obtain accelerated first-order stochastic optimization algorithms when the objective function is convex or strongly convex. Specifically, we extend the Catalyst approach originally designed…
In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…
Many statistical estimators for high-dimensional linear regression are M-estimators, formed through minimizing a data-dependent square loss function plus a regularizer. This work considers a new class of estimators implicitly defined…
Statistical inference, a central tool of science, revolves around the study and the usage of statistical estimators: functions that map finite samples to predictions about unknown distribution parameters. In the frequentist framework,…
Novel sparse reconstruction algorithms are proposed for beamspace channel estimation in massive multiple-input multiple-output systems. The proposed algorithms minimize a least-squares objective having a nonconvex regularizer. This…
We provide novel theoretical results regarding local optima of regularized $M$-estimators, allowing for nonconvexity in both loss and penalty functions. Under restricted strong convexity on the loss and suitable regularity conditions on the…
We propose an extended primal-dual algorithm framework for solving a general nonconvex optimization model. This work is motivated by image reconstruction problems in a class of nonlinear imaging, where the forward operator can be formulated…
For the problem of high-dimensional sparse linear regression, it is known that an $\ell_0$-based estimator can achieve a $1/n$ "fast" rate on the prediction error without any conditions on the design matrix, whereas in absence of…
Image deblurring is an ill-posed problem with multiple plausible solutions for a given input image. However, most existing methods produce a deterministic estimate of the clean image and are trained to minimize pixel-level distortion. These…
We present a framework for performing efficient regression in general metric spaces. Roughly speaking, our regressor predicts the value at a new point by computing a Lipschitz extension --- the smoothest function consistent with the…