Related papers: Estimating Noisy Order Statistics
We study the Inexact Restoration framework with random models for minimizing functions whose evaluation is subject to errors. We propose a constrained formulation that includes well-known stochastic problems and an algorithm applicable when…
In this paper we derive information theoretic performance bounds to sensing and reconstruction of sparse phenomena from noisy projections. We consider two settings: output noise models where the noise enters after the projection and input…
This paper investigates the state estimation problem for a class of complex networks, in which the dynamics of each node is subject to Gaussian noise, system uncertainties and nonlinearities. Based on a regularized least-squares approach,…
We investigate a power-constrained sensing matrix design problem for a compressed sensing framework. We adopt a mean square error (MSE) performance criterion for sparse source reconstruction in a system where the source-to-sensor channel…
Subspace clustering refers to the task of finding a multi-subspace representation that best fits a collection of points taken from a high-dimensional space. This paper introduces an algorithm inspired by sparse subspace clustering (SSC) [In…
Linear minimum mean square error (MMSE) detector has been shown to alleviate the noise amplification problem, resulting in the conventional zero-forcing (ZF) detector. In this paper, we analyze the performance improvement by the MMSE…
We study the problem of estimating a random process from the observations collected by a network of sensors that operate under resource constraints. When the dynamics of the process and sensor observations are described by a state-space…
Usually, hearing impaired people use hearing aids which are implemented with speech enhancement algorithms. Estimation of speech and estimation of nose are the components in single channel speech enhancement system. The main objective of…
Recovery of the sparsity pattern (or support) of an unknown sparse vector from a small number of noisy linear measurements is an important problem in compressed sensing. In this paper, the high-dimensional setting is considered. It is shown…
In nonlinear deterministic parameter estimation, the maximum likelihood estimator (MLE) is unable to attain the Cramer-Rao lower bound at low and medium signal-to-noise ratios (SNR) due the threshold and ambiguity phenomena. In order to…
In this paper, we consider the problem of recovering a sparse signal from noisy linear measurements using the so called LASSO formulation. We assume a correlated Gaussian design matrix with additive Gaussian noise. We precisely analyze the…
We study the problem of exact support recovery based on noisy observations and present Refined Least Squares (RLS). Given a set of noisy measurement $$ \myvec{y} = \myvec{X}\myvec{\theta}^* + \myvec{\omega},$$ and $\myvec{X} \in…
In this paper, we study a generalized Kalman-Bucy filtering problem under uncertainty. The drift uncertainty for both signal process and observation process is considered and the attitude to uncertainty is characterized by a convex operator…
Since its development, the minimax framework has been one of the corner stones of theoretical statistics, and has contributed to the popularity of many well-known estimators, such as the regularized M-estimators for high-dimensional…
We present a sample- and time-efficient differentially private algorithm for ordinary least squares, with error that depends linearly on the dimension and is independent of the condition number of $X^\top X$, where $X$ is the design matrix.…
This dissertation shows that careful injection of noise into sample data can substantially speed up Expectation-Maximization algorithms. Expectation-Maximization algorithms are a class of iterative algorithms for extracting maximum…
In this article we provide some nonnegative and positive estimators of the mean squared errors(MSEs) for shrinkage estimators of multivariate normal means. Proposed estimators are shown to improve on the uniformly minimum variance unbiased…
This paper provides a unified framework for analyzing tensor estimation problems that allow for nonlinear observations, heteroskedastic noise, and covariate information. We study a general class of high-dimensional models where each…
Sparsity promoting norms are frequently used in high dimensional regression. A limitation of such Lasso-type estimators is that the optimal regularization parameter depends on the unknown noise level. Estimators such as the concomitant…
This paper focuses on a networked state estimation problem for a spatially large linear system with a distributed array of sensors, each of which offers partial state measurements, and the transmission is lossy. We propose a measurement…