Related papers: Near-Optimal Estimation of Linear Functionals with…
We analyze the performance of a data-assimilation algorithm based on a linear feedback control when used with observational data that contains measurement errors. Our model problem consists of dynamics governed by the two-dimension…
We present a statistical framework to benchmark the performance of reconstruction algorithms for linear inverse problems, in particular, neural-network-based methods that require large quantities of training data. We generate synthetic…
In the context of high-dimensional linear regression models, we propose an algorithm of exact support recovery in the setting of noisy compressed sensing where all entries of the design matrix are independent and identically distributed…
We propose an algorithm to actively estimate the parameters of a linear dynamical system. Given complete control over the system's input, our algorithm adaptively chooses the inputs to accelerate estimation. We show a finite time bound…
Reduced-rank approach has been used for decades in robust linear estimation of both deterministic and random vector of parameters in linear model y=Hx+\sqrt{epsilon}n. In practical settings, estimation is frequently performed under…
We deal with the problem of optimal estimation of the linear functionals constructed from unobserved values of a continuous time stochastic process with periodically correlated increments based on past observations of this process. To solve…
In this paper we are concerned with fully automatic and locally adaptive estimation of functions in a "signal + noise"-model where the regression function may additionally be blurred by a linear operator, e.g. by a convolution. To this end,…
In many applications we seek to recover signals from linear measurements far fewer than the ambient dimension, given the signals have exploitable structures such as sparse vectors or low rank matrices. In this paper we work in a general…
A general framework with a series of different methods is proposed to improve the estimate of convex function (or functional) values when only noisy observations of the true input are available. Technically, our methods catch the bias…
Much of statistics relies upon four key elements: a law of large numbers, a calculus to operationalize stochastic convergence, a central limit theorem, and a framework for constructing local approximations. These elements are…
We consider the estimation of quadratic functionals in a Gaussian sequence model where the eigenvalues are supposed to be unknown and accessible through noisy observations only. Imposing smoothness assumptions both on the signal and the…
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…
This paper presents a finite difference quasi-Newton method for the minimization of noisy functions. The method takes advantage of the scalability and power of BFGS updating, and employs an adaptive procedure for choosing the differencing…
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…
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…
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 paper considers a sequential estimation and sensor scheduling problem with one sensor and one estimator. The sensor makes sequential observations about the state of an underlying memoryless stochastic process, and makes a decision as…
We study the problem of global maximization of a function f given a finite number of evaluations perturbed by noise. We consider a very weak assumption on the function, namely that it is locally smooth (in some precise sense) with respect…
We consider the problem of optimizing an approximately convex function over a bounded convex set in $\mathbb{R}^n$ using only function evaluations. The problem is reduced to sampling from an \emph{approximately} log-concave distribution…
We study the problem of super-resolution, where we recover the locations and weights of non-negative point sources from a few samples of their convolution with a Gaussian kernel. It has been shown that exact recovery is possible by…