相关论文: Estimation of projection operators with Gaussian n…

In this letter, we consider two sets of observations defined as subspace signals embedded in noise and we wish to analyze the distance between these two subspaces. The latter entails evaluating the angles between the subspaces, an issue…

We examine the behaviour of the pseudo-marginal random walk Metropolis algorithm, where evaluations of the target density for the accept/reject probability are estimated rather than computed precisely. Under relatively general conditions on…

We consider the high-dimensional linear regression model and assume that a fraction of the measurements are altered by an adversary with complete knowledge of the data and the underlying distribution. We are interested in a scenario where…

We consider the estimation of a bounded regression function with nonparametric heteroscedastic noise and random design. We study the true and empirical excess risks of the least-squares estimator on finite-dimensional vector spaces. We give…

This work performs a non-asymptotic analysis of the generalized Lasso under the assumption of sub-exponential data. Our main results continue recent research on the benchmark case of (sub-)Gaussian sample distributions and thereby explore…

Provided an arbitrary nonintrusive load monitoring (NILM) algorithm, we seek bounds on the probability of distinguishing between scenarios, given an aggregate power consumption signal. We introduce a framework for studying a general NILM…

Sinopoli et al. (TAC, 2004) considered the problem of optimal estimation for linear systems with Gaussian noise and intermittent observations, available according to a Bernoulli arrival process. They showed that there is a "critical"…

Operator-theoretic analysis of nonlinear dynamical systems has attracted much attention in a variety of engineering and scientific fields, endowed with practical estimation methods using data such as dynamic mode decomposition. In this…

In array processing, a common problem is to estimate the angles of arrival of $K$ deterministic sources impinging on an array of $M$ antennas, from $N$ observations of the source signal, corrupted by gaussian noise. The problem reduces to…

We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…

There is growing interest in improving our algorithmic understanding of fundamental statistical problems such as mean estimation, driven by the goal of understanding the limits of what we can extract from valuable data. The state of the art…

We consider the dynamic linear regression problem, where the predictor vector may vary with time. This problem can be modeled as a linear dynamical system, with non-constant observation operator, where the parameters that need to be learned…

We consider two problems of estimation in high-dimensional Gaussian models. The first problem is that of estimating a linear functional of the means of $n$ independent $p$-dimensional Gaussian vectors, under the assumption that most of…

Generalized alternating projections is an algorithm that alternates relaxed projections onto a finite number of sets to find a point in their intersection. We consider the special case of two linear subspaces, for which the algorithm…

Noise is an unavoidable part of most measurements which can hinder a correct interpretation of the data. Uncertainties propagate in the data analysis and can lead to biased results even in basic descriptive statistics such as the central…

Shot noise is an important ingredient to any measurement or theoretical modeling of discrete tracers of the large scale structure. Recent work has shown that the shot noise in the halo power spectrum becomes increasingly sub-Poissonian at…

We present an algorithm for resampling a function from its values on a non-Cartesian grid onto a Cartesian grid. This problem arises in many applications such as MRI, CT, radio astronomy and geophysics. Our algorithm, termed SParse Uniform…

In this paper we study constrained subspace approximation problem. Given a set of $n$ points $\{a_1,\ldots,a_n\}$ in $\mathbb{R}^d$, the goal of the {\em subspace approximation} problem is to find a $k$ dimensional subspace that best…

In imaging inverse problems with Poisson-distributed measurements, it is common to use objectives derived from the Poisson likelihood. But performance is often evaluated by mean squared error (MSE), which raises a practical question: how…

This paper examines fundamental error characteristics for a general class of matrix completion problems, where the matrix of interest is a product of two a priori unknown matrices, one of which is sparse, and the observations are noisy. Our…