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We are concerned with the reconstruction of inclusions in elastic bodies based on measurements from a laboratory experiment. In doing so, we solve the inverse problem of the time-harmonic elastic wave equation, in contrast to the stationary…
We consider random non-normal matrices constructed by removing one row and column from samples from Dyson's circular ensembles or samples from the classical compact groups. We develop sparse matrix models whose spectral measures match these…
We demonstrate the first algorithms for the problem of regression for generalized linear models (GLMs) in the presence of additive oblivious noise. We assume we have sample access to examples $(x, y)$ where $y$ is a noisy measurement of…
I present here some results on the statistical behaviour of large random matrices in an ensemble where the probability distribution is not a function of the eigenvalues only. The perturbative expansion can be cast in a closed form and the…
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 develop new statistical theory for probabilistic principal component analysis models in high dimensions. The focus is the estimation of the noise variance, which is an important and unresolved issue when the number of…
Robust estimators of large covariance matrices are considered, comprising regularized (linear shrinkage) modifications of Maronna's classical M-estimators. These estimators provide robustness to outliers, while simultaneously being…
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…
A class of robust estimators of scatter applied to information-plus-impulsive noise samples is studied, where the sample information matrix is assumed of low rank; this generalizes the study of (Couillet et al., 2013b) to spiked random…
We analyze a class of estimators based on convex relaxation for solving high-dimensional matrix decomposition problems. The observations are noisy realizations of a linear transformation $\mathfrak{X}$ of the sum of an approximately) low…
There has been a recent surge of interest in the study of asymptotic reconstruction performance in various cases of generalized linear estimation problems in the teacher-student setting, especially for the case of i.i.d standard normal…
We compute analytically the joint probability density of eigenvalues and the level spacing statistics for an ensemble of random matrices with interesting features. It is invariant under the standard symmetry groups (orthogonal and unitary)…
This paper investigates the asymptotic properties of quantile regression estimators in linear models, with a particular focus on polynomial regressors and robustness to heavy-tailed noise. Under independent and identically distributed…
In this paper we study the influence of additive noise in randomized consensus algorithms. Assuming that the update matrices are symmetric, we derive a closed form expression for the mean square error induced by the noise, together with…
We consider the group testing problem, in which one seeks to identify a subset of defective items within a larger set of items based on a number of noisy tests. While matching achievability and converse bounds are known in several cases of…
We present novel, convex relaxations for rotation and pose estimation problems that can a posteriori guarantee global optimality for practical measurement noise levels. Some such relaxations exist in the literature for specific problem…
We propose a new pivotal method for estimating high-dimensional matrices. Assume that we observe a small set of entries or linear combinations of entries of an unknown matrix $A\_0$ corrupted by noise. We propose a new method for estimating…
Combining information both within and across trajectories, we propose a simple estimator for the local regularity of the trajectories of a stochastic process. Independent trajectories are measured with errors at randomly sampled time…
This paper deals with recovering an unknown vector $\theta$ from the noisy data $Y=A\theta+\sigma\xi$, where $A$ is a known $(m\times n)$-matrix and $\xi$ is a white Gaussian noise. It is assumed that $n$ is large and $A$ may be severely…
We consider sparse matrix estimation where the goal is to estimate an $n\times n$ matrix from noisy observations of a small subset of its entries. We analyze the estimation error of the popularly utilized collaborative filtering algorithm…