Related papers: Extreme Compressive Sampling for Covariance Estima…
We solve the compressive sensing problem via convolutional factor analysis, where the convolutional dictionaries are learned {\em in situ} from the compressed measurements. An alternating direction method of multipliers (ADMM) paradigm for…
We study the problem of robust estimation under heterogeneous corruption rates, where each sample may be independently corrupted with a known but non-identical probability. This setting arises naturally in distributed and federated…
This paper considers covariance matrix estimation of tensor data under high dimensionality. A multi-bandable covariance class is established to accommodate the need for complex covariance structures of multi-layer lattices and general…
We study joint compression and detection in distributed sensing systems motivated by emerging applications such as IoT-based localization. Two spatially separated sensors observe noisy signals and can exchange only a $k$-bit message over a…
Quantile regression is an important tool for estimation of conditional quantiles of a response Y given a vector of covariates X. It can be used to measure the effect of covariates not only in the center of a distribution, but also in the…
High-dimensional matrix regression has been studied in various aspects, such as statistical properties, computational efficiency and application to specific instances including multivariate regression, system identification and matrix…
We consider planning longitudinal covariate measurements in follow-up studies where covariates are time-varying. We assume that the entire cohort cannot be selected for longitudinal measurements due to financial limitations and study how a…
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…
This paper establishes sharp dimension-free concentration and expectation bounds for the deviation of a sample cross-covariance matrix from its mean. For sub-Gaussian random vectors, we prove a high-probability operator-norm bound governed…
We study linear models under heavy-tailed priors from a probabilistic viewpoint. Instead of computing a single sparse most probable (MAP) solution as in standard deterministic approaches, the focus in the Bayesian compressed sensing…
This paper proposes a novel non-parametric multidimensional convex regression estimator which is designed to be robust to adversarial perturbations in the empirical measure. We minimize over convex functions the maximum (over Wasserstein…
The goal of compressed sensing is to estimate a high dimensional vector from an underdetermined system of noisy linear equations. In analogy to classical compressed sensing, here we assume a generative model as a prior, that is, we assume…
We study multivariate normal models that are described by linear constraints on the inverse of the covariance matrix. Maximum likelihood estimation for such models leads to the problem of maximizing the determinant function over a…
We introduce a novel Bayesian approach for both covariate selection and sparse precision matrix estimation in the context of high-dimensional Gaussian graphical models involving multiple responses. Our approach provides a sparse estimation…
We study the problem of high-dimensional covariance estimation under the constraint that the partial correlations are nonnegative. The sign constraints dramatically simplify estimation: the Gaussian maximum likelihood estimator is well…
This study introduces a novel estimation method for the entries and structure of a matrix $A$ in the linear factor model $\mathbf{X} = A\textbf{Z} + \textbf{E}$. This is applied to an observable vector $\mathbf{X} \in \mathbb{R}^d$ with…
We characterize the extremal points of the convex set of quantum measurements that are covariant under a finite-dimensional projective representation of a compact group, with action of the group on the measurement probability space which is…
In this paper we consider two closely related problems : estimation of eigenvalues and eigenfunctions of the covariance kernel of functional data based on (possibly) irregular measurements, and the problem of estimating the eigenvalues and…
We study the high-dimensional linear regression problem with categorical predictors that have many levels. We propose a new estimation approach, which performs model compression via two mechanisms by simultaneously encouraging (a)…
We study the problem of estimating the leading eigenvectors of a high-dimensional population covariance matrix based on independent Gaussian observations. We establish lower bounds on the rates of convergence of the estimators of the…