Tag: covariance
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Fast and Robust: Computationally Efficient Covariance Estimation for Sub-Weibull Vectors
Fast and Robust: Computationally Efficient Covariance Estimation for Sub-Weibull Vectors arXiv:2512.17632v1 Announce Type: new Abstract: High-dimensional covariance estimation is notoriously sensitive to outliers. While statistically optimal estimators exist for general heavy-tailed distributions, they often rely on computationally expensive techniques like semidefinite programming or iterative M-estimation ($O(d^3)$). In this work, we target the specific regime of…
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SCOPE: Spectral Concentration by Distributionally Robust Joint Covariance-Precision Estimation
SCOPE: Spectral Concentration by Distributionally Robust Joint Covariance-Precision Estimation arXiv:2511.14146v1 Announce Type: new Abstract: We propose a distributionally robust formulation for simultaneously estimating the covariance matrix and the precision matrix of a random vector.The proposed model minimizes the worst-case weighted sum of the Frobenius loss of the covariance estimator and Stein’s loss of the precision…
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Optimal Variance and Covariance Estimation under Differential Privacy in the Add-Remove Model and Beyond
Optimal Variance and Covariance Estimation under Differential Privacy in the Add-Remove Model and Beyond arXiv:2509.04919v1 Announce Type: new Abstract: In this paper, we study the problem of estimating the variance and covariance of datasets under differential privacy in the add-remove model. While estimation in the swap model has been extensively studied in the literature, the…
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Fundamental limits of distributed covariance matrix estimation via a conditional strong data processing inequality
Fundamental limits of distributed covariance matrix estimation via a conditional strong data processing inequality arXiv:2507.16953v1 Announce Type: new Abstract: Estimating high-dimensional covariance matrices is a key task across many fields. This paper explores the theoretical limits of distributed covariance estimation in a feature-split setting, where communication between agents is constrained. Specifically, we study a scenario…
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Online Covariance Estimation in Nonsmooth Stochastic Approximation
Online Covariance Estimation in Nonsmooth Stochastic Approximation arXiv:2502.05305v1 Announce Type: new Abstract: We consider applying stochastic approximation (SA) methods to solve nonsmooth variational inclusion problems. Existing studies have shown that the averaged iterates of SA methods exhibit asymptotic normality, with an optimal limiting covariance matrix in the local minimax sense of H’ajek and Le Cam.…