{"id":9273,"date":"2025-12-22T07:02:49","date_gmt":"2025-12-22T07:02:49","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/12\/22\/2512-17632\/"},"modified":"2025-12-22T07:02:49","modified_gmt":"2025-12-22T07:02:49","slug":"2512-17632","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/12\/22\/2512-17632\/","title":{"rendered":"Fast and Robust: Computationally Efficient Covariance Estimation for Sub-Weibull Vectors"},"content":{"rendered":"

Fast and Robust: Computationally Efficient Covariance Estimation for Sub-Weibull Vectors
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arXiv:2512.17632v1 Announce Type: new
\nAbstract: 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 textbf{Sub-Weibull distributions} (characterized by stretched exponential tails $exp(-t^alpha)$). We investigate a computationally efficient alternative: the textbf{Cross-Fitted Norm-Truncated Estimator}. Unlike element-wise truncation, our approach preserves the spectral geometry while requiring $O(Nd^2)$ operations, which represents the theoretical lower bound for constructing a full covariance matrix. Although spherical truncation is geometrically suboptimal for anisotropic data, we prove that within the Sub-Weibull class, the exponential tail decay compensates for this mismatch. Leveraging weighted Hanson-Wright inequalities, we derive non-asymptotic error bounds showing that our estimator recovers the optimal sub-Gaussian rate $tilde{O}(sqrt{r(Sigma)\/N})$ with high probability. This provides a scalable solution for high-dimensional data that exhibits tails heavier than Gaussian but lighter than polynomial decay.<\/div>\n

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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 […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,482,112],"tags":[4473,1705,3554],"class_list":["post-9273","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-stat-co","category-stat-ml","tag-computationally","tag-covariance","tag-sub"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/9273"}],"collection":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/comments?post=9273"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/9273\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=9273"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=9273"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=9273"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}