{"paper":{"title":"From Graphical Lasso to Atomic Norms: High-Dimensional Pattern Recovery","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Bartosz Ko{\\l}odziejek, Hideto Nakashima, Maciej Wilczy\\'nski, Piotr Graczyk","submitted_at":"2025-06-16T10:45:51Z","abstract_excerpt":"Estimating high-dimensional precision matrices is a fundamental problem in modern statistics, with the graphical lasso and its $\\ell_1$-penalty being a standard approach for recovering sparsity patterns. However, many statistical models, e.g. colored graphical models, exhibit richer structures like symmetry or equality constraints, which the $\\ell_1$-norm cannot adequately capture. This paper addresses the gap by extending the high-dimensional analysis of pattern recovery to a general class of atomic norm penalties, particularly those whose unit balls are polytopes, where patterns correspond t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.13353","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.13353/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}