{"paper":{"title":"Finding Skewed Subcubes Under a Distribution","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC","math.PR"],"primary_cat":"cs.DS","authors_text":"Parikshit Gopalan, Roie Levin, Udi Wieder","submitted_at":"2019-11-18T00:32:58Z","abstract_excerpt":"Say that we are given samples from a distribution $\\psi$ over an $n$-dimensional space. We expect or desire $\\psi$ to behave like a product distribution (or a $k$-wise independent distribution over its marginals for small $k$). We propose the problem of enumerating/list-decoding all large subcubes where the distribution $\\psi$ deviates markedly from what we expect; we refer to such subcubes as skewed subcubes. Skewed subcubes are certificates of dependencies between small subsets of variables in $\\psi$. We motivate this problem by showing that it arises naturally in the context of algorithmic "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.07378","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/1911.07378/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"}