{"paper":{"title":"Debiased Distribution Compression","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","stat.CO","stat.ME"],"primary_cat":"stat.ML","authors_text":"Lester Mackey, Lingxiao Li, Raaz Dwivedi","submitted_at":"2024-04-18T16:11:16Z","abstract_excerpt":"Modern compression methods can summarize a target distribution $\\mathbb{P}$ more succinctly than i.i.d. sampling but require access to a low-bias input sequence like a Markov chain converging quickly to $\\mathbb{P}$. We introduce a new suite of compression methods suitable for compression with biased input sequences. Given $n$ points targeting the wrong distribution and quadratic time, Stein kernel thinning (SKT) returns $\\sqrt{n}$ equal-weighted points with $\\widetilde{O}(n^{-1/2})$ maximum mean discrepancy (MMD) to $\\mathbb{P}$. For larger-scale compression tasks, low-rank SKT achieves the s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.12290","kind":"arxiv","version":3},"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/2404.12290/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"}