{"paper":{"title":"Reconstructing decision trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.LG"],"primary_cat":"cs.DS","authors_text":"Guy Blanc, Jane Lange, Li-Yang Tan","submitted_at":"2020-12-16T04:18:00Z","abstract_excerpt":"We give the first {\\sl reconstruction algorithm} for decision trees: given queries to a function $f$ that is $\\mathrm{opt}$-close to a size-$s$ decision tree, our algorithm provides query access to a decision tree $T$ where:\n  $\\circ$ $T$ has size $S = s^{O((\\log s)^2/\\varepsilon^3)}$;\n  $\\circ$ $\\mathrm{dist}(f,T)\\le O(\\mathrm{opt})+\\varepsilon$;\n  $\\circ$ Every query to $T$ is answered with $\\mathrm{poly}((\\log s)/\\varepsilon)\\cdot \\log n$ queries to $f$ and in $\\mathrm{poly}((\\log s)/\\varepsilon)\\cdot n\\log n$ time.\n  This yields a {\\sl tolerant tester} that distinguishes functions that are"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.08735","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/2012.08735/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"}