{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:PG462D7OPEYMRFLJBK7JGADMIA","short_pith_number":"pith:PG462D7O","schema_version":"1.0","canonical_sha256":"79b9ed0fee7930c895690abe93006c401453b9bd09aa49c4a856933f009fdd25","source":{"kind":"arxiv","id":"1707.04602","version":1},"attestation_state":"computed","paper":{"title":"An Efficient and Distribution-Free Two-Sample Test Based on Energy Statistics and Random Projections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Cheng Huang, Xiaoming Huo","submitted_at":"2017-07-14T18:38:41Z","abstract_excerpt":"A common disadvantage in existing distribution-free two-sample testing approaches is that the computational complexity could be high. Specifically, if the sample size is $N$, the computational complexity of those two-sample tests is at least $O(N^2)$. In this paper, we develop an efficient algorithm with complexity $O(N \\log N)$ for computing energy statistics in univariate cases. For multivariate cases, we introduce a two-sample test based on energy statistics and random projections, which enjoys the $O(K N \\log N)$ computational complexity, where $K$ is the number of random projections. We n"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1707.04602","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-07-14T18:38:41Z","cross_cats_sorted":[],"title_canon_sha256":"5fc1547c92c916903fded32fe5c2e4ca70f3f00e47e7b99e2515f3f399f3258a","abstract_canon_sha256":"829643073488be8f12bd094a29ba59b50ac7bc06cc49309084be6f5dfc06bd73"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:17.126536Z","signature_b64":"pAqqZu+GRJs57ly+lOzSoq/EQ4iIXu3UPVCAxyy8wHmXVbTf9WQnp836GkoNdXFJ2ab2gXvLLTSYb/k5qP5/AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"79b9ed0fee7930c895690abe93006c401453b9bd09aa49c4a856933f009fdd25","last_reissued_at":"2026-05-18T00:40:17.125776Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:17.125776Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Efficient and Distribution-Free Two-Sample Test Based on Energy Statistics and Random Projections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Cheng Huang, Xiaoming Huo","submitted_at":"2017-07-14T18:38:41Z","abstract_excerpt":"A common disadvantage in existing distribution-free two-sample testing approaches is that the computational complexity could be high. Specifically, if the sample size is $N$, the computational complexity of those two-sample tests is at least $O(N^2)$. In this paper, we develop an efficient algorithm with complexity $O(N \\log N)$ for computing energy statistics in univariate cases. For multivariate cases, we introduce a two-sample test based on energy statistics and random projections, which enjoys the $O(K N \\log N)$ computational complexity, where $K$ is the number of random projections. We n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.04602","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1707.04602","created_at":"2026-05-18T00:40:17.125892+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.04602v1","created_at":"2026-05-18T00:40:17.125892+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.04602","created_at":"2026-05-18T00:40:17.125892+00:00"},{"alias_kind":"pith_short_12","alias_value":"PG462D7OPEYM","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_16","alias_value":"PG462D7OPEYMRFLJ","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_8","alias_value":"PG462D7O","created_at":"2026-05-18T12:31:37.085036+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PG462D7OPEYMRFLJBK7JGADMIA","json":"https://pith.science/pith/PG462D7OPEYMRFLJBK7JGADMIA.json","graph_json":"https://pith.science/api/pith-number/PG462D7OPEYMRFLJBK7JGADMIA/graph.json","events_json":"https://pith.science/api/pith-number/PG462D7OPEYMRFLJBK7JGADMIA/events.json","paper":"https://pith.science/paper/PG462D7O"},"agent_actions":{"view_html":"https://pith.science/pith/PG462D7OPEYMRFLJBK7JGADMIA","download_json":"https://pith.science/pith/PG462D7OPEYMRFLJBK7JGADMIA.json","view_paper":"https://pith.science/paper/PG462D7O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.04602&json=true","fetch_graph":"https://pith.science/api/pith-number/PG462D7OPEYMRFLJBK7JGADMIA/graph.json","fetch_events":"https://pith.science/api/pith-number/PG462D7OPEYMRFLJBK7JGADMIA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PG462D7OPEYMRFLJBK7JGADMIA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PG462D7OPEYMRFLJBK7JGADMIA/action/storage_attestation","attest_author":"https://pith.science/pith/PG462D7OPEYMRFLJBK7JGADMIA/action/author_attestation","sign_citation":"https://pith.science/pith/PG462D7OPEYMRFLJBK7JGADMIA/action/citation_signature","submit_replication":"https://pith.science/pith/PG462D7OPEYMRFLJBK7JGADMIA/action/replication_record"}},"created_at":"2026-05-18T00:40:17.125892+00:00","updated_at":"2026-05-18T00:40:17.125892+00:00"}