{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:AYMWLUI4P6DQFNC4DSELOPIS44","short_pith_number":"pith:AYMWLUI4","canonical_record":{"source":{"id":"1805.09948","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-05-25T02:00:53Z","cross_cats_sorted":["stat.ML","stat.TH"],"title_canon_sha256":"8419b7aaba5410cc4d8f378e06cf6f929e7a40e6d52460ce9054158c3f5bb535","abstract_canon_sha256":"1c797994d3d3bf06400b5be2b9cbf7b3c9331f3dc81b5bda16bb8b8eaa396c43"},"schema_version":"1.0"},"canonical_sha256":"061965d11c7f8702b45c1c88b73d12e702d271363736153d7a7c419ef4ceadd2","source":{"kind":"arxiv","id":"1805.09948","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.09948","created_at":"2026-05-17T23:52:53Z"},{"alias_kind":"arxiv_version","alias_value":"1805.09948v3","created_at":"2026-05-17T23:52:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.09948","created_at":"2026-05-17T23:52:53Z"},{"alias_kind":"pith_short_12","alias_value":"AYMWLUI4P6DQ","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"AYMWLUI4P6DQFNC4","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"AYMWLUI4","created_at":"2026-05-18T12:32:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:AYMWLUI4P6DQFNC4DSELOPIS44","target":"record","payload":{"canonical_record":{"source":{"id":"1805.09948","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-05-25T02:00:53Z","cross_cats_sorted":["stat.ML","stat.TH"],"title_canon_sha256":"8419b7aaba5410cc4d8f378e06cf6f929e7a40e6d52460ce9054158c3f5bb535","abstract_canon_sha256":"1c797994d3d3bf06400b5be2b9cbf7b3c9331f3dc81b5bda16bb8b8eaa396c43"},"schema_version":"1.0"},"canonical_sha256":"061965d11c7f8702b45c1c88b73d12e702d271363736153d7a7c419ef4ceadd2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:53.044717Z","signature_b64":"kpXPzmaoG+ES/1/4IThHkFBr7QlDT3Kp3AfGn+m3wiYa4x6Lwp6Uwez7MMmMRcCDslZC4VkN2EVybzHoVVc4DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"061965d11c7f8702b45c1c88b73d12e702d271363736153d7a7c419ef4ceadd2","last_reissued_at":"2026-05-17T23:52:53.043912Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:53.043912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.09948","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:52:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w73P2linCZDEWdeb7DpTG7TPUo3MS/DY1A4cr/AII6uRfMVXOCbiLg+s5wU46ThgjOD0JnFUbIlwqlguluDLDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T11:10:11.059732Z"},"content_sha256":"56e65a236a5149177ec44ab6dd49b94828864112ba0077555e145d5325ef0131","schema_version":"1.0","event_id":"sha256:56e65a236a5149177ec44ab6dd49b94828864112ba0077555e145d5325ef0131"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:AYMWLUI4P6DQFNC4DSELOPIS44","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"How Many Machines Can We Use in Parallel Computing for Kernel Ridge Regression?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Guang Cheng, Meimei Liu, Zuofeng Shang","submitted_at":"2018-05-25T02:00:53Z","abstract_excerpt":"This paper aims to solve a basic problem in distributed statistical inference: how many machines can we use in parallel computing? In kernel ridge regression, we address this question in two important settings: nonparametric estimation and hypothesis testing. Specifically, we find a range for the number of machines under which optimal estimation/testing is achievable. The employed empirical processes method provides a unified framework, that allows us to handle various regression problems (such as thin-plate splines and nonparametric additive regression) under different settings (such as univa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.09948","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:52:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SL9fpPnZ/kjdU77rMtjV5+jCO7CR4g6TGbfc6aICpXixmCGgbNlioj6XBhufs0N7f5++t1SdQhvb2wim6su1Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T11:10:11.060371Z"},"content_sha256":"16d184c2a20526ee0f39a45d43e960d1e22753443a7b0cc18ce412f84c604e02","schema_version":"1.0","event_id":"sha256:16d184c2a20526ee0f39a45d43e960d1e22753443a7b0cc18ce412f84c604e02"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AYMWLUI4P6DQFNC4DSELOPIS44/bundle.json","state_url":"https://pith.science/pith/AYMWLUI4P6DQFNC4DSELOPIS44/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AYMWLUI4P6DQFNC4DSELOPIS44/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-25T11:10:11Z","links":{"resolver":"https://pith.science/pith/AYMWLUI4P6DQFNC4DSELOPIS44","bundle":"https://pith.science/pith/AYMWLUI4P6DQFNC4DSELOPIS44/bundle.json","state":"https://pith.science/pith/AYMWLUI4P6DQFNC4DSELOPIS44/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AYMWLUI4P6DQFNC4DSELOPIS44/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:AYMWLUI4P6DQFNC4DSELOPIS44","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"1c797994d3d3bf06400b5be2b9cbf7b3c9331f3dc81b5bda16bb8b8eaa396c43","cross_cats_sorted":["stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-05-25T02:00:53Z","title_canon_sha256":"8419b7aaba5410cc4d8f378e06cf6f929e7a40e6d52460ce9054158c3f5bb535"},"schema_version":"1.0","source":{"id":"1805.09948","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.09948","created_at":"2026-05-17T23:52:53Z"},{"alias_kind":"arxiv_version","alias_value":"1805.09948v3","created_at":"2026-05-17T23:52:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.09948","created_at":"2026-05-17T23:52:53Z"},{"alias_kind":"pith_short_12","alias_value":"AYMWLUI4P6DQ","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"AYMWLUI4P6DQFNC4","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"AYMWLUI4","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:16d184c2a20526ee0f39a45d43e960d1e22753443a7b0cc18ce412f84c604e02","target":"graph","created_at":"2026-05-17T23:52:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"This paper aims to solve a basic problem in distributed statistical inference: how many machines can we use in parallel computing? In kernel ridge regression, we address this question in two important settings: nonparametric estimation and hypothesis testing. Specifically, we find a range for the number of machines under which optimal estimation/testing is achievable. The employed empirical processes method provides a unified framework, that allows us to handle various regression problems (such as thin-plate splines and nonparametric additive regression) under different settings (such as univa","authors_text":"Guang Cheng, Meimei Liu, Zuofeng Shang","cross_cats":["stat.ML","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-05-25T02:00:53Z","title":"How Many Machines Can We Use in Parallel Computing for Kernel Ridge Regression?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.09948","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:56e65a236a5149177ec44ab6dd49b94828864112ba0077555e145d5325ef0131","target":"record","created_at":"2026-05-17T23:52:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1c797994d3d3bf06400b5be2b9cbf7b3c9331f3dc81b5bda16bb8b8eaa396c43","cross_cats_sorted":["stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-05-25T02:00:53Z","title_canon_sha256":"8419b7aaba5410cc4d8f378e06cf6f929e7a40e6d52460ce9054158c3f5bb535"},"schema_version":"1.0","source":{"id":"1805.09948","kind":"arxiv","version":3}},"canonical_sha256":"061965d11c7f8702b45c1c88b73d12e702d271363736153d7a7c419ef4ceadd2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"061965d11c7f8702b45c1c88b73d12e702d271363736153d7a7c419ef4ceadd2","first_computed_at":"2026-05-17T23:52:53.043912Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:53.043912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kpXPzmaoG+ES/1/4IThHkFBr7QlDT3Kp3AfGn+m3wiYa4x6Lwp6Uwez7MMmMRcCDslZC4VkN2EVybzHoVVc4DA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:53.044717Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.09948","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56e65a236a5149177ec44ab6dd49b94828864112ba0077555e145d5325ef0131","sha256:16d184c2a20526ee0f39a45d43e960d1e22753443a7b0cc18ce412f84c604e02"],"state_sha256":"2913cd4a120f56199b14f693b3a125a56419114a116460d8cdc119f25461f3c4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t+lowaxiJWYvUDNm27xmKltHl+1jV3EGZuCKKqQ/ks2GK1ZKpjA5X0h1qZ1chDwc9b2MHtsMuNn9F0vSvXWtCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T11:10:11.063500Z","bundle_sha256":"1779effc577ac44431dad9967e820374ac5d3b09a697737640ea313f39efb3ca"}}