{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:ZE46RX3S2SOWX3WHRCNQ6YHQ3W","short_pith_number":"pith:ZE46RX3S","canonical_record":{"source":{"id":"1710.06595","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-10-18T06:57:03Z","cross_cats_sorted":[],"title_canon_sha256":"0c96c8e327699b4c5ef1b10d40ccb5b23b4b405734c008ebaaf64960e95d90c1","abstract_canon_sha256":"62e33c691c0468e19d95ca48fad21aaecbe3ed6f844ad013740a11f8948a6225"},"schema_version":"1.0"},"canonical_sha256":"c939e8df72d49d6beec7889b0f60f0dda63e406016586d10bdae69dc8c370bdf","source":{"kind":"arxiv","id":"1710.06595","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.06595","created_at":"2026-05-18T00:22:20Z"},{"alias_kind":"arxiv_version","alias_value":"1710.06595v2","created_at":"2026-05-18T00:22:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.06595","created_at":"2026-05-18T00:22:20Z"},{"alias_kind":"pith_short_12","alias_value":"ZE46RX3S2SOW","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZE46RX3S2SOWX3WH","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZE46RX3S","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:ZE46RX3S2SOWX3WHRCNQ6YHQ3W","target":"record","payload":{"canonical_record":{"source":{"id":"1710.06595","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-10-18T06:57:03Z","cross_cats_sorted":[],"title_canon_sha256":"0c96c8e327699b4c5ef1b10d40ccb5b23b4b405734c008ebaaf64960e95d90c1","abstract_canon_sha256":"62e33c691c0468e19d95ca48fad21aaecbe3ed6f844ad013740a11f8948a6225"},"schema_version":"1.0"},"canonical_sha256":"c939e8df72d49d6beec7889b0f60f0dda63e406016586d10bdae69dc8c370bdf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:20.640251Z","signature_b64":"ZMcE/dK1idfOWYkUSsXqF0sgF1HdA+cU2UqaedAxPzov96yu2zBWx3Nvec91Fdoe6Zz/SfGf6+6N9MOYgks5Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c939e8df72d49d6beec7889b0f60f0dda63e406016586d10bdae69dc8c370bdf","last_reissued_at":"2026-05-18T00:22:20.639691Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:20.639691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.06595","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:22:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"79gjixLSCrv3H127Ha6yY+39CEt89yLiozKs9VRw80KOPKa2D5osLM3lSrBz0thi4jqmCR76MmHW+1HAhS1iBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T12:15:16.135494Z"},"content_sha256":"4f8d9dff9cddd39da735bc09f6f2e57fabc21823277c7568f0e5ed2bcbc31fae","schema_version":"1.0","event_id":"sha256:4f8d9dff9cddd39da735bc09f6f2e57fabc21823277c7568f0e5ed2bcbc31fae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:ZE46RX3S2SOWX3WHRCNQ6YHQ3W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Variational Inference based on Robust Divergences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"Futoshi Futami, Issei Sato, Masashi Sugiyama","submitted_at":"2017-10-18T06:57:03Z","abstract_excerpt":"Robustness to outliers is a central issue in real-world machine learning applications. While replacing a model to a heavy-tailed one (e.g., from Gaussian to Student-t) is a standard approach for robustification, it can only be applied to simple models. In this paper, based on Zellner's optimization and variational formulation of Bayesian inference, we propose an outlier-robust pseudo-Bayesian variational method by replacing the Kullback-Leibler divergence used for data fitting to a robust divergence such as the beta- and gamma-divergences. An advantage of our approach is that superior but comp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.06595","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":""},"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":"2026-05-18T00:22:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5J3+uwOSGffg+QXhw0fLXKkeiaURhJjg+d2Hk454uLIadzORryckFriuVwMrYGMslVa0orG1XX2ms3/xuqpjCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T12:15:16.136266Z"},"content_sha256":"8e602b1ce153afcd838ff401023964dac7792c3c992850a97b3fb6f5e4e42f66","schema_version":"1.0","event_id":"sha256:8e602b1ce153afcd838ff401023964dac7792c3c992850a97b3fb6f5e4e42f66"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZE46RX3S2SOWX3WHRCNQ6YHQ3W/bundle.json","state_url":"https://pith.science/pith/ZE46RX3S2SOWX3WHRCNQ6YHQ3W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZE46RX3S2SOWX3WHRCNQ6YHQ3W/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":"2026-05-30T12:15:16Z","links":{"resolver":"https://pith.science/pith/ZE46RX3S2SOWX3WHRCNQ6YHQ3W","bundle":"https://pith.science/pith/ZE46RX3S2SOWX3WHRCNQ6YHQ3W/bundle.json","state":"https://pith.science/pith/ZE46RX3S2SOWX3WHRCNQ6YHQ3W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZE46RX3S2SOWX3WHRCNQ6YHQ3W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZE46RX3S2SOWX3WHRCNQ6YHQ3W","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":"62e33c691c0468e19d95ca48fad21aaecbe3ed6f844ad013740a11f8948a6225","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-10-18T06:57:03Z","title_canon_sha256":"0c96c8e327699b4c5ef1b10d40ccb5b23b4b405734c008ebaaf64960e95d90c1"},"schema_version":"1.0","source":{"id":"1710.06595","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.06595","created_at":"2026-05-18T00:22:20Z"},{"alias_kind":"arxiv_version","alias_value":"1710.06595v2","created_at":"2026-05-18T00:22:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.06595","created_at":"2026-05-18T00:22:20Z"},{"alias_kind":"pith_short_12","alias_value":"ZE46RX3S2SOW","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZE46RX3S2SOWX3WH","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZE46RX3S","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:8e602b1ce153afcd838ff401023964dac7792c3c992850a97b3fb6f5e4e42f66","target":"graph","created_at":"2026-05-18T00:22:20Z","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":"Robustness to outliers is a central issue in real-world machine learning applications. While replacing a model to a heavy-tailed one (e.g., from Gaussian to Student-t) is a standard approach for robustification, it can only be applied to simple models. In this paper, based on Zellner's optimization and variational formulation of Bayesian inference, we propose an outlier-robust pseudo-Bayesian variational method by replacing the Kullback-Leibler divergence used for data fitting to a robust divergence such as the beta- and gamma-divergences. An advantage of our approach is that superior but comp","authors_text":"Futoshi Futami, Issei Sato, Masashi Sugiyama","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-10-18T06:57:03Z","title":"Variational Inference based on Robust Divergences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.06595","kind":"arxiv","version":2},"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":"sha256:4f8d9dff9cddd39da735bc09f6f2e57fabc21823277c7568f0e5ed2bcbc31fae","target":"record","created_at":"2026-05-18T00:22:20Z","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":"62e33c691c0468e19d95ca48fad21aaecbe3ed6f844ad013740a11f8948a6225","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-10-18T06:57:03Z","title_canon_sha256":"0c96c8e327699b4c5ef1b10d40ccb5b23b4b405734c008ebaaf64960e95d90c1"},"schema_version":"1.0","source":{"id":"1710.06595","kind":"arxiv","version":2}},"canonical_sha256":"c939e8df72d49d6beec7889b0f60f0dda63e406016586d10bdae69dc8c370bdf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c939e8df72d49d6beec7889b0f60f0dda63e406016586d10bdae69dc8c370bdf","first_computed_at":"2026-05-18T00:22:20.639691Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:20.639691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZMcE/dK1idfOWYkUSsXqF0sgF1HdA+cU2UqaedAxPzov96yu2zBWx3Nvec91Fdoe6Zz/SfGf6+6N9MOYgks5Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:20.640251Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.06595","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f8d9dff9cddd39da735bc09f6f2e57fabc21823277c7568f0e5ed2bcbc31fae","sha256:8e602b1ce153afcd838ff401023964dac7792c3c992850a97b3fb6f5e4e42f66"],"state_sha256":"d9f6058a192f839deaa687018df3eeda4ac2873ab69d6729ffbee1e590dc7553"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WETyEl3jIJrDdi+JM/obY4cg1V6e6ZXHhFBAjcjlDn9DqJoZdOn91cg+B7hvX1fTQ2wP/5gk1gei7LHkTFapDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T12:15:16.141589Z","bundle_sha256":"30a6cb681d9009df9f22bd0eb3b0112b0a1e6fbd47993a5492a670cf8f7c2f8f"}}