{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:RST4KWLTH4XRTWJBIABBO6NFZI","short_pith_number":"pith:RST4KWLT","canonical_record":{"source":{"id":"2202.10951","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2022-02-22T14:44:22Z","cross_cats_sorted":["stat.AP"],"title_canon_sha256":"d247104fdbdc073a9ab9ba147ef8832af82f57da950ced54791a57f1bd93dd22","abstract_canon_sha256":"3a7ceedc265b28b7ebc8b08d642c769733b3823cf4fb4056328eaa041b5ed04e"},"schema_version":"1.0"},"canonical_sha256":"8ca7c559733f2f19d92140021779a5ca325680b99356c986f32be5150da896e1","source":{"kind":"arxiv","id":"2202.10951","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2202.10951","created_at":"2026-07-05T03:59:10Z"},{"alias_kind":"arxiv_version","alias_value":"2202.10951v1","created_at":"2026-07-05T03:59:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.10951","created_at":"2026-07-05T03:59:10Z"},{"alias_kind":"pith_short_12","alias_value":"RST4KWLTH4XR","created_at":"2026-07-05T03:59:10Z"},{"alias_kind":"pith_short_16","alias_value":"RST4KWLTH4XRTWJB","created_at":"2026-07-05T03:59:10Z"},{"alias_kind":"pith_short_8","alias_value":"RST4KWLT","created_at":"2026-07-05T03:59:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:RST4KWLTH4XRTWJBIABBO6NFZI","target":"record","payload":{"canonical_record":{"source":{"id":"2202.10951","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2022-02-22T14:44:22Z","cross_cats_sorted":["stat.AP"],"title_canon_sha256":"d247104fdbdc073a9ab9ba147ef8832af82f57da950ced54791a57f1bd93dd22","abstract_canon_sha256":"3a7ceedc265b28b7ebc8b08d642c769733b3823cf4fb4056328eaa041b5ed04e"},"schema_version":"1.0"},"canonical_sha256":"8ca7c559733f2f19d92140021779a5ca325680b99356c986f32be5150da896e1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:59:10.189178Z","signature_b64":"eGZ2QrgEkxt7ylgZoFvRt43pHNJ2w46PuaDYm1yWNjkkDd/iUNhnG8qCtdwkkqqj8dWGOoevi1DZyGvigCdjDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ca7c559733f2f19d92140021779a5ca325680b99356c986f32be5150da896e1","last_reissued_at":"2026-07-05T03:59:10.188642Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:59:10.188642Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2202.10951","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:59:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dQshGaoWfMuvQ/5iQ9DZ7dyCoB6j32bDIrAsGwalDZTWbuZffYMNA4ZCNk5Ow+t/v9GoDD/6BbVHk4B4XIpKCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T10:44:11.124583Z"},"content_sha256":"219a238f7922ffe290d070723e68681ba81d15e350eb81d9414b97c6649d7818","schema_version":"1.0","event_id":"sha256:219a238f7922ffe290d070723e68681ba81d15e350eb81d9414b97c6649d7818"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:RST4KWLTH4XRTWJBIABBO6NFZI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multiple Importance Sampling ELBO and Deep Ensembles of Variational Approximations","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["stat.AP"],"primary_cat":"cs.LG","authors_text":"Harald Melin, Hazal Koptagel, Jens Lagergren, Oskar Kviman, V\\'ictor Elvira","submitted_at":"2022-02-22T14:44:22Z","abstract_excerpt":"In variational inference (VI), the marginal log-likelihood is estimated using the standard evidence lower bound (ELBO), or improved versions as the importance weighted ELBO (IWELBO). We propose the multiple importance sampling ELBO (MISELBO), a \\textit{versatile} yet \\textit{simple} framework. MISELBO is applicable in both amortized and classical VI, and it uses ensembles, e.g., deep ensembles, of independently inferred variational approximations. As far as we are aware, the concept of deep ensembles in amortized VI has not previously been established. We prove that MISELBO provides a tighter "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.10951","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2202.10951/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:59:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i/oGRQM1dV81n9xOClvIgo+IZIjNL4gbwpyXYOknb6Sd5OhVGdYrq1QFpJNZj/hURc2x3pEHdZwk4HgnGzmgBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T10:44:11.124950Z"},"content_sha256":"a900bf638b461c7ec87bb071dad7010281c0b8c61d11676f48a64e1c1b3fec2f","schema_version":"1.0","event_id":"sha256:a900bf638b461c7ec87bb071dad7010281c0b8c61d11676f48a64e1c1b3fec2f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RST4KWLTH4XRTWJBIABBO6NFZI/bundle.json","state_url":"https://pith.science/pith/RST4KWLTH4XRTWJBIABBO6NFZI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RST4KWLTH4XRTWJBIABBO6NFZI/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":"2026-07-07T10:44:11Z","links":{"resolver":"https://pith.science/pith/RST4KWLTH4XRTWJBIABBO6NFZI","bundle":"https://pith.science/pith/RST4KWLTH4XRTWJBIABBO6NFZI/bundle.json","state":"https://pith.science/pith/RST4KWLTH4XRTWJBIABBO6NFZI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RST4KWLTH4XRTWJBIABBO6NFZI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:RST4KWLTH4XRTWJBIABBO6NFZI","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":"3a7ceedc265b28b7ebc8b08d642c769733b3823cf4fb4056328eaa041b5ed04e","cross_cats_sorted":["stat.AP"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2022-02-22T14:44:22Z","title_canon_sha256":"d247104fdbdc073a9ab9ba147ef8832af82f57da950ced54791a57f1bd93dd22"},"schema_version":"1.0","source":{"id":"2202.10951","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2202.10951","created_at":"2026-07-05T03:59:10Z"},{"alias_kind":"arxiv_version","alias_value":"2202.10951v1","created_at":"2026-07-05T03:59:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.10951","created_at":"2026-07-05T03:59:10Z"},{"alias_kind":"pith_short_12","alias_value":"RST4KWLTH4XR","created_at":"2026-07-05T03:59:10Z"},{"alias_kind":"pith_short_16","alias_value":"RST4KWLTH4XRTWJB","created_at":"2026-07-05T03:59:10Z"},{"alias_kind":"pith_short_8","alias_value":"RST4KWLT","created_at":"2026-07-05T03:59:10Z"}],"graph_snapshots":[{"event_id":"sha256:a900bf638b461c7ec87bb071dad7010281c0b8c61d11676f48a64e1c1b3fec2f","target":"graph","created_at":"2026-07-05T03:59:10Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2202.10951/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In variational inference (VI), the marginal log-likelihood is estimated using the standard evidence lower bound (ELBO), or improved versions as the importance weighted ELBO (IWELBO). We propose the multiple importance sampling ELBO (MISELBO), a \\textit{versatile} yet \\textit{simple} framework. MISELBO is applicable in both amortized and classical VI, and it uses ensembles, e.g., deep ensembles, of independently inferred variational approximations. As far as we are aware, the concept of deep ensembles in amortized VI has not previously been established. We prove that MISELBO provides a tighter ","authors_text":"Harald Melin, Hazal Koptagel, Jens Lagergren, Oskar Kviman, V\\'ictor Elvira","cross_cats":["stat.AP"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2022-02-22T14:44:22Z","title":"Multiple Importance Sampling ELBO and Deep Ensembles of Variational Approximations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.10951","kind":"arxiv","version":1},"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":"sha256:219a238f7922ffe290d070723e68681ba81d15e350eb81d9414b97c6649d7818","target":"record","created_at":"2026-07-05T03:59:10Z","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":"3a7ceedc265b28b7ebc8b08d642c769733b3823cf4fb4056328eaa041b5ed04e","cross_cats_sorted":["stat.AP"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2022-02-22T14:44:22Z","title_canon_sha256":"d247104fdbdc073a9ab9ba147ef8832af82f57da950ced54791a57f1bd93dd22"},"schema_version":"1.0","source":{"id":"2202.10951","kind":"arxiv","version":1}},"canonical_sha256":"8ca7c559733f2f19d92140021779a5ca325680b99356c986f32be5150da896e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ca7c559733f2f19d92140021779a5ca325680b99356c986f32be5150da896e1","first_computed_at":"2026-07-05T03:59:10.188642Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:59:10.188642Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eGZ2QrgEkxt7ylgZoFvRt43pHNJ2w46PuaDYm1yWNjkkDd/iUNhnG8qCtdwkkqqj8dWGOoevi1DZyGvigCdjDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:59:10.189178Z","signed_message":"canonical_sha256_bytes"},"source_id":"2202.10951","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:219a238f7922ffe290d070723e68681ba81d15e350eb81d9414b97c6649d7818","sha256:a900bf638b461c7ec87bb071dad7010281c0b8c61d11676f48a64e1c1b3fec2f"],"state_sha256":"cb13262ea78c5fec623d15c1bd8de975ef7563e03a07ad6c081a7a88da208dde"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9tSEdLt9xSWD3MZq1XeuIRS9BtxTB1TU3SQhkR6GA3LN2RkZfy8GJ2eu0ohtEWwVBxzTop3wy6LhfwgZjBsQBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T10:44:11.126884Z","bundle_sha256":"4391f2fbc140dfd0ec4d2618f427d40527893246d9826ebdf367da235ab849fa"}}