{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/simple-and-scalable-predictive-uncertainty","title":"Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles","arxiv_id":"1612.01474","date":"2016-12-05","proceeding":"NeurIPS 2017 12","authors":["Balaji Lakshminarayanan","Alexander Pritzel","Charles Blundell"],"abstract":"Deep neural networks (NNs) are powerful black box predictors that have\nrecently achieved impressive performance on a wide spectrum of tasks.\nQuantifying predictive uncertainty in NNs is a challenging and yet unsolved\nproblem. Bayesian NNs, which learn a distribution over weights, are currently\nthe state-of-the-art for estimating predictive uncertainty; however these\nrequire significant modifications to the training procedure and are\ncomputationally expensive compared to standard (non-Bayesian) NNs. We propose\nan alternative to Bayesian NNs that is simple to implement, readily\nparallelizable, requires very little hyperparameter tuning, and yields high\nquality predictive uncertainty estimates. Through a series of experiments on\nclassification and regression benchmarks, we demonstrate that our method\nproduces well-calibrated uncertainty estimates which are as good or better than\napproximate Bayesian NNs. To assess robustness to dataset shift, we evaluate\nthe predictive uncertainty on test examples from known and unknown\ndistributions, and show that our method is able to express higher uncertainty\non out-of-distribution examples. We demonstrate the scalability of our method\nby evaluating predictive uncertainty estimates on ImageNet.","url_abs":"http://arxiv.org/abs/1612.01474v3","url_pdf":"http://arxiv.org/pdf/1612.01474v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"simple-and-scalable-predictive-uncertainty","repo_url":"https://github.com/Glutamat42/epistemic_ensemble_toy_dataset","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"simple-and-scalable-predictive-uncertainty","repo_url":"https://github.com/JoonHyung-Park/DeepEnsemble","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"simple-and-scalable-predictive-uncertainty","repo_url":"https://github.com/Junghwan-brian/SDE-Net","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":null},{"paper_slug":"simple-and-scalable-predictive-uncertainty","repo_url":"https://github.com/Kyushik/Predictive-Uncertainty-Estimation-using-Deep-Ensemble","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok"}},{"paper_slug":"simple-and-scalable-predictive-uncertainty","repo_url":"https://github.com/StanfordASL/SCOD","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"simple-and-scalable-predictive-uncertainty","repo_url":"https://github.com/arnavc1712/DeepEnsembles","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"simple-and-scalable-predictive-uncertainty","repo_url":"https://github.com/axelbrando/Mixture-Density-Networks-for-distribution-and-uncertainty-estimation","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"Apache-2.0"}},{"paper_slug":"simple-and-scalable-predictive-uncertainty","repo_url":"https://github.com/cameronccohen/deep-ensembles","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}},{"paper_slug":"simple-and-scalable-predictive-uncertainty","repo_url":"https://github.com/cpark321/bayesian-neural-networks","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"unanswered"}},{"paper_slug":"simple-and-scalable-predictive-uncertainty","repo_url":"https://github.com/cpark321/uncertainty-deep-learning","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"unanswered"}},{"paper_slug":"simple-and-scalable-predictive-uncertainty","repo_url":"https://github.com/dougbrion/pytorch-deep-ensembles","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"simple-and-scalable-predictive-uncertainty","repo_url":"https://github.com/hayoung-kim/tf2-deep-ensemble-uncertainty","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok"}},{"paper_slug":"simple-and-scalable-predictive-uncertainty","repo_url":"https://github.com/hoidn/ptychopinn","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"GPL-3.0"}},{"paper_slug":"simple-and-scalable-predictive-uncertainty","repo_url":"https://github.com/huyng/incertae","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok"}},{"paper_slug":"simple-and-scalable-predictive-uncertainty","repo_url":"https://github.com/omegafragger/DDU","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"simple-and-scalable-predictive-uncertainty","repo_url":"https://github.com/pycroscopy/atomai","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"simple-and-scalable-predictive-uncertainty","repo_url":"https://github.com/stat-ml/dpp-dropout-uncertainty","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}},{"paper_slug":"simple-and-scalable-predictive-uncertainty","repo_url":"https://github.com/statsu1990/deep_ensembles","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"simple-and-scalable-predictive-uncertainty","repo_url":"https://github.com/tkerscher/blast","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"simple-and-scalable-predictive-uncertainty","repo_url":"https://github.com/tykurtz/tensorflow_models","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok"}},{"paper_slug":"simple-and-scalable-predictive-uncertainty","repo_url":"https://github.com/vvanirudh/deep-ensembles-uncertainty","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"GPL-3.0"}},{"paper_slug":"simple-and-scalable-predictive-uncertainty","repo_url":"https://github.com/xuyxu/Ensemble-Pytorch","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"BSD-3-Clause"}},{"paper_slug":"simple-and-scalable-predictive-uncertainty","repo_url":"https://github.com/ENSTA-U2IS-AI/torch-uncertainty","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok","spdx":"Apache-2.0"}},{"paper_slug":"simple-and-scalable-predictive-uncertainty","repo_url":"https://github.com/github-jnauta/pytorch-pne","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":null},{"paper_slug":"simple-and-scalable-predictive-uncertainty","repo_url":"https://github.com/lightning-uq-box/lightning-uq-box","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":null},{"paper_slug":"simple-and-scalable-predictive-uncertainty","repo_url":"https://github.com/mvaldenegro/keras-uncertainty","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"tf","reach":{"status":"ok","spdx":"LGPL-3.0"}}],"tasks":[{"task_slug":"image-classification","task_name":"Image Classification"},{"task_slug":"uncertainty-quantification","task_name":"Uncertainty Quantification"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[{"method_slug":"deep-ensembles","method_name":"Deep Ensembles"}],"datasets_introduced":[],"methods_introduced":[{"slug":"deep-ensembles","name":"Deep Ensembles","full_name":"Deep Ensembles"}],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1612.01474","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1612.01474"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/ENSTA-U2IS-AI/torch-uncertainty","reach":{"status":"ok","spdx":"Apache-2.0"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/JoonHyung-Park/DeepEnsemble","reach":null},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/statsu1990/deep_ensembles","reach":{"status":"ok","spdx":"MIT"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/lightning-uq-box/lightning-uq-box","reach":null},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/cameronccohen/deep-ensembles","reach":{"status":"ok"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/StanfordASL/SCOD","reach":null},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/hoidn/ptychopinn","reach":{"status":"ok","spdx":"GPL-3.0"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/hayoung-kim/tf2-deep-ensemble-uncertainty","reach":{"status":"ok"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/github-jnauta/pytorch-pne","reach":null},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/tykurtz/tensorflow_models","reach":{"status":"ok"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/stat-ml/dpp-dropout-uncertainty","reach":{"status":"ok"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/pycroscopy/atomai","reach":{"status":"ok","spdx":"MIT"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/Kyushik/Predictive-Uncertainty-Estimation-using-Deep-Ensemble","reach":{"status":"ok"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/tkerscher/blast","reach":{"status":"ok","spdx":"MIT"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/mvaldenegro/keras-uncertainty","reach":{"status":"ok","spdx":"LGPL-3.0"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/omegafragger/DDU","reach":null},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/dougbrion/pytorch-deep-ensembles","reach":{"status":"ok","spdx":"MIT"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/Junghwan-brian/SDE-Net","reach":null},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/axelbrando/Mixture-Density-Networks-for-distribution-and-uncertainty-estimation","reach":{"status":"ok","spdx":"Apache-2.0"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/arnavc1712/DeepEnsembles","reach":{"status":"ok"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/xuyxu/Ensemble-Pytorch","reach":{"status":"ok","spdx":"BSD-3-Clause"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/vvanirudh/deep-ensembles-uncertainty","reach":{"status":"ok","spdx":"GPL-3.0"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/cpark321/bayesian-neural-networks","reach":{"status":"unanswered"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/cpark321/uncertainty-deep-learning","reach":{"status":"unanswered"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/Glutamat42/epistemic_ensemble_toy_dataset","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"ran":8,"ran_draft_wrong":1,"unverified":2},"by_repo_kind":{"listed":{"samples":11,"ran":9,"repositories":6}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":6,"samples":[{"code_sha256_prefix":"59b274fed1c2f7d5","entry":"Diffusion","repo":"Junghwan-brian/SDE-Net","repo_kind":"listed","path":"model/SDENet.py","file_url":"https://github.com/Junghwan-brian/SDE-Net/blob/HEAD/model/SDENet.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"59b274fed1c2f7d5"}},{"code_sha256_prefix":"9ceff01e171db846","entry":"Drift","repo":"Junghwan-brian/SDE-Net","repo_kind":"listed","path":"model/SDENet.py","file_url":"https://github.com/Junghwan-brian/SDE-Net/blob/HEAD/model/SDENet.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"9ceff01e171db846"}},{"code_sha256_prefix":"cfe90024d387377b","entry":"Ensemble","repo":"StanfordASL/SCOD","repo_kind":"listed","path":"nn_ood/posteriors/ensemble.py","file_url":"https://github.com/StanfordASL/SCOD/blob/HEAD/nn_ood/posteriors/ensemble.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":"deterministic","behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"cfe90024d387377b"}},{"code_sha256_prefix":"2bb0022c0652839d","entry":"GaussianMLP","repo":"JoonHyung-Park/DeepEnsemble","repo_kind":"listed","path":"complete_ver/model.py","file_url":"https://github.com/JoonHyung-Park/DeepEnsemble/blob/HEAD/complete_ver/model.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":"deterministic","behaviour_fingerprint":true,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"2bb0022c0652839d"}},{"code_sha256_prefix":"8f0ebe8c1a69cb4b","entry":"MLP","repo":"JoonHyung-Park/DeepEnsemble","repo_kind":"listed","path":"complete_ver/model.py","file_url":"https://github.com/JoonHyung-Park/DeepEnsemble/blob/HEAD/complete_ver/model.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":"deterministic","behaviour_fingerprint":true,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"8f0ebe8c1a69cb4b"}},{"code_sha256_prefix":"1fbc81b2bd6ea48b","entry":"Model","repo":"github-jnauta/pytorch-pne","repo_kind":"listed","path":"models/pnn.py","file_url":"https://github.com/github-jnauta/pytorch-pne/blob/HEAD/models/pnn.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"1fbc81b2bd6ea48b"}},{"code_sha256_prefix":"b8e6a0ddc977191d","entry":"_DeepEnsembles","repo":"ENSTA-U2IS-AI/torch-uncertainty","repo_kind":"listed","path":"src/torch_uncertainty/methods/deep_ensembles.py","file_url":"https://github.com/ENSTA-U2IS-AI/torch-uncertainty/blob/HEAD/src/torch_uncertainty/methods/deep_ensembles.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":"deterministic","behaviour_fingerprint":true,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"b8e6a0ddc977191d"}},{"code_sha256_prefix":"5425e2595166ea3a","entry":"_RegDeepEnsembles","repo":"ENSTA-U2IS-AI/torch-uncertainty","repo_kind":"listed","path":"src/torch_uncertainty/methods/deep_ensembles.py","file_url":"https://github.com/ENSTA-U2IS-AI/torch-uncertainty/blob/HEAD/src/torch_uncertainty/methods/deep_ensembles.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":"deterministic","behaviour_fingerprint":true,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"5425e2595166ea3a"}},{"code_sha256_prefix":"a76c86e0e721e4b2","entry":"deep_ensembles","repo":"ENSTA-U2IS-AI/torch-uncertainty","repo_kind":"listed","path":"src/torch_uncertainty/methods/deep_ensembles.py","file_url":"https://github.com/ENSTA-U2IS-AI/torch-uncertainty/blob/HEAD/src/torch_uncertainty/methods/deep_ensembles.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":"deterministic","behaviour_fingerprint":false,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"a76c86e0e721e4b2"}},{"code_sha256_prefix":"9c625ca32e821ccc","entry":"SDENet","repo":"Junghwan-brian/SDE-Net","repo_kind":"listed","path":"model/SDENet.py","file_url":"https://github.com/Junghwan-brian/SDE-Net/blob/HEAD/model/SDENet.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"9c625ca32e821ccc"}},{"code_sha256_prefix":"a03d09d6f461b685","entry":"parse_sed","repo":"tkerscher/blast","repo_kind":"listed","path":"blast/parser.py","file_url":"https://github.com/tkerscher/blast/blob/HEAD/blast/parser.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"a03d09d6f461b685"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}