{"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/conformal-prediction-under-ambiguous-ground","title":"Conformal prediction under ambiguous ground truth","arxiv_id":"2307.09302","date":"2023-07-18","proceeding":null,"authors":["David Stutz","Abhijit Guha Roy","Tatiana Matejovicova","Patricia Strachan","Ali Taylan Cemgil","Arnaud Doucet"],"abstract":"Conformal Prediction (CP) allows to perform rigorous uncertainty quantification by constructing a prediction set $C(X)$ satisfying $\\mathbb{P}(Y \\in C(X))\\geq 1-\\alpha$ for a user-chosen $\\alpha \\in [0,1]$ by relying on calibration data $(X_1,Y_1),...,(X_n,Y_n)$ from $\\mathbb{P}=\\mathbb{P}^{X} \\otimes \\mathbb{P}^{Y|X}$. It is typically implicitly assumed that $\\mathbb{P}^{Y|X}$ is the \"true\" posterior label distribution. However, in many real-world scenarios, the labels $Y_1,...,Y_n$ are obtained by aggregating expert opinions using a voting procedure, resulting in a one-hot distribution $\\mathbb{P}_{vote}^{Y|X}$. For such ``voted'' labels, CP guarantees are thus w.r.t. $\\mathbb{P}_{vote}=\\mathbb{P}^X \\otimes \\mathbb{P}_{vote}^{Y|X}$ rather than the true distribution $\\mathbb{P}$. In cases with unambiguous ground truth labels, the distinction between $\\mathbb{P}_{vote}$ and $\\mathbb{P}$ is irrelevant. However, when experts do not agree because of ambiguous labels, approximating $\\mathbb{P}^{Y|X}$ with a one-hot distribution $\\mathbb{P}_{vote}^{Y|X}$ ignores this uncertainty. In this paper, we propose to leverage expert opinions to approximate $\\mathbb{P}^{Y|X}$ using a non-degenerate distribution $\\mathbb{P}_{agg}^{Y|X}$. We develop Monte Carlo CP procedures which provide guarantees w.r.t. $\\mathbb{P}_{agg}=\\mathbb{P}^X \\otimes \\mathbb{P}_{agg}^{Y|X}$ by sampling multiple synthetic pseudo-labels from $\\mathbb{P}_{agg}^{Y|X}$ for each calibration example $X_1,...,X_n$. In a case study of skin condition classification with significant disagreement among expert annotators, we show that applying CP w.r.t. $\\mathbb{P}_{vote}$ under-covers expert annotations: calibrated for $72\\%$ coverage, it falls short by on average $10\\%$; our Monte Carlo CP closes this gap both empirically and theoretically.","url_abs":"https://arxiv.org/abs/2307.09302v2","url_pdf":"https://arxiv.org/pdf/2307.09302v2.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":"conformal-prediction-under-ambiguous-ground","repo_url":"https://github.com/google-deepmind/uncertain_ground_truth","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"jax","reach":null},{"paper_slug":"conformal-prediction-under-ambiguous-ground","repo_url":"https://github.com/alaalab/webcp","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"conformal-prediction","task_name":"Conformal Prediction"},{"task_slug":"prediction","task_name":"Prediction"},{"task_slug":"uncertainty-quantification","task_name":"Uncertainty Quantification"}],"methods":[],"datasets_introduced":[{"slug":"dermatology-ddx-dataset","name":"Dermatology ddx dataset","full_name":""}],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2307.09302","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2307.09302"}},"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/alaalab/webcp","reach":{"status":"ok","spdx":"MIT"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/google-deepmind/uncertain_ground_truth","reach":null}],"summary":{"ran_draft_wrong":2,"ran_fixture":3,"ran_honours":1,"unverified":13},"by_repo_kind":{"official":{"samples":6,"ran":6,"repositories":1},"listed":{"samples":13,"ran":0,"repositories":1}},"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":0,"samples":[{"code_sha256_prefix":"9454afd876c4a7c7","entry":"calibrate_mc_threshold","repo":"google-deepmind/uncertain_ground_truth","repo_kind":"official","path":"monte_carlo.py","file_url":"https://github.com/google-deepmind/uncertain_ground_truth/blob/HEAD/monte_carlo.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"MISDECLARED","metamorphic_tier":"invariant","behaviour_fingerprint":false,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"9454afd876c4a7c7"}},{"code_sha256_prefix":"9dbcb314e6aad51b","entry":"calibrate_threshold","repo":"google-deepmind/uncertain_ground_truth","repo_kind":"official","path":"conformal_prediction.py","file_url":"https://github.com/google-deepmind/uncertain_ground_truth/blob/HEAD/conformal_prediction.py","link_basis":"first_harvest_node","language":"python","status":"ran_fixture","verification_level":1,"contract_check":"RAISES","metamorphic_tier":"invariant","behaviour_fingerprint":false,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"9dbcb314e6aad51b"}},{"code_sha256_prefix":"c293ce6b6a5d4d3d","entry":"conformal_quantile","repo":"google-deepmind/uncertain_ground_truth","repo_kind":"official","path":"conformal_prediction.py","file_url":"https://github.com/google-deepmind/uncertain_ground_truth/blob/HEAD/conformal_prediction.py","link_basis":"first_harvest_node","language":"python","status":"ran_fixture","verification_level":1,"contract_check":"RAISES","metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"c293ce6b6a5d4d3d"}},{"code_sha256_prefix":"2436571bd53cdc72","entry":"mc_conformal_quantile","repo":"google-deepmind/uncertain_ground_truth","repo_kind":"official","path":"monte_carlo.py","file_url":"https://github.com/google-deepmind/uncertain_ground_truth/blob/HEAD/monte_carlo.py","link_basis":"first_harvest_node","language":"python","status":"ran_fixture","verification_level":1,"contract_check":"RAISES","metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"2436571bd53cdc72"}},{"code_sha256_prefix":"792f08759b26f4dc","entry":"predict_threshold","repo":"google-deepmind/uncertain_ground_truth","repo_kind":"official","path":"conformal_prediction.py","file_url":"https://github.com/google-deepmind/uncertain_ground_truth/blob/HEAD/conformal_prediction.py","link_basis":"first_harvest_node","language":"python","status":"ran_honours","verification_level":1,"contract_check":"HONOURS","metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"792f08759b26f4dc"}},{"code_sha256_prefix":"63fb282a3dc3fb0a","entry":"sample_mc_labels","repo":"google-deepmind/uncertain_ground_truth","repo_kind":"official","path":"monte_carlo.py","file_url":"https://github.com/google-deepmind/uncertain_ground_truth/blob/HEAD/monte_carlo.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"MISDECLARED","metamorphic_tier":"deterministic","behaviour_fingerprint":false,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"63fb282a3dc3fb0a"}},{"code_sha256_prefix":"981bb17491bde067","entry":"class_stratified_coverage","repo":"alaalab/webcp","repo_kind":"listed","path":"ambiguous_cp/metrics.py","file_url":"https://github.com/alaalab/webcp/blob/HEAD/ambiguous_cp/metrics.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":"981bb17491bde067"}},{"code_sha256_prefix":"3776f69137111df4","entry":"compute_prediction_sets","repo":"alaalab/webcp","repo_kind":"listed","path":"ambiguous_cp/conformal_risk_control.py","file_url":"https://github.com/alaalab/webcp/blob/HEAD/ambiguous_cp/conformal_risk_control.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":"3776f69137111df4"}},{"code_sha256_prefix":"d57df6bb388ac156","entry":"compute_prediction_sets_threshold","repo":"alaalab/webcp","repo_kind":"listed","path":"ambiguous_cp/conformal_prediction_methods.py","file_url":"https://github.com/alaalab/webcp/blob/HEAD/ambiguous_cp/conformal_prediction_methods.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":"d57df6bb388ac156"}},{"code_sha256_prefix":"1a976aa6e853fa6b","entry":"compute_simscores","repo":"alaalab/webcp","repo_kind":"listed","path":"compute_alignments/generate_context_alignments.py","file_url":"https://github.com/alaalab/webcp/blob/HEAD/compute_alignments/generate_context_alignments.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":"1a976aa6e853fa6b"}},{"code_sha256_prefix":"9b4f33f1fb0e29e7","entry":"compute_threshold","repo":"alaalab/webcp","repo_kind":"listed","path":"ambiguous_cp/conformal_prediction_methods.py","file_url":"https://github.com/alaalab/webcp/blob/HEAD/ambiguous_cp/conformal_prediction_methods.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":"9b4f33f1fb0e29e7"}},{"code_sha256_prefix":"d9ea461f5d5de794","entry":"get_fileidx_list","repo":"alaalab/webcp","repo_kind":"listed","path":"compute_alignments/generate_context_alignments.py","file_url":"https://github.com/alaalab/webcp/blob/HEAD/compute_alignments/generate_context_alignments.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":"d9ea461f5d5de794"}},{"code_sha256_prefix":"a3b4517e7249c4cf","entry":"openclip_image_preprocess","repo":"alaalab/webcp","repo_kind":"listed","path":"ambiguous_cp/experiment.py","file_url":"https://github.com/alaalab/webcp/blob/HEAD/ambiguous_cp/experiment.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":"a3b4517e7249c4cf"}},{"code_sha256_prefix":"33202b9bd3d95c68","entry":"openclip_process","repo":"alaalab/webcp","repo_kind":"listed","path":"ambiguous_cp/experiment.py","file_url":"https://github.com/alaalab/webcp/blob/HEAD/ambiguous_cp/experiment.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":"33202b9bd3d95c68"}},{"code_sha256_prefix":"4692dedab0106411","entry":"openclip_process","repo":"alaalab/webcp","repo_kind":"listed","path":"ambiguous_cp/plausibility_generation.py","file_url":"https://github.com/alaalab/webcp/blob/HEAD/ambiguous_cp/plausibility_generation.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":"4692dedab0106411"}},{"code_sha256_prefix":"cc19e29ec50fcdf5","entry":"openclip_text_preprocess","repo":"alaalab/webcp","repo_kind":"listed","path":"ambiguous_cp/experiment.py","file_url":"https://github.com/alaalab/webcp/blob/HEAD/ambiguous_cp/experiment.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":"cc19e29ec50fcdf5"}},{"code_sha256_prefix":"829b99fa5448188b","entry":"overall_coverage","repo":"alaalab/webcp","repo_kind":"listed","path":"ambiguous_cp/metrics.py","file_url":"https://github.com/alaalab/webcp/blob/HEAD/ambiguous_cp/metrics.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":"829b99fa5448188b"}},{"code_sha256_prefix":"ad14a67ac002ed26","entry":"performance_report","repo":"alaalab/webcp","repo_kind":"listed","path":"ambiguous_cp/analysis.py","file_url":"https://github.com/alaalab/webcp/blob/HEAD/ambiguous_cp/analysis.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":"ad14a67ac002ed26"}},{"code_sha256_prefix":"395fb2dace74ef7e","entry":"samplewise_loss","repo":"alaalab/webcp","repo_kind":"listed","path":"ambiguous_cp/conformal_prediction_methods.py","file_url":"https://github.com/alaalab/webcp/blob/HEAD/ambiguous_cp/conformal_prediction_methods.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":"395fb2dace74ef7e"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}