{"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/conditional-optimal-transport-on-function","title":"Conditional Optimal Transport on Function Spaces","arxiv_id":"2311.05672","date":"2023-11-09","proceeding":null,"authors":["Bamdad Hosseini","Alexander W. Hsu","Amirhossein Taghvaei"],"abstract":"We present a systematic study of conditional triangular transport maps in function spaces from the perspective of optimal transportation and with a view towards amortized Bayesian inference. More specifically, we develop a theory of constrained optimal transport problems that describe block-triangular Monge maps that characterize conditional measures along with their Kantorovich relaxations. This generalizes the theory of optimal triangular transport to separable infinite-dimensional function spaces with general cost functions. We further tailor our results to the case of Bayesian inference problems and obtain regularity estimates on the conditioning maps from the prior to the posterior. Finally, we present numerical experiments that demonstrate the computational applicability of our theoretical results for amortized and likelihood-free inference of functional parameters.","url_abs":"https://arxiv.org/abs/2311.05672v3","url_pdf":"https://arxiv.org/pdf/2311.05672v3.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":"conditional-optimal-transport-on-function","repo_url":"https://github.com/tadsgroup/conditionalot2023","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"bayesian-inference","task_name":"Bayesian Inference"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2311.05672","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2311.05672"}},"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/tadsgroup/conditionalot2023","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"ran":14,"unverified":2},"by_repo_kind":{"official":{"samples":16,"ran":14,"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":"6b60e9fbda76a974","entry":"build_regression_problem","repo":"tadsgroup/conditionalot2023","repo_kind":"official","path":"ConditionalTransport/conditioningMaps.py","file_url":"https://github.com/tadsgroup/conditionalot2023/blob/HEAD/ConditionalTransport/conditioningMaps.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"6b60e9fbda76a974"}},{"code_sha256_prefix":"072b07c325f02ef4","entry":"constant_rhs","repo":"tadsgroup/conditionalot2023","repo_kind":"official","path":"pCN/darcy_pCN.py","file_url":"https://github.com/tadsgroup/conditionalot2023/blob/HEAD/pCN/darcy_pCN.py","link_basis":"harvester_set","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"072b07c325f02ef4"}},{"code_sha256_prefix":"e4ebd0c28e19be69","entry":"get_bimodal_1d_dataloader","repo":"tadsgroup/conditionalot2023","repo_kind":"official","path":"WaMGAN/dataloaders.py","file_url":"https://github.com/tadsgroup/conditionalot2023/blob/HEAD/WaMGAN/dataloaders.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"e4ebd0c28e19be69"}},{"code_sha256_prefix":"8993535c74afd84b","entry":"get_epsilon_quadratic_cost_mat","repo":"tadsgroup/conditionalot2023","repo_kind":"official","path":"ConditionalTransport/conditioningMaps.py","file_url":"https://github.com/tadsgroup/conditionalot2023/blob/HEAD/ConditionalTransport/conditioningMaps.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"8993535c74afd84b"}},{"code_sha256_prefix":"c1b7d8da9b0a2598","entry":"get_quadratic_dataloader","repo":"tadsgroup/conditionalot2023","repo_kind":"official","path":"WaMGAN/dataloaders.py","file_url":"https://github.com/tadsgroup/conditionalot2023/blob/HEAD/WaMGAN/dataloaders.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"c1b7d8da9b0a2598"}},{"code_sha256_prefix":"e9d02478c371c9f3","entry":"interpolate_for_fenics","repo":"tadsgroup/conditionalot2023","repo_kind":"official","path":"pCN/darcy_pCN.py","file_url":"https://github.com/tadsgroup/conditionalot2023/blob/HEAD/pCN/darcy_pCN.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"e9d02478c371c9f3"}},{"code_sha256_prefix":"2940dc9a7f977c9b","entry":"matern_five_half","repo":"tadsgroup/conditionalot2023","repo_kind":"official","path":"build_dataset.py","file_url":"https://github.com/tadsgroup/conditionalot2023/blob/HEAD/build_dataset.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"2940dc9a7f977c9b"}},{"code_sha256_prefix":"5f2adff30f6d818a","entry":"matern_one_half","repo":"tadsgroup/conditionalot2023","repo_kind":"official","path":"build_dataset.py","file_url":"https://github.com/tadsgroup/conditionalot2023/blob/HEAD/build_dataset.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"5f2adff30f6d818a"}},{"code_sha256_prefix":"6cc668424138d363","entry":"matern_three_half","repo":"tadsgroup/conditionalot2023","repo_kind":"official","path":"build_dataset.py","file_url":"https://github.com/tadsgroup/conditionalot2023/blob/HEAD/build_dataset.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"6cc668424138d363"}},{"code_sha256_prefix":"9504b044a236bceb","entry":"normalize","repo":"tadsgroup/conditionalot2023","repo_kind":"official","path":"ConditionalTransport/data_generators.py","file_url":"https://github.com/tadsgroup/conditionalot2023/blob/HEAD/ConditionalTransport/data_generators.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"9504b044a236bceb"}},{"code_sha256_prefix":"1784bcd5bae0df79","entry":"pointset_pushforward_ot","repo":"tadsgroup/conditionalot2023","repo_kind":"official","path":"ConditionalTransport/conditioningMaps.py","file_url":"https://github.com/tadsgroup/conditionalot2023/blob/HEAD/ConditionalTransport/conditioningMaps.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"1784bcd5bae0df79"}},{"code_sha256_prefix":"2482399593e22d2f","entry":"rand_covar","repo":"tadsgroup/conditionalot2023","repo_kind":"official","path":"ConditionalTransport/data_generators.py","file_url":"https://github.com/tadsgroup/conditionalot2023/blob/HEAD/ConditionalTransport/data_generators.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"2482399593e22d2f"}},{"code_sha256_prefix":"30bbc4a811d0b3b3","entry":"replace_zeros","repo":"tadsgroup/conditionalot2023","repo_kind":"official","path":"ConditionalTransport/data_generators.py","file_url":"https://github.com/tadsgroup/conditionalot2023/blob/HEAD/ConditionalTransport/data_generators.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"30bbc4a811d0b3b3"}},{"code_sha256_prefix":"794c860b8251bde0","entry":"zero_boundary_conditions","repo":"tadsgroup/conditionalot2023","repo_kind":"official","path":"darcySolver.py","file_url":"https://github.com/tadsgroup/conditionalot2023/blob/HEAD/darcySolver.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"794c860b8251bde0"}},{"code_sha256_prefix":"93a7f9a664b6bd00","entry":"get_darcy_data_transformers","repo":"tadsgroup/conditionalot2023","repo_kind":"official","path":"ConditionalTransport/dataloader.py","file_url":"https://github.com/tadsgroup/conditionalot2023/blob/HEAD/ConditionalTransport/dataloader.py","link_basis":"first_harvest_node","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":"93a7f9a664b6bd00"}},{"code_sha256_prefix":"9e4fc5c2d7d76f5a","entry":"get_darcy_dataloader_transformers","repo":"tadsgroup/conditionalot2023","repo_kind":"official","path":"WaMGAN/dataloaders.py","file_url":"https://github.com/tadsgroup/conditionalot2023/blob/HEAD/WaMGAN/dataloaders.py","link_basis":"first_harvest_node","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":"9e4fc5c2d7d76f5a"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}