{"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/robust-estimation-of-causal-heteroscedastic","title":"Robust Estimation of Causal Heteroscedastic Noise Models","arxiv_id":"2312.10102","date":"2023-12-15","proceeding":null,"authors":["Quang-Duy Tran","Bao Duong","Phuoc Nguyen","Thin Nguyen"],"abstract":"Distinguishing the cause and effect from bivariate observational data is the foundational problem that finds applications in many scientific disciplines. One solution to this problem is assuming that cause and effect are generated from a structural causal model, enabling identification of the causal direction after estimating the model in each direction. The heteroscedastic noise model is a type of structural causal model where the cause can contribute to both the mean and variance of the noise. Current methods for estimating heteroscedastic noise models choose the Gaussian likelihood as the optimization objective which can be suboptimal and unstable when the data has a non-Gaussian distribution. To address this limitation, we propose a novel approach to estimating this model with Student's $t$-distribution, which is known for its robustness in accounting for sampling variability with smaller sample sizes and extreme values without significantly altering the overall distribution shape. This adaptability is beneficial for capturing the parameters of the noise distribution in heteroscedastic noise models. Our empirical evaluations demonstrate that our estimators are more robust and achieve better overall performance across synthetic and real benchmarks.","url_abs":"https://arxiv.org/abs/2312.10102v1","url_pdf":"https://arxiv.org/pdf/2312.10102v1.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":"robust-estimation-of-causal-heteroscedastic","repo_url":"https://github.com/quangdzuytran/ROCHE","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2312.10102","atlas_url":"https://app.syntology.ai/?focus=2312.10102","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2312.10102"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+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/quangdzuytran/ROCHE","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"ran":4,"unverified":2},"by_repo_kind":{"official":{"samples":6,"ran":4,"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":"97c4e23c2181e7fd","entry":"HSIC","repo":"quangdzuytran/ROCHE","repo_kind":"official","path":"causa/hsic_torch.py","file_url":"https://github.com/quangdzuytran/ROCHE/blob/HEAD/causa/hsic_torch.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":"97c4e23c2181e7fd"}},{"code_sha256_prefix":"268c670e12c7fb1b","entry":"build_het_network","repo":"quangdzuytran/ROCHE","repo_kind":"official","path":"causa/roche.py","file_url":"https://github.com/quangdzuytran/ROCHE/blob/HEAD/causa/roche.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":"268c670e12c7fb1b"}},{"code_sha256_prefix":"bceca8207f63f53b","entry":"gaussian_grammat","repo":"quangdzuytran/ROCHE","repo_kind":"official","path":"causa/hsic_torch.py","file_url":"https://github.com/quangdzuytran/ROCHE/blob/HEAD/causa/hsic_torch.py","link_basis":"first_harvest_node","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":"bceca8207f63f53b"}},{"code_sha256_prefix":"4a43f04570f2e3bd","entry":"loss_func","repo":"quangdzuytran/ROCHE","repo_kind":"official","path":"causa/roche.py","file_url":"https://github.com/quangdzuytran/ROCHE/blob/HEAD/causa/roche.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":"4a43f04570f2e3bd"}},{"code_sha256_prefix":"a8c3780224cc4a67","entry":"centering","repo":"quangdzuytran/ROCHE","repo_kind":"official","path":"causa/hsic_torch.py","file_url":"https://github.com/quangdzuytran/ROCHE/blob/HEAD/causa/hsic_torch.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":"a8c3780224cc4a67"}},{"code_sha256_prefix":"fa635d3cdd4d9a5e","entry":"map_optimization","repo":"quangdzuytran/ROCHE","repo_kind":"official","path":"causa/roche.py","file_url":"https://github.com/quangdzuytran/ROCHE/blob/HEAD/causa/roche.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":"fa635d3cdd4d9a5e"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}