{"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/a-unifying-network-architecture-for-semi","title":"Semi-Structured Distributional Regression -- Extending Structured Additive Models by Arbitrary Deep Neural Networks and Data Modalities","arxiv_id":"2002.05777","date":"2020-02-13","proceeding":null,"authors":["David Rügamer","Chris Kolb","Nadja Klein"],"abstract":"Combining additive models and neural networks allows to broaden the scope of statistical regression and extend deep learning-based approaches by interpretable structured additive predictors at the same time. Existing attempts uniting the two modeling approaches are, however, limited to very specific combinations and, more importantly, involve an identifiability issue. As a consequence, interpretability and stable estimation are typically lost. We propose a general framework to combine structured regression models and deep neural networks into a unifying network architecture. To overcome the inherent identifiability issues between different model parts, we construct an orthogonalization cell that projects the deep neural network into the orthogonal complement of the statistical model predictor. This enables proper estimation of structured model parts and thereby interpretability. We demonstrate the framework's efficacy in numerical experiments and illustrate its special merits in benchmarks and real-world applications.","url_abs":"https://arxiv.org/abs/2002.05777v5","url_pdf":"https://arxiv.org/pdf/2002.05777v5.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":"a-unifying-network-architecture-for-semi","repo_url":"https://github.com/davidruegamer/semi-structured_distributional_regression","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"GPL-3.0"}},{"paper_slug":"a-unifying-network-architecture-for-semi","repo_url":"https://github.com/HelmholtzAI-Consultants-Munich/PySDDR","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"additive-models","task_name":"Additive models"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[{"method_slug":"interpretability","method_name":"Interpretability"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2002.05777","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2002.05777"}},"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/HelmholtzAI-Consultants-Munich/PySDDR","reach":{"status":"ok","spdx":"MIT"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/davidruegamer/semi-structured_distributional_regression","reach":{"status":"ok","spdx":"GPL-3.0"}}],"summary":{"unverified":3},"by_repo_kind":{"listed":{"samples":3,"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":"d483b0d5e12eb328","entry":"checkups","repo":"HelmholtzAI-Consultants-Munich/PySDDR","repo_kind":"listed","path":"sddr/utils/utils.py","file_url":"https://github.com/HelmholtzAI-Consultants-Munich/PySDDR/blob/HEAD/sddr/utils/utils.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":"d483b0d5e12eb328"}},{"code_sha256_prefix":"a55ddeb2f6421121","entry":"make_matrix_positive_semi_definite","repo":"HelmholtzAI-Consultants-Munich/PySDDR","repo_kind":"listed","path":"sddr/utils/utils.py","file_url":"https://github.com/HelmholtzAI-Consultants-Munich/PySDDR/blob/HEAD/sddr/utils/utils.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":"a55ddeb2f6421121"}},{"code_sha256_prefix":"3f25612a536fcc27","entry":"split_formula","repo":"HelmholtzAI-Consultants-Munich/PySDDR","repo_kind":"listed","path":"sddr/utils/utils.py","file_url":"https://github.com/HelmholtzAI-Consultants-Munich/PySDDR/blob/HEAD/sddr/utils/utils.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":"3f25612a536fcc27"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}