{"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/geometry-aware-maximum-likelihood-estimation","title":"Geometry-Aware Maximum Likelihood Estimation of Intrinsic Dimension","arxiv_id":"1904.06151","date":"2019-04-12","proceeding":null,"authors":["Marina Gomtsyan","Nikita Mokrov","Maxim Panov","Yury Yanovich"],"abstract":"The existing approaches to intrinsic dimension estimation usually are not\nreliable when the data are nonlinearly embedded in the high dimensional space.\nIn this work, we show that the explicit accounting to geometric properties of\nunknown support leads to the polynomial correction to the standard maximum\nlikelihood estimate of intrinsic dimension for flat manifolds. The proposed\nalgorithm (GeoMLE) realizes the correction by regression of standard MLEs based\non distances to nearest neighbors for different sizes of neighborhoods.\nMoreover, the proposed approach also efficiently handles the case of nonuniform\nsampling of the manifold. We perform numerous experiments on different\nsynthetic and real-world datasets. The results show that our algorithm achieves\nstate-of-the-art performance, while also being computationally efficient and\nrobust to noise in the data.","url_abs":"http://arxiv.org/abs/1904.06151v1","url_pdf":"http://arxiv.org/pdf/1904.06151v1.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":"geometry-aware-maximum-likelihood-estimation","repo_url":"https://github.com/stat-ml/GeoMLE","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"regression-1","task_name":"regression"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1904.06151","atlas_url":"https://app.syntology.ai/?focus=1904.06151","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1904.06151"}},"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/stat-ml/GeoMLE","reach":null}],"summary":{"ran_fixture":1,"ran_draft_wrong":1,"ran_honours":1},"by_repo_kind":{"listed":{"samples":3,"ran":3,"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":"c3e52574ec7f8090","entry":"drop_zero_values","repo":"stat-ml/GeoMLE","repo_kind":"listed","path":"geomle/geomle.py","file_url":"https://github.com/stat-ml/GeoMLE/blob/HEAD/geomle/geomle.py","link_basis":"first_harvest_node","language":"python","status":"ran_fixture","verification_level":1,"contract_check":"RAISES","metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"c3e52574ec7f8090"}},{"code_sha256_prefix":"4d8973a5a883d7dd","entry":"mle_center","repo":"stat-ml/GeoMLE","repo_kind":"listed","path":"geomle/geomle.py","file_url":"https://github.com/stat-ml/GeoMLE/blob/HEAD/geomle/geomle.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":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"4d8973a5a883d7dd"}},{"code_sha256_prefix":"a67a7b23ea7331c5","entry":"tolist","repo":"stat-ml/GeoMLE","repo_kind":"listed","path":"geomle/geomle.py","file_url":"https://github.com/stat-ml/GeoMLE/blob/HEAD/geomle/geomle.py","link_basis":"first_harvest_node","language":"python","status":"ran_honours","verification_level":1,"contract_check":"HONOURS","metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"a67a7b23ea7331c5"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}