{"paper":{"title":"Identifying Causal Direction via Dense Functional Classes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","stat.CO"],"primary_cat":"stat.ML","authors_text":"Katerina Hlavackova-Schindler, Suzana Marsela","submitted_at":"2025-08-30T15:42:31Z","abstract_excerpt":"We address the problem of determining the causal direction between two univariate, continuous-valued variables, X and Y, under the assumption of no hidden confounders. In general, it is not possible to make definitive statements about causality without some assumptions on the underlying model. To distinguish between cause and effect, we propose a bivariate causal score based on the Minimum Description Length (MDL) principle, using functions that possess the density property on a compact real interval. We prove the identifiability of these causal scores under specific conditions. These conditio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.00538","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.00538/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}