{"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/estimating-density-models-with-complex","title":"Estimating Density Models with Truncation Boundaries using Score Matching","arxiv_id":"1910.03834","date":"2019-10-09","proceeding":null,"authors":["Song Liu","Takafumi Kanamori","Daniel J. Williams"],"abstract":"Truncated densities are probability density functions defined on truncated domains. They share the same parametric form with their non-truncated counterparts up to a normalizing constant. Since the computation of their normalizing constants is usually infeasible, Maximum Likelihood Estimation cannot be easily applied to estimate truncated density models. Score Matching (SM) is a powerful tool for fitting parameters using only unnormalized models. However, it cannot be directly applied here as boundary conditions used to derive a tractable SM objective are not satisfied by truncated densities. In this paper, we study parameter estimation for truncated probability densities using SM. The estimator minimizes a weighted Fisher divergence. The weight function is simply the shortest distance from a data point to the boundary of the domain. We show this choice of weight function naturally arises from minimizing the Stein discrepancy as well as upperbounding the finite-sample estimation error. The usefulness of our method is demonstrated by numerical experiments and a study on the Chicago crime data set. We also show that the proposed density estimation can correct the outlier-trimming bias caused by aggressive outlier detection methods.","url_abs":"https://arxiv.org/abs/1910.03834v5","url_pdf":"https://arxiv.org/pdf/1910.03834v5.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":"estimating-density-models-with-complex","repo_url":"https://github.com/anewgithubname/Truncated-Score-Matching","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"estimating-density-models-with-complex","repo_url":"https://github.com/dannyjameswilliams/truncsm","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"density-estimation","task_name":"Density Estimation"},{"task_slug":"outlier-detection","task_name":"Outlier Detection"},{"task_slug":"parameter-estimation","task_name":"parameter estimation"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1910.03834","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}