{"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/approximating-likelihood-ratios-with","title":"Approximating Likelihood Ratios with Calibrated Discriminative Classifiers","arxiv_id":"1506.02169","date":"2015-06-06","proceeding":null,"authors":["Kyle Cranmer","Juan Pavez","Gilles Louppe"],"abstract":"In many fields of science, generalized likelihood ratio tests are established\ntools for statistical inference. At the same time, it has become increasingly\ncommon that a simulator (or generative model) is used to describe complex\nprocesses that tie parameters $\\theta$ of an underlying theory and measurement\napparatus to high-dimensional observations $\\mathbf{x}\\in \\mathbb{R}^p$.\nHowever, simulator often do not provide a way to evaluate the likelihood\nfunction for a given observation $\\mathbf{x}$, which motivates a new class of\nlikelihood-free inference algorithms. In this paper, we show that likelihood\nratios are invariant under a specific class of dimensionality reduction maps\n$\\mathbb{R}^p \\mapsto \\mathbb{R}$. As a direct consequence, we show that\ndiscriminative classifiers can be used to approximate the generalized\nlikelihood ratio statistic when only a generative model for the data is\navailable. This leads to a new machine learning-based approach to\nlikelihood-free inference that is complementary to Approximate Bayesian\nComputation, and which does not require a prior on the model parameters.\nExperimental results on artificial problems with known exact likelihoods\nillustrate the potential of the proposed method.","url_abs":"http://arxiv.org/abs/1506.02169v2","url_pdf":"http://arxiv.org/pdf/1506.02169v2.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":"approximating-likelihood-ratios-with","repo_url":"https://github.com/diana-hep/carl","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"BSD-3-Clause"}},{"paper_slug":"approximating-likelihood-ratios-with","repo_url":"https://github.com/leonoravesterbacka/carl-torch","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"dimensionality-reduction","task_name":"Dimensionality Reduction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=1506.02169","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1506.02169"}},"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. 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