{"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/pathwise-derivatives-beyond-the","title":"Pathwise Derivatives Beyond the Reparameterization Trick","arxiv_id":"1806.01851","date":"2018-06-05","proceeding":"ICML 2018 7","authors":["Martin Jankowiak","Fritz Obermeyer"],"abstract":"We observe that gradients computed via the reparameterization trick are in\ndirect correspondence with solutions of the transport equation in the formalism\nof optimal transport. We use this perspective to compute (approximate) pathwise\ngradients for probability distributions not directly amenable to the\nreparameterization trick: Gamma, Beta, and Dirichlet. We further observe that\nwhen the reparameterization trick is applied to the Cholesky-factorized\nmultivariate Normal distribution, the resulting gradients are suboptimal in the\nsense of optimal transport. We derive the optimal gradients and show that they\nhave reduced variance in a Gaussian Process regression task. We demonstrate\nwith a variety of synthetic experiments and stochastic variational inference\ntasks that our pathwise gradients are competitive with other methods.","url_abs":"http://arxiv.org/abs/1806.01851v2","url_pdf":"http://arxiv.org/pdf/1806.01851v2.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":"pathwise-derivatives-beyond-the","repo_url":"https://github.com/lucadellalib/sac-beta","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"Apache-2.0"}}],"tasks":[{"task_slug":"variational-inference","task_name":"Variational Inference"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[{"method_slug":"gaussian-process","method_name":"Gaussian Process"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1806.01851","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}