{"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/early-stopping-is-nonparametric-variational","title":"Early Stopping is Nonparametric Variational Inference","arxiv_id":"1504.01344","date":"2015-04-06","proceeding":null,"authors":["Dougal Maclaurin","David Duvenaud","Ryan P. Adams"],"abstract":"We show that unconverged stochastic gradient descent can be interpreted as a\nprocedure that samples from a nonparametric variational approximate posterior\ndistribution. This distribution is implicitly defined as the transformation of\nan initial distribution by a sequence of optimization updates. By tracking the\nchange in entropy over this sequence of transformations during optimization, we\nform a scalable, unbiased estimate of the variational lower bound on the log\nmarginal likelihood. We can use this bound to optimize hyperparameters instead\nof using cross-validation. This Bayesian interpretation of SGD suggests\nimproved, overfitting-resistant optimization procedures, and gives a\ntheoretical foundation for popular tricks such as early stopping and\nensembling. We investigate the properties of this marginal likelihood estimator\non neural network models.","url_abs":"http://arxiv.org/abs/1504.01344v1","url_pdf":"http://arxiv.org/pdf/1504.01344v1.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":"early-stopping-is-nonparametric-variational","repo_url":"https://github.com/HIPS/maxwells-daemon","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"variational-inference","task_name":"Variational Inference"}],"methods":[{"method_slug":"early-stopping","method_name":"Early Stopping"},{"method_slug":"sgd","method_name":"SGD"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1504.01344","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}