{"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/active-probabilistic-inference-on-matrices","title":"Active Probabilistic Inference on Matrices for Pre-Conditioning in Stochastic Optimization","arxiv_id":"1902.07557","date":"2019-02-20","proceeding":null,"authors":["Filip de Roos","Philipp Hennig"],"abstract":"Pre-conditioning is a well-known concept that can significantly improve the\nconvergence of optimization algorithms. For noise-free problems, where good\npre-conditioners are not known a priori, iterative linear algebra methods offer\none way to efficiently construct them. For the stochastic optimization problems\nthat dominate contemporary machine learning, however, this approach is not\nreadily available. We propose an iterative algorithm inspired by classic\niterative linear solvers that uses a probabilistic model to actively infer a\npre-conditioner in situations where Hessian-projections can only be constructed\nwith strong Gaussian noise. The algorithm is empirically demonstrated to\nefficiently construct effective pre-conditioners for stochastic gradient\ndescent and its variants. Experiments on problems of comparably low\ndimensionality show improved convergence. In very high-dimensional problems,\nsuch as those encountered in deep learning, the pre-conditioner effectively\nbecomes an automatic learning-rate adaptation scheme, which we also empirically\nshow to work well.","url_abs":"http://arxiv.org/abs/1902.07557v1","url_pdf":"http://arxiv.org/pdf/1902.07557v1.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":"active-probabilistic-inference-on-matrices","repo_url":"https://github.com/fderoos/probabilistic_hessian","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"stochastic-optimization","task_name":"Stochastic Optimization"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}