{"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/the-conditional-cauchy-schwarz-divergence","title":"The Conditional Cauchy-Schwarz Divergence with Applications to Time-Series Data and Sequential Decision Making","arxiv_id":"2301.08970","date":"2023-01-21","proceeding":null,"authors":["Shujian Yu","Hongming Li","Sigurd Løkse","Robert Jenssen","José C. Príncipe"],"abstract":"The Cauchy-Schwarz (CS) divergence was developed by Pr\\'{i}ncipe et al. in 2000. In this paper, we extend the classic CS divergence to quantify the closeness between two conditional distributions and show that the developed conditional CS divergence can be simply estimated by a kernel density estimator from given samples. We illustrate the advantages (e.g., rigorous faithfulness guarantee, lower computational complexity, higher statistical power, and much more flexibility in a wide range of applications) of our conditional CS divergence over previous proposals, such as the conditional KL divergence and the conditional maximum mean discrepancy. We also demonstrate the compelling performance of conditional CS divergence in two machine learning tasks related to time series data and sequential inference, namely time series clustering and uncertainty-guided exploration for sequential decision making. The code of conditional CS divergence is available at https://github.com/SJYuCNEL/conditional_CS_divergence.","url_abs":"https://arxiv.org/abs/2301.08970v3","url_pdf":"https://arxiv.org/pdf/2301.08970v3.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":"the-conditional-cauchy-schwarz-divergence","repo_url":"https://github.com/sjyucnel/conditional_cs_divergence","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"decision-making","task_name":"Decision Making"},{"task_slug":"sequential-decision-making","task_name":"Sequential Decision Making"},{"task_slug":"time-series-1","task_name":"Time Series"},{"task_slug":"time-series","task_name":"Time Series Analysis"},{"task_slug":"time-series-clustering","task_name":"Time Series Clustering"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2301.08970","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2301.08970"}},"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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