{"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/pac-mode-estimation-using-ppr-martingale","title":"PAC Mode Estimation using PPR Martingale Confidence Sequences","arxiv_id":"2109.05047","date":"2021-09-10","proceeding":null,"authors":["Shubham Anand Jain","Rohan Shah","Sanit Gupta","Denil Mehta","Inderjeet Jayakumar Nair","Jian Vora","Sushil Khyalia","Sourav Das","Vinay J. Ribeiro","Shivaram Kalyanakrishnan"],"abstract":"We consider the problem of correctly identifying the \\textit{mode} of a discrete distribution $\\mathcal{P}$ with sufficiently high probability by observing a sequence of i.i.d. samples drawn from $\\mathcal{P}$. This problem reduces to the estimation of a single parameter when $\\mathcal{P}$ has a support set of size $K = 2$. After noting that this special case is tackled very well by prior-posterior-ratio (PPR) martingale confidence sequences \\citep{waudby-ramdas-ppr}, we propose a generalisation to mode estimation, in which $\\mathcal{P}$ may take $K \\geq 2$ values. To begin, we show that the \"one-versus-one\" principle to generalise from $K = 2$ to $K \\geq 2$ classes is more efficient than the \"one-versus-rest\" alternative. We then prove that our resulting stopping rule, denoted PPR-1v1, is asymptotically optimal (as the mistake probability is taken to $0$). PPR-1v1 is parameter-free and computationally light, and incurs significantly fewer samples than competitors even in the non-asymptotic regime. We demonstrate its gains in two practical applications of sampling: election forecasting and verification of smart contracts in blockchains.","url_abs":"https://arxiv.org/abs/2109.05047v3","url_pdf":"https://arxiv.org/pdf/2109.05047v3.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":"pac-mode-estimation-using-ppr-martingale","repo_url":"https://github.com/rohanshah13/pac_mode_estimation","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2109.05047","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}