{"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/retrospective-higher-order-markov-processes","title":"Retrospective Higher-Order Markov Processes for User Trails","arxiv_id":"1704.05982","date":"2017-04-20","proceeding":null,"authors":["Tao Wu","David Gleich"],"abstract":"Users form information trails as they browse the web, checkin with a\ngeolocation, rate items, or consume media. A common problem is to predict what\na user might do next for the purposes of guidance, recommendation, or\nprefetching. First-order and higher-order Markov chains have been widely used\nmethods to study such sequences of data. First-order Markov chains are easy to\nestimate, but lack accuracy when history matters. Higher-order Markov chains,\nin contrast, have too many parameters and suffer from overfitting the training\ndata. Fitting these parameters with regularization and smoothing only offers\nmild improvements. In this paper we propose the retrospective higher-order\nMarkov process (RHOMP) as a low-parameter model for such sequences. This model\nis a special case of a higher-order Markov chain where the transitions depend\nretrospectively on a single history state instead of an arbitrary combination\nof history states. There are two immediate computational advantages: the number\nof parameters is linear in the order of the Markov chain and the model can be\nfit to large state spaces. Furthermore, by providing a specific structure to\nthe higher-order chain, RHOMPs improve the model accuracy by efficiently\nutilizing history states without risks of overfitting the data. We demonstrate\nhow to estimate a RHOMP from data and we demonstrate the effectiveness of our\nmethod on various real application datasets spanning geolocation data, review\nsequences, and business locations. The RHOMP model uniformly outperforms\nhigher-order Markov chains, Kneser-Ney regularization, and tensor\nfactorizations in terms of prediction accuracy.","url_abs":"http://arxiv.org/abs/1704.05982v1","url_pdf":"http://arxiv.org/pdf/1704.05982v1.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":"retrospective-higher-order-markov-processes","repo_url":"https://github.com/wutao27/RHOMP","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}