[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85727-en":3,"doc-seo-85727-105":29,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},85727,4398048950312,"Violet","https://ap-avatar.wpscdn.com/avatar/400002538284de19e3c?_k=1778320343897328908",8,"Research & Report","Estimation, Prediction, and Assortment Optimization for Markov Chain Choice Models with Panel Data","A framework is developed for Markov chain (MC) choice models using panel data, covering parameter estimation, personalized choice prediction, and personalized assortment optimization. Unlike traditional models that treat transactions as independent draws from a random utility model, the approach captures dependencies across a customer’s historical transactions via partial-ordering preference information. Novel EM algorithms incorporate partial-order preferences to estimate MC parameters, outperforming prior EM baselines and partial-order benchmarks on synthetic and sushi datasets, and extend to computational hardness results for conditional prediction and optimization.","arXiv :2607 .098 17v 1 [ cs .LG] 10 Jul 2026  \nEstimation, Prediction, and Assortment Optimization for Markov Chain Choice Models with Panel Data  \nYalcin Akcay∗, Gerardo Berbeglia∗, Young-San Lin∗  \nJuly 14, 2026  \nAbstract  \nWe propose a framework for the Markov chain (MC) choice model with panel data, including parameter estimation, personalized choice prediction, and personalized assortment optimization. In contrast to the traditional setting, which assumes that each transaction is independently drawn from a random utility model, our framework accounts for dependencies among transactions for the same customer in historical data, captured by partial-ordering preference information. To the best of our knowledge, our framework initiates the study of choice modeling with panel data under MC. As our primary result, we propose novel expectation-maximization (EM) algorithms for MC parameter estimation by incorporating partial-ordering-based customer preference information. On synthetic datasets and the sushi dataset, our EM algorithms outperform the traditional EM algorithm of S¸im¸sek and Topaloglu (Operations Research, 66, 2018) and multinomial-logit-based partial-order benchmarks adapted from Jagabathula and Vulcano (Management Science, 64, 2018) . As our secondary contribution, we present hardness and computational results for conditional choice prediction and assortment optimization problems. These results complement our estimation framework and clarify the computational landscape of conditional choice and assortment optimization, which may be of independent interest.  \n1 Introduction  \nIncorporating customer choice behavior into assortment planning is a central problem in revenue management. A standard roadmap for assortment planning consists of two key steps: choice model estimation and assortment optimization. In the literature, traditional choice model estimation algorithms typically assume that transactions in historical datasets are independent, while the assortment optimization problem seeks to maximize the expected revenue aggregated over the entire customer population. A crucial feature of these traditional frameworks is their reliance on unconditional choice probabilities—that is, choice probabilities are assumed to be identical across customers and independent of customer-specific transaction histories.  \nRecent advances in data collection and e-commerce technologies now allow retailers to observe detailed transaction histories at the individual customer level. This information, popularly referred to as panel data, reveals correlations among transactions made by the same customer, challenging the independence assumptions underlying classical models. This development naturally motivates the following questions:  \nCan customer choice probabilities be estimated more precisely by incorporating individual historical transaction information into a choice model? What is the computational effort needed for this task?  \nThese questions take the choice model as given and focus on personalization at the level of choice probability estimation. Specifically, we study how to compute customer-specific choice probabilities conditional on individual transaction histories, while assuming that the unconditional choice probabilities are governed by an underlying choice model that is common to all customers.  \n∗ Melbourne Business School, Email: {y.akcay, g.berbeglia, [y.lin](y.lin}@mbs.edu)[}](y.lin}@mbs.edu)[@mbs.edu](y.lin}@mbs.edu)  \nIntuitively, transaction histories provide additional information about individual preferences, as repeated choices made by the same customer are inherently correlated. From a broader perspective, this raises a second complementary question.  \nCan the estimation of the choice model for the entire population improve by exploiting individual historical transaction information? When is this approach more beneficial?  \nHere, the emphasis shifts from prediction to inference, asking whether exploiting infor","cbCaigGXZwHmlfe0","https://ap.wps.com/l/cbCaigGXZwHmlfe0","pdf",1102236,1,37,"English","en",105,"# Abstract\n# Introduction\n## Our Results","[{\"question\":\"How does the framework differ from traditional choice modeling in using historical customer data?\",\"answer\":\"Traditional approaches assume transactions are independent and rely on unconditional choice probabilities. The framework instead models dependencies among transactions for the same customer using partial-ordering preference information from historical panel data.\"},{\"question\":\"What are the primary methodological contributions?\",\"answer\":\"The main contribution is new expectation-maximization (EM) algorithms for estimating Markov chain (MC) parameters while incorporating customer-level partial-order preference information.\"},{\"question\":\"What additional results are provided beyond estimation?\",\"answer\":\"The work includes hardness and computational results for conditional choice prediction and assortment optimization problems, clarifying the computational landscape of these tasks.\"}]",1784205846,93,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":27},"estimation-prediction-and-assortment-optimization-for-markov-chain-choice-models-with-panel-data","",{"@graph":35,"@context":84},[36,53,67],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/estimation-prediction-and-assortment-optimization-for-markov-chain-choice-models-with-panel-data/85727/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":61,"encodingFormat":60,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-16",true,{"@type":64,"interactionType":65,"userInteractionCount":4},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"How does the framework differ from traditional choice modeling in using historical customer data?","Question",{"text":74,"@type":75},"Traditional approaches assume transactions are independent and rely on unconditional choice probabilities. The framework instead models dependencies among transactions for the same customer using partial-ordering preference information from historical panel data.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"What are the primary methodological contributions?",{"text":79,"@type":75},"The main contribution is new expectation-maximization (EM) algorithms for estimating Markov chain (MC) parameters while incorporating customer-level partial-order preference information.",{"name":81,"@type":72,"acceptedAnswer":82},"What additional results are provided beyond estimation?",{"text":83,"@type":75},"The work includes hardness and computational results for conditional choice prediction and assortment optimization problems, clarifying the computational landscape of these tasks.","https://schema.org",{"og:url":51,"og:type":86,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":88,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":91},[92,96,100,104,109,114,119,122,127,130,134],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":93,"show_sort_weight":94,"slug":95},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":97,"show_sort_weight":98,"slug":99},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":101,"show_sort_weight":102,"slug":103},"Exam",70,"exam",{"id":105,"doc_module":4,"doc_module_name":45,"category_name":106,"show_sort_weight":107,"slug":108},5,"Comic",60,"comic",{"id":110,"doc_module":4,"doc_module_name":45,"category_name":111,"show_sort_weight":112,"slug":113},6,"Technology",50,"technology",{"id":115,"doc_module":4,"doc_module_name":45,"category_name":116,"show_sort_weight":117,"slug":118},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":45,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":45,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":45,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":45,"category_name":136,"show_sort_weight":105,"slug":137},19,"General","general"]