[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-127537-en":3,"doc-seo-127537-105":30,"detail-sidebar-cat-0-en-105":92},{"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":20,"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":27,"seo_description":14,"update_tm":28,"read_time":29},127537,687207017582,"Himbo","https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d",8,"Research & Report","A reduced-rank approach to predicting multiple binary responses through machine learning","This paper investigates how to simultaneously predict multiple binary responses using a shared set of covariates. A machine-learning-based binary classification strategy is developed without assumptions on the underlying observations, targeting the predictor group that minimizes prediction error. The method’s prediction error is analyzed directly via PAC-Bayesian bounds, and a pseudo-Bayesian framework supports incomplete response data. Implementation uses Langevin Monte Carlo, with simulations and real-data experiments showing performance comparable or superior to state-of-the-art.","Statistics and Computing (2023) 33:136  \n[https://doi.org/10.1007/s1](https://doi.org/10.1007/s1) 1222-023-10314-3  \nA reduced-rank approach to predicting multiple binary responses through machine learning  \nThe Tien Mai1  \nReceived: 12 June 2023 / Accepted: 26 September 2023 © The Author(s) 2023  \nAbstract  \nThis paper investigates the problem of simultaneously predicting multiple binary responses by utilizing a shared set ofcovariates. Our approach incorporates machine learning techniques for binary classification, without making assumptions about the underlying observations. Instead, our focus lies on a group of predictors, aiming to identify the one that minimizes prediction error. Unlike previous studies that primarily address estimation error, we directly analyze the prediction error of our method using PAC-Bayesian bounds techniques. In this paper, we introduce a pseudo-Bayesian approach capable of handling incomplete response data. Our strategy is efficiently implemented using the Langevin Monte Carlo method. Through simulation studies and a practical application using real data, we demonstrate the effectiveness of our proposed method, producing comparable or sometimes superior results compared to the current state-of-the-art method.  \nKeywords Binary responses · Low-rank predictors · PAC-Bayesian inequalities · Langevin Monte Carlo · Missing data  \n1 Introduction  \nThe relationship between multiple response variables and a set of predictors has been a topic of ongoing research and interest in the literature, with numerous studies dedicated to understanding and exploring this connection. One area of particular interest in this field is the use of reduced rank regression, which involves using a low-rank constraint to linearly connect the response variables and the predictors, see e.g. Izenman (2008), Cook (2018), Reinsel et al. (2023) and Giraud (2021) . This approach has been widely studied and applied, with numerous works published on the topic, including those by Anderson (1951), Izenman (1975), Bunea et al.(2011), Geweke(1996), and many others. From frequentist to Bayesian approaches, there have been a wide range of methods and techniques employed to analyze and model these relationships, Corander and Villani(2004), Chakrabortyet al.(2020), Alquier (2013), Goh et al. (2017), Yang et al. (2020), Kleibergen and Paap (2002), Chen et al. (2013), She and Chen (2017) .  \nB The Tien Mai [the.t.mai@ntnu.no](the.t.mai@ntnu.no)  \n1 Department of Mathematical Sciences, Norwegian University of Science and Technology, 7034 Trondheim, Norway  \nHowever, despite the extensive research in this area, most studies have focused on real-valued responses. Inmanyapplications, the entries of the response matrix are binary, that is, they are in the set {−1 , 1} . For example, the treatment responses from multiple drugs can be recoded as binary or categorical when measured from each cell line, as seen in studies by Hayes et al. (2006), Greenlund et al. (2005), Mishra and Müller (2022) . This highlights the need for further research on the use of binary or categorical response variables in reduced rank regression and other multivariate modeling techniques.  \nThe problem of modeling multiple binary response variables has received some limited attention in recent years, with few studies proposing reduced-rank regression models as a solution. One notable example is the paper by Luo et al.(2018), which proposed a mixed-outcome reduced-rank regression model to handle response matrices that include both binary and count data, and also addressed the issue of missing data in the responses. Another recent study, carried out independently of Luo et al. (2018), is the paper by Park et al. (2022), which additionally considered row-wise sparse constraints in addition to the low-rank assumption, but only for fully observed binary response matrices. The main idea behind these studies is to assume a marginal logistic regression model to relate the binary respon","cbCaicCxFjXJLKs7","https://ap.wps.com/l/cbCaicCxFjXJLKs7","pdf",446727,1,15,"English","en",105,"# Introduction\n# Related Work\n# Problem Setup and Motivation\n# Learning-Theoretic Approach (PAC-Bayesian)\n# Optimization and Implementation","[{\"question\":\"How does the paper predict multiple binary responses simultaneously?\",\"answer\":\"It uses a shared set of covariates and a machine-learning binary classification method that searches for the predictor (within a low-rank/reduced-rank structure) that minimizes prediction error.\"},{\"question\":\"What theoretical guarantee is provided for the proposed method?\",\"answer\":\"The paper directly analyzes prediction error using PAC-Bayesian bounds rather than only estimation-error guarantees.\"},{\"question\":\"How are incomplete response data handled and implemented?\",\"answer\":\"A pseudo-Bayesian approach is introduced to manage incomplete response data, and the resulting strategy is implemented efficiently with Langevin Monte Carlo.\"}]","A reduced-rank approach to predicting multiple binary responses through machine learning | 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does the paper predict multiple binary responses simultaneously?","Question",{"text":76,"@type":77},"It uses a shared set of covariates and a machine-learning binary classification method that searches for the predictor (within a low-rank/reduced-rank structure) that minimizes prediction error.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"What theoretical guarantee is provided for the proposed method?",{"text":81,"@type":77},"The paper directly analyzes prediction error using PAC-Bayesian bounds rather than only estimation-error guarantees.",{"name":83,"@type":74,"acceptedAnswer":84},"How are incomplete response data handled and implemented?",{"text":85,"@type":77},"A pseudo-Bayesian approach is introduced to manage incomplete response data, and the resulting strategy is implemented efficiently with Langevin Monte 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