[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-117585-en":3,"doc-seo-117585-105":30,"detail-sidebar-cat-0-en-105":91},{"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":27,"seo_description":14,"update_tm":28,"read_time":29},117585,1374391974468,"Eden","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","High-Dimensional Inference for Generalized Linear Models with Hidden Confounding","High-dimensional regression inference is challenged by potential unmeasured confounders that simultaneously affect the response and covariates, invalidating standard debiasing strategies. The study develops a generalized linear regression framework with hidden confounding and introduces a debiasing approach that corrects for effects induced by latent confounders. The work proves consistency and asymptotic normality of the proposed debiased estimator. Extensive simulations and a genetic-data application validate finite-sample performance and practicality.","High-Dimensional Inference for Generalized Linear Models  \nwith Hidden Confounding  \nJing Ouyang [jingoy@umich.edu](jingoy@umich.edu)  \nKean Ming Tan [keanming@umich.edu](keanming@umich.edu)  \nGongjun Xu [gongjun@umich.edu](gongjun@umich.edu)  \nDepartment of Statistics University of Michigan Ann Arbor, MI 48109, USA  \nEditor: Mladen Kolar  \nAbstract  \nStatistical inferences for high-dimensional regression models have been extensively studied for their wide applications ranging from genomics, neuroscience, to economics. However, in practice, there are often potential unmeasured confounders associated with both the response and covariates, which can lead to invalidity of standard debiasing methods. This paper focuses on a generalized linear regression framework with hidden confounding and proposes a debiasing approach to address this high-dimensional problem, by adjusting for the e􀀋ects induced by the unmeasured confounders. We establish consistency and asymptotic normality for the proposed debiased estimator. The 􀀌nite sample performance of the proposed method is demonstrated through extensive numerical studies and an application to a genetic data set.  \nKeywords: High-dimensional inference; Generalized linear model; Latent variable; Unmeasured confounder.  \n1. Introduction  \nStatistical inferences for high-dimensional regression models have received a growing interest due to the increasing number of complex data sets with high-dimensional covariatesthat are collected across many di􀀋erent scienti􀀌c disciplines ranging from genomics to social science to econometrics (Peng et al., 2010; Belloni et al., 2012; Fan et al., 2014; B􀁿uhlmann et al., 2014) . One of the most popularly used high-dimensional regression methods is the lasso linear regression, which assumes that the underlying regression coe􀀎cients are sparse (Tibshirani, 1996) . However, the lasso penalty introduces non-negligible bias that renders high-dimensional statistical inference challenging (Wainwright, 2019) . To address this challenge, Zhang and Zhang (2014) and van de Geer et al. (2014) proposed the debiasing method to construct con􀀌dence intervals for the lasso regression coe􀀎cients: the main idea is to 􀀌rst obtain the lasso estimator, and then correct for the bias of the lasso estimator using a lowdimensional projection method. We refer the reader to Javanmard and Montanari (2014), Belloni et al. (2014), Ning and Liu (2017), Chernozhukov et al. (2018), among others, for detailed discussions of the debiasing approach, and also Wainwright (2019) for an overview of high-dimensional statistical inference.  \n􀀍c2023 Jing Ouyang, Kean Ming Tan and Gongjun Xu.  \nLicense: CC-BY 4.0, see [https://creativecommons.org/licenses/by/4.0/](https://creativecommons.org/licenses/by/4.0/. Attribution)[. Attribution](https://creativecommons.org/licenses/by/4.0/. Attribution) requirements are provided  \nat [http://jmlr.org/papers/v24/22-0834.html](http://jmlr.org/papers/v24/22-0834.html).  \nOuyang, Tan and Xu  \nThe aforementioned studies were established under the assumption that there are nounmeasured confounders that are associated with both the response and covariates. However, this assumption is often violated in observational studies. For instance, in genetic studies, the e􀀋ect of certain segments of DNA on the gene expression may be confounded by population structure and microarray expression artifacts (Listgarten et al., 2010) . Another example is in healthcare studies where the e􀀋ect of nutrients intake on the risk of cancer may be confounded by physical wellness, social class, and behavioral factors (Fewellet al., 2007) . Without adjusting for the unmeasured confounders, the resulting inferences from the standard debiasing methods could be biased and consequently, lead to spurious scienti􀀌c discoveries.  \nVarious methods have been proposed to perform valid statistical inferences for regression parameters in the presence of hidden confounders. One commonly used approach is i","cbCaibZ6SNnNtJjc","https://ap.wps.com/l/cbCaibZ6SNnNtJjc","pdf",738130,1,61,"English","en",105,"# Introduction\n## High-dimensional regression and debiasing\n## Hidden confounding and limitations of existing methods\n## Proposed framework for generalized linear models\n## Theoretical results and validation","[{\"question\":\"Why do standard high-dimensional debiasing methods fail under hidden confounding?\",\"answer\":\"Because unmeasured confounders can affect both the response and covariates, the usual bias correction no longer guarantees valid inference, leading to biased results and potentially spurious discoveries.\"},{\"question\":\"What is the core idea of the proposed method?\",\"answer\":\"The method estimates unmeasured confounders via high-dimensional factor analysis and then applies debiasing to the regression coefficient of interest, treating the estimated confounders as surrogate variables.\"},{\"question\":\"What theoretical properties are established for the debiased estimator?\",\"answer\":\"The paper proves consistency and asymptotic normality under mild scaling conditions, with estimation error rates comparable to models that omit unmeasured confounders.\"}]","High-Dimensional Inference for Generalized Linear Models with Hidden Confounding | 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do standard high-dimensional debiasing methods fail under hidden confounding?","Question",{"text":75,"@type":76},"Because unmeasured confounders can affect both the response and covariates, the usual bias correction no longer guarantees valid inference, leading to biased results and potentially spurious discoveries.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What is the core idea of the proposed method?",{"text":80,"@type":76},"The method estimates unmeasured confounders via high-dimensional factor analysis and then applies debiasing to the regression coefficient of interest, treating the estimated confounders as surrogate variables.",{"name":82,"@type":73,"acceptedAnswer":83},"What theoretical properties are established for the debiased estimator?",{"text":84,"@type":76},"The paper proves consistency and asymptotic normality under mild scaling conditions, with estimation error rates comparable to models that omit unmeasured 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