[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-120525-en":3,"doc-seo-120525-105":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},120525,1374391974564,"Clementine","https://ap-avatar.wpscdn.com/avatar/14000253aa45c000a9e?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779874745381141002",8,"Research & Report","Systematic Bias of Machine Learning Regression Models and Its Correction - An Application to Imaging","Machine learning models for continuous outcomes often generate systematically biased predictions, especially for values far from the mean. Large true outcomes are typically underestimated, while small true outcomes are overestimated, creating a linear central-tendency warp termed “systematic bias of machine learning regression.” The study shows this bias appears across diverse regression models, analyzes its theoretical basis, and introduces a general constrained optimization correction with efficient algorithms. Simulations confirm bias removal, and neuroimaging experiments yield unbiased brain-age predictions.","Systematic Bias of Machine Learning Regression  \nModels and Correction  \nHwiyoung Lee 1,2,3 and Shuo Chen 1,2,3  \n1Division of Biostatistics and Bioinformatics, Department of Epidemiology and Public Health, School of Medicine, University of Maryland  \n2Maryland Psychiatric Research Center, Department of Psychiatry, School of Medicine, University of Maryland  \n3The University of Maryland Institute for Health Computing (UM-IHC)  \narXiv :2405 . 15950v2 [ stat .ML] 4 Sep 2024  \nAbstract—Machine learning models for continuous outcomes often yield systematically biased predictions, particularly for values that largely deviate from the mean. Speci􀀂cally, predictions for large-valued outcomes tend to be negatively biased (underestimating actual values), while those for small-valued outcomes are positively biased (overestimating actual values). We refer to this linear central tendency warped bias as the “systematic bias of machine learning regression”. In this paper, we 􀀂rst demonstrate that this systematic prediction bias persists across various machine learning regression models, and then delve into its theoretical underpinnings. To address this issue, we propose a general constrained optimization approach designed to correct this bias and develop computationally ef􀀂cient implementation algorithms. Simulation results indicate that our correction method effectively eliminates the bias from the predicted outcomes. We apply the proposed approach to the prediction of brain age using neuroimaging data. In comparison to competing machine learning regression models, our method effectively addresses the longstanding issue of “systematic bias of machine learning regression” in neuroimaging-based brain age calculation, yielding unbiased predictions of brain age.  \nIndex Terms—Systematic Bias, Constrained Optimization, Machine Learning Regression, variance-bias trade-off.  \nI. INTRODUCTION  \nCONSTRUCTING predictive models with continuous out  \ncomes is a fundamental aspect of modern data science. Numerous tools have been developed for this purpose, including statistical methods such as ordinary linear regression, regression shrinkage, and Generalized Additive Models (GAM), as well as machine learning methods such as random forests, XGBoost, and support vector regression, among others [1] . A general objective of these methods is to minimize the discrepancy between the predicted continuous outcomes and the true values, particularly in independent testing datasets. Using this heuristic, the predicted outcome is unbiased under the classic linear regression setting. In contrast, the predicted outcome from a machine learning model for continuous outcomes is often systematically biased [2],[3] . This systematic bias is problematic for the applications of machine learning regression models, leading to inaccurate conclusions and forecasts.  \nWe 􀀂rst illustrate the systematic bias introduced by machine learning regression through a simulation study, examining several existing models including Kernel Ridge Regression  \n(KRR), LASSO, XGBoost, Random Forest, Neural Network, and Support Vector Regression (SVR) . Speci􀀂cally, we 􀀂rst rlNeg,at0tivpree0a(0rss0res,yoia􀀆diionbtcntse)t,heternoworcoicvatrmheXef􀀂r,trioaeicanl d􀀆eieinsin,.anprutTXithd tedionhe􀀌etinorithspoǫ Hcg ds Xdneoeatwimseref􀀂aeeny, 􀀌ci,eresisenlchenn pineRpsetmpate20lya0rd0rev1esiro(iatctangmeedornd,ǫ denotes random noise, which follows the standard normal distribution.  \nvaleFluarigeniusn1vresg.ptrererussseieonontustcmsoocatmdetelessrybplbasoyetsdthooenftafohouererpmsimreedntulicioattednedion oumantaacclohyminsiees T􀀂ahtdeoosfttolthedidelliprinneeediwinctiteaedh achvaslsuluopbeseut1reoitsrepheinrtcesruludeentvedsa, thlureeepsrlinyeseeaAntr rddineiggtitreohsnesalilionlyne, whtheeresol yne. I(fiteh, etmhearcehginreesslieoarnnoinfregonreys)sioshnoisulduncboiiansedcide, with the dotted line. As shown in this 􀀂gure, a systematic regression error is observed across all machine learning regression m","cbCaihmMzXbeeZih","https://ap.wps.com/l/cbCaihmMzXbeeZih","pdf",1193718,1,9,"English","en",105,"# Introduction\n## Systematic bias in continuous-outcome regression\n## Simulation across multiple regression models\n## Theoretical explanation via mean squared error\n# Proposed correction method\n## Constrained optimization framework\n## Efficient computational implementation\n# Application to imaging\n## Brain age prediction and evaluation","[{\"question\":\"What is meant by “systematic bias of machine learning regression”?\",\"answer\":\"It is a linear central-tendency warped error where predictions are biased depending on how far the true outcomes deviate from the mean. Large outcomes tend to be underestimated and small outcomes tend to be overestimated.\"},{\"question\":\"Does the systematic bias occur across different regression models?\",\"answer\":\"Yes. The document reports the bias persists across multiple machine learning regression approaches, including KRR, LASSO, XGBoost, Random Forest, Neural Networks, and SVR, with stronger effects in testing data.\"},{\"question\":\"How does the proposed method correct the bias and what evidence supports it?\",\"answer\":\"The method formulates a general constrained optimization approach to remove the bias. Simulation results indicate the correction effectively eliminates bias in predicted outcomes, and the imaging application produces unbiased brain-age estimates versus competing models.\"}]","Systematic Bias of Machine Learning Regression Models and Its Correction - An Application to Imaging | PDF",1785730486,23,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"systematic-bias-of-machine-learning-regression-models-and-its-correction-an-application-to-imaging","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/systematic-bias-of-machine-learning-regression-models-and-its-correction-an-application-to-imaging/120525/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-03",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What is meant by “systematic bias of machine learning regression”?","Question",{"text":75,"@type":76},"It is a linear central-tendency warped error where predictions are biased depending on how far the true outcomes deviate from the mean. Large outcomes tend to be underestimated and small outcomes tend to be overestimated.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Does the systematic bias occur across different regression models?",{"text":80,"@type":76},"Yes. The document reports the bias persists across multiple machine learning regression approaches, including KRR, LASSO, XGBoost, Random Forest, Neural Networks, and SVR, with stronger effects in testing data.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the proposed method correct the bias and what evidence supports it?",{"text":84,"@type":76},"The method formulates a general constrained optimization approach to remove the bias. Simulation results indicate the correction effectively eliminates bias in predicted outcomes, and the imaging application produces unbiased brain-age estimates versus competing models.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,127,130,134],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":21,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":125,"slug":126},"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]