[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84012-en":3,"doc-seo-84012-105":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":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},84012,7971461740909,"Levi","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",8,"Research & Report","Heckman-Corrected Epistemic Uncertainty: Selection on Unobservables Defeats Importance Weighting","Training data for machine-learning models is routinely filtered by a selection process the model never observes, creating systematic bias in unobserved regions. Default fixes for selection on observables—importance weighting, covariate-shift correction, and MAR imputation—assume ignorable selection. The paper applies Heckman’s two-equation econometric model to deep epistemic uncertainty via a joint selection and outcome likelihood, comparing against deep ensembles, MC dropout, and GP baselines on both controlled and MNAR tabular datasets.","arXiv :2607 .05806v 1 [ cs .LG] 7 Jul 2026  \nHeckman-Corrected Epistemic Uncertainty: Selection on Unobservables Defeats Importance Weighting  \nGunner Levi Howe  \nIndependent Researcher  \n[gunnerlevihowe@gmail. com](gunnerlevihowe@gmail. com)  \nJuly 2026  \nAbstract  \nTraining data for machine-learning models is routinely collected by a selection process the model never sees: loans are observed only when granted, outcomes only when a test was ordered, regions of input space sampled only when someone chose to sample them. The field’s default fixes—importance weighting, covariate-shift correction, MAR imputation—assume selection is ignorable given observables. Econometrics solved the harder problem in 1979: Heckman’s two-equation model jointly fits a probit selection equation and an outcome equation linked through correlated errors, and the inverse-Millsratio term corrects the outcome model for selection on unobservables — the case where importance weighting is structurally helpless. We instantiate that machinery for deep epistemic uncertainty: a deep outcome network, a linear selection head, and a joint bivariate-normal likelihood over all units (observed and not), ensembled for epistemic variance. Our implementations first reproduce the seven-digit Stata reference output for both the classic two-step and the maximum-likelihood estimator on the RAND Health Insurance data (max coefficient deviation 2 .8 × 10 −6 two-step, 5 .0 × 10 −7 MLE) . In a controlled generator where sampling probability depends on an unobservable correlated (ρ swept 0 → 0.9) with the outcome noise, deep ensembles, MC dropout, and GP baselines are overconfident exactly where data was avoided for reasons correlated with the outcome (coverage of nominal-90% intervals falls to 64.4% at ρ = 0 .9), and importance weighting with oracle propensities does not fix it (43.1%)—reweighting corrects the covariate distribution, not the conditional bias E [y | x, s=1]  E [y | x] . The Heckman-corrected predictive distribution restores coverage (88.9%) when the selection equation contains an instrument —a variable affecting selection but not the outcome — and degrades gracefully but measurably without one (40.3%); we sweep this honesty curve rather than hide it. The joint MLE needs a warm-up schedule to match the two-step’s stability with deep feature maps (otherwise the flexible outcome net absorbs the correction), a methods finding we characterize. On real tabular data with induced, documented MNAR selection, the corrected intervals are the best-calibrated (lowest region-ECE) of every non-oracle method in selected-against regions on both datasets; baselines that match its raw coverage do so only by overwidening everywhere, which region-ECE exposes. A discussion vignette fits the same two-equation model to public benchmark reporting panels (Papers-with-Code tables), where the no-instrument pathology our controlled experiments quantify appears in the wild: most fits hit the | ρˆ| = 1 boundary. We state plainly which identification regime a practitioner is in, and release the faithfulness-gated implementation.  \n1 Introduction  \nEvery published treatment of distribution shift in uncertainty quantification (UQ) that we are aware of corrects for selection on observables: importance weighting and covariate-shift adaptation reweight by a propensity that depends on x [4, 23 , 24], and evaluations of predictive uncertainty under shift perturb the marginal p (x) [18] . The harder and, in deployed systems, common case is selection on unobservables: the probability that a unit enters the training set depends on latent determinants of the outcome itself. A bank observes repayment only for granted loans, and the loan officer’s side-information correlates with default risk; a hospital records disease severity only for admitted patients; a simulation campaign samples parameter regions an expert already believed well-behaved. In all these cases E[y | x, s=1]  E [y | x], so noreweighting o","cbCairM9lMMr9uDM","https://ap.wps.com/l/cbCairM9lMMr9uDM","pdf",464832,3,1,9,"English","en",105,"# Abstract\n# Introduction\n## Identification caveat and instrument requirement\n## Contributions","[{\"question\":\"Why does importance weighting fail under selection on unobservables?\",\"answer\":\"Importance weighting reweights the covariate distribution but cannot remove conditional bias when E[y | x, s=1] ≠ E[y | x], i.e., when selection depends on latent factors correlated with the outcome.\"},{\"question\":\"What is the role of the instrument in Heckman identification?\",\"answer\":\"Heckman identification is robust when the selection equation includes an exclusion restriction (an instrument affecting selection but not the outcome). Without an instrument, identification becomes fragile, so the paper reports both instrument-present and instrument-absent conditions.\"},{\"question\":\"How are the epistemic-uncertainty methods evaluated in the paper?\",\"answer\":\"The study compares interval coverage and calibration behavior across controlled MNAR generators with correlated selection/outcome noise and on real tabular datasets, using metrics such as region-ECE and observing degradation without an instrument.\"}]",1784192006,23,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"heckman-corrected-epistemic-uncertainty-selection-on-unobservables-defeats-importance-weighting","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,50],{"item":41,"name":42,"@type":43,"position":21},"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":20},"https://docshare.wps.com/document/research-report/",{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/heckman-corrected-epistemic-uncertainty-selection-on-unobservables-defeats-importance-weighting/84012/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-27","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Why does importance weighting fail under selection on unobservables?","Question",{"text":75,"@type":76},"Importance weighting reweights the covariate distribution but cannot remove conditional bias when E[y | x, s=1] ≠ E[y | x], i.e., when selection depends on latent factors correlated with the outcome.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What is the role of the instrument in Heckman identification?",{"text":80,"@type":76},"Heckman identification is robust when the selection equation includes an exclusion restriction (an instrument affecting selection but not the outcome). Without an instrument, identification becomes fragile, so the paper reports both instrument-present and instrument-absent conditions.",{"name":82,"@type":73,"acceptedAnswer":83},"How are the epistemic-uncertainty methods evaluated in the paper?",{"text":84,"@type":76},"The study compares interval coverage and calibration behavior across controlled MNAR generators with correlated selection/outcome noise and on real tabular datasets, using metrics such as region-ECE and observing degradation without an instrument.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,127,130,134],{"id":21,"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":52,"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":22,"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"]