Selection Bias

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Overview

Selection bias arises when the people, examples, or outcomes observed differ systematically from the population a study or model is meant to represent. Researchers use methods such as inverse-probability weighting, post-stratification, robust optimization, and Heckman-style models to correct for selection, while causal inference asks when effects remain identifiable. Work also examines how biased samples affect medical prediction, federated learning, surveys, and model evaluation, using tools such as negative controls, calibration checks, and controlled exploration. A central challenge is that weighting can address measured differences but may fail when selection depends on unobserved factors, so reliable correction often requires explicit assumptions, external information, or better data collection.

Latest papers

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44 papers8 papers in the last four weeks, level with the four weeks before. 0.1% of all new papers.

Oct 29, 2026

Confidence Filtering in Video-Based Gait Assessment: Measurement Error versus Selection Shift

Video-based gait assessment often keeps only high-confidence pose observations, which can lower measurement error but change the movement assessed. We compared confidence selection with budget-matched random selection in a Parkinson-related cohort (n = 96) and an NF2-related replication cohort (n = 18). In the Parkinson-related cohort, confidence selection produced a small but consistent shift in the observed movement summary (+0.05 SD, 95% CI 0.03 to 0.07), while held-out Mini-BESTest error stayed flat (-0.04 points, -0.13 to 0.05); a policy preserving motion-group proportions reduced the shift, while NF2 showed no shift and its predictor did not beat a constant baseline. Because this shift mixes measurement error with selection shift, we decompose and simulate both on the cohort's window structure. Filtering lowers local error when error depends on confidence, but biases the endpoint once confidence tracks movement more than error. In the Parkinson-related data, confidence was only weakly tied to movement (rho = 0.14). There, filtering is harmless if well-tracked windows are unbiased. If instead systematic error only redistributes within participants, filtering can add up to 0.58 degrees. Unchanged clinical error from such small-cohort predictors therefore cannot show that quality filtering preserves the assessed movement.

David Regev, Eran Beeri Bamani

Department of Information Science and Applied Artificial Intelligence, Bar-Ilan University, Ramat Gan, Israel.

Selection BiasGait AnalysisConfidence EstimationMarkerless Motion Capture
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Oct 22, 2026

Sharp Bounds on the Winner's Bias under Independent and Nonnegatively Correlated Noise

Reporting the best of MM noisy, unbiased scores overstates the winner's value by up to cVc\sqrt{V}, where VV is the total noise variance and the sharp constant cc depends on how the noise is dependent. It was known only at the two extremes, arbitrary dependence ((M−1)/M\sqrt{(M-1)/M}) and i.i.d. noise. We determine it for two classes in between: for independent, not identically distributed noise it is (M−1)/(2M)\sqrt{(M-1)/(2M)}, and for pairwise nonnegatively correlated noise it is (M−1)/M(M-1)/M; for uncorrelated noise this answers the maximum version of an open question about the expected range. Explicit finite constructions attain both. As a corollary, the bias of the cross-validation estimator is bounded sharply within each class. All theorems are formally verified in Lean 4. Across 448 language-model and classifier selection pipelines, designs with per-candidate items realize a median 0.75 of the independent-class ceiling. At a fixed item budget, scoring all candidates on shared items is markedly less optimistic than giving each candidate its own items.

Ivan Viakhirev, Kirill Borodin, Grach Mkrtchian

lab260 (lab260.ru) · BitmanagerAI (bitmanager.ai)

Cross-ValidationSelection BiasStatistical Learning Theory
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Oct 19, 2026

Wet-Biased Data Pipelines Mislead the Training and Evaluation of Generative Precipitation Nowcasting

Generative models for precipitation nowcasting are trained and evaluated predominantly on wet-biased datasets, which over-represent precipitation events to emphasize rare extremes. Selecting test cases based on target observations is known to favor forecasts that match the selected distribution rather than the intended deployment distribution. We show analytically how this target-dependent sampling also shifts the conditional distribution learned by generative models. When training and test sampling match, even an ideal model learns precisely the distribution favored by evaluation, allowing the evaluation bias to conceal the training bias. Using a fixed satellite-to-radar diffusion model, we demonstrate that target-dependent test sampling can reverse the calibration assessment. The model appears under-predictive on a wet-biased test set but over-predictive on a deployment-representative test set. This result is replicated outside the model's training domain after a seven-year gap. Utilizing classifier-free guidance as an example, we demonstrate how the contradictory calibration assessment can misdirect downstream model development.

Christoph Metzl, Stefan Kapsreiter, Kianusch Vahid Yousefnia +4

Deutsches Zentrum für Luft- und Raumfahrt, Institut für Physik der Atmosphäre, Oberpfaffenhofen, Germany · Wismar University of Applied Sciences, Wismar, Germany · Arpae Emilia-Romagna, Hydro-Meteo-Climate Service (SIMC), Bologna, Italy +1

Precipitation NowcastingGenerative AI EvaluationSelection BiasModel CalibrationProbabilistic Forecasting
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Oct 19, 2026

Reliable Estimation of Differential Privacy under Selection Bias

Statistical privacy audits are essential for verifying the theoretical privacy guarantees of differentially private (DP) mechanisms. Auditors typically use Membership Inference Attacks (MIAs) to estimate a lower bound on the true privacy leakage of DP mechanisms at a specified confidence level, which should not exceed the theoretical privacy upper bound guaranteed by DP. However, we found that many auditing implementations in prior work introduce a selection bias when running MIAs, which leads to statistically invalid and overestimated lower bounds. Because most audits are not tight, this bias has thus far gone unnoticed: the estimated lower bounds remained well below the theoretical upper bounds. Nevertheless, accurately evaluating this lower bound is critical, as a flawed statistical assessment could lead to false alarms on correct mechanisms or an incorrect evaluation of the guarantee's tightness. This work employs tools from the statistical literature to correct this bias. We present an overview of the different correction methods and assess their respective advantages. Furthermore, we perform a comprehensive re-analysis of results returned by prior audit implementations and show that without statistical correction, these audits violate the theoretical upper bounds up to four times more often than their claimed confidence level implies. With correction applied, the resulting lower bounds are statistically valid, and violations occur at no more than the nominal rate.

Valentin Dorseuil, Meenatchi Sundaram Muthu Selva Annamalai, Jamal Atif +2

DI-ENS · UCL · CMAP +1

Privacy AuditingDifferential PrivacySelection BiasMembership Inference Attacks
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Oct 15, 2026

INCONVENIENT: A Benchmark to Assess LLM Generalization Capabilities from Convenience Samples

Machine learning models for tabular prediction typically assume that training data are representative of the population on which they will be deployed. In practice, however, data are often collected based on convenience, availability, or cost, resulting in systematic sampling biases that can distort feature--target relationships and undermine real-world generalization. Existing tabular distribution-shift benchmarks primarily construct out-of-distribution (OOD) settings by partitioning observations across naturally occurring domains. While such partitions may induce changes in P(Y | X), the resulting shifts are neither explicitly controlled nor isolated, and the evaluation distributions themselves are often not representative of the broader target population. We introduce INCONVENIENT, a benchmark designed to study robustness to convenience-sample bias. Rather than relying on naturally occurring domain partitions, INCONVENIENT directly perturbs feature--target relationships in the training distribution while preserving the original population distribution as the deployment environment. This setting more closely reflects real-world scenarios in which models are developed from unrepresentative samples and subsequently deployed on a broader population. The distinction is particularly relevant for large language models (LLMs), whose pretraining may encode population-level knowledge that extends beyond the relationships observed in a biased training dataset. Unlike existing distribution-shift benchmarks, INCONVENIENT provides explicit control over both the direction and severity of relationship shifts, enabling a systematic assessment of robustness to convenience sampling. The benchmark comprises 200 tabular classification and regression datasets spanning diverse application domains and generates around 15,500 shifted training distributions which lead to substantial downstream degradation.

Sara Rezaeimanesh, Chad Klochko, Kundan Thind +1

Michigan State University, East Lansing, MI, USA · Henry Ford Health, Detroit, MI, USA

Distribution Shift RobustnessTabular MLSelection BiasLLM Evaluation
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Oct 14, 2026

One Bias Score, Two Factors: How Mitigations Affect Option Bias in Multiple-Choice Evaluation

Reordering multiple-choice options can change a model's answer, an effect studied as selection bias (a preference for certain option letters) and as order sensitivity (changes in answers across option orderings). We connect these perspectives through the pooled selection-rate standard deviation (pooled SD), which measures how unevenly option letters are selected across questions and orderings. When every option of each question appears equally often at each position, the pooled SD is exactly the product of two label-free factors: the flip rate and the positional skew. The flip rate is the fraction of questions whose chosen option changes across orderings; the positional skew is the standard deviation of option-letter selection rates among those questions. Across 41 checkpoints and 12 benchmarks, the flip rate tracks accuracy and output uncertainty, while the positional skew tracks the estimated option-symbol prior. Prior correction for selection bias mainly reduces the positional skew. Aggregating each ordering with its reversal, a mitigation for order sensitivity, mainly reduces the flip rate. Both reduce the range of accuracy across correct-answer letters by similar amounts, but aggregation leaves fewer model-rank reversals. Applying prior correction before aggregation reduces both factors and further narrows this accuracy range. However, aggregation lowers the flip rate partly by settling questions on the same wrong option. We therefore recommend reporting both factors to distinguish mitigation effects, alongside accuracy to distinguish stability from correctness.

Hyunjong Ok, Minjae Park, Jaeho Lee

Pohang University of Science and Technology (POSTECH)

Input Order Sensitivity in Language ModelsLanguage Model Bias EvaluationSelection BiasMultiple-Choice Question Answering
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Oct 13, 2026

Causal Discovery Under Hard Selection Bias: A New Robust Score-Matching Approach

Selection bias is a difficult yet widespread problem in causal discovery, occurring whenever non-random selection processes lead to data that is not representative of the underlying populations. Due to its practical importance, related works have been proposed to address the problem under local [Versteeg et al., 2022] or interventional settings [Dai et al., 2025a], but general algorithms for observational data remain elusive. In this paper, we focus on truncated data (hard selection), and provide a general result for Additive Noise Models (ANM). We show that score-based methods are a surprisingly suitable candidate due to a special property of the score function (∇log⁡p(x)\nabla \log p(x)): deterministic truncation preserves both the score of the joint distribution as well as the Jacobian of the score. While established score-matching algorithms still fail in most settings, we actively leverage this observation to propose a new method for causal discovery that is robust under truncated data with ANMs. Overall, our approach offers a general, robust solution that is agnostic to external information about the selection process and still achieves comparable performance to the state-of-the-art approaches when selection is not present.

Yiwen Qiu, Francesco Montagna, Shimeng Huang +1

IST Austria, Am Campus 1, Klosterneuburg, 3400

Causal DiscoverySelection BiasScore-Based Causal DiscoveryScore Matching
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Oct 7, 2026

Shared and structured inputs undermine collective random choice by reasoning AI agents

Random selection is widely used in resource allocation and auditing, making reliable implementation essential for AI-agent systems. Behavioural tests across six reasoning models uncovered threshold and divisibility rules used in identifier-based choices. For threshold-following GPT-6 Sol and Gemini 3.8 Flash, single-agent measurements prospectively predicted correlated participation under shared identifiers and biased participation under distinct identifiers with common timestamp bits. Changing dates, formats and identifier labels revealed when these predictions held. Explicit instructions to randomize independently reduced but did not eliminate shared-input correlation. To test implications for oversight, we asked four models to select customer requests randomly for human review. GPT-6 Sol approached the target rate while selecting predictably from identifiers; the others rarely selected requests. All four closely followed supplied random draws. These findings expose collective and audit vulnerabilities that selection rates alone miss, making input-dependent bias, correlation and predictability central targets for agent evaluation.

Takahiro Ezaki, Naoto Imura, Katsuhiro Nishinari

Research Center for Advanced Science and Technology, The University of Tokyo 4-6-1 Komaba, Meguro-ku, Tokyo 153-8904, Japan · Department of Aeronautics and Astronautics, School of Engineering, The University of Tokyo 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan

AI Agent EvaluationSelection BiasAlgorithmic Auditing
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Oct 3, 2026

EasyClassifier: Honest, Reproducible Machine-Learning Classification for Researchers Who Do Not Program

Machine-learning classification is now used across medicine, the social sciences, economics, education and engineering, very often by researchers who do not program. Two errors recur in such work: preprocessing learned on all rows before cross-validation (data leakage), and reporting the cross-validation score of the classifier that won a comparison (selection bias). Both make published scores optimistic. We present EasyClassifier, an open-source Python package that guides a user from a CSV or Excel file to a finished analysis through a sequence of plain-language, multiple-choice questions, with no code. It makes the correct procedure the default rather than an option: every preprocessing step is learned inside each training fold; the selected classifier receives a separate final score from nested cross-validation (up to 2,000 rows), or an untouched 20% test set; classifiers run with fixed default parameters and fixed random seeds; and every run writes a report with a ready-to-adapt Methods paragraph, the references to cite, and figures prepared for publication. On ten public datasets from seven fields and a random-label control, split in half so that one half served as an untouched external test, the common practice overstated balanced accuracy by 2.9 percentage points on average (up to 9.9 on small data), whereas the score EasyClassifier reports had a mean signed bias of +0.7 points and a mean absolute error of 2.3 points (one-sided Wilcoxon p = 3.2 x 10^{-4}, 30 runs). On random labels it reported 48.8% balanced accuracy against a chance level of 50%. EasyClassifier is available under the MIT license from PyPI (pip install easyclassifier), GitHub, and Zenodo.

Ahmad B. A. Hassanat, Ghada A. Altarawneh

Faculty of Information Technology, Mutah University, Karak, Jordan · Department of Accounting, Mutah University, Karak, Jordan

ML ReproducibilityClassificationData LeakageTabular MLCross-ValidationSelection Bias
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Oct 1, 2026

Oracle headroom without signal: null-calibrated evaluation of candidate selection for thermal heart rate estimation

Camera-based physiological monitoring can produce multiple estimates from several facial regions, extraction methods, and processing settings. Signal quality indices aim to select reliable estimates without a physiological reference, and their potential is often assessed with an oracle that selects the estimate closest to the reference in each window. This retrospective selection can reward chance agreement. We model the effect with order statistics. For K independent candidates unrelated to the reference, the expected oracle error decreases approximately as 1/K. We analyze thermal heart rate estimation on 96 iBVP recordings with 168 candidates per 10 s window. The oracle achieves a mean absolute error of 0.91 bpm, compared with 10.74 bpm for the best fixed configuration, 18.03 bpm for the best quality index, and 8.61 bpm for a constant predictor. With K = 24, a forehead signal from another recording matches the correct one, with 4.62 against 4.61 bpm. Oracle evaluations should report candidate count, valid coverage, and matched null controls.

Mohammad Rakibur Rahman, Nhi Nguyen, Sasan Sharifipour +4

Center for Machine Vision and Signal Analysis (CMVS), University of Oulu, Finland

Heart Rate EstimationSelection BiasThermal Imaging
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Oct 1, 2026

False Floors: LLM Safety Routing Evaluations Break Under Distribution Shift

Safety routers send each request to one of several models and are judged against the best single model. A major routing benchmark picks that comparator on the evaluation data. In the benchmark's own setting this is harmless, but under distribution shift it is not. On HELM Safety the selection cost is 0.003-0.030 of harm under random splits and 0.045-0.113 under held-out categories, comparable to the whole deficit attributed to routing, with its direction holding under either published judge alone. It rises seven- to ninefold on AgentDojo when suites are held out. Across seven safety corpora chosen by rules fixed in advance, three meet a registered interval test and four beat a later permutation null, and three of the four interval misses are corpora where some models have zero observed harm. Prior work proves the direction of this bias. We size it on harm and accuracy, show that it is larger under the held-out splits we measure, and bound it by optimism plus a shift-dependent regret. Scored honestly under shift, routing buys little on these benchmarks. In most pool cells the nested router serves the honest baseline's model, and on the nearly saturated AgentDojo corpus a perfect pre-dispatch router is worth at most two points of harm. We also find a model's expressed recognition of a late injection steerable. On held-out reruns an attacker who knows which model it faces lowers GPT-5.4's judged recognition by 19.6 points, confirmed by an independent label. In an offline counterfactual composition into a controller, the same attack raises or lowers estimated harm depending on the fallback model. Safety routing should be evaluated under shift, against a baseline chosen without the test labels, and recognition-based defences should be scored on harm against an attacker who chooses what the model sees.

Amit Singh Bhatti, Vishal Vaddina

Quantiphi Analytics

LLM Safety BenchmarksDistribution Shift RobustnessAdaptive Model RoutingLanguage Model Safety EvaluationSelection Bias
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Sep 29, 2026

Learning-Enabled Estimation: Tight Characterizations under Sample Selection Biases

When can we learn from biased samples? We study regression when outcomes are observed only after passing through selection filters that depend on both covariates and outcomes themselves, a ubiquitous challenge spanning clinical trials with patient dropout, labor markets with self-selection, and auctions with strategic entry. Ignoring such selection yields systematically biased conclusions with real-world consequences. This challenge has a long history in econometrics and statistics, starting with Heckman's seminal two-stage model and followed by numerous generalizations. While these works provide various sufficient conditions for identification, a complete characterization of when such regression is possible has remained elusive. In this work, we provide a characterization for when regression is possible in the presence of sample selection bias. Our results establish the minimal assumptions required on the functional forms of selection processes under which regression remains possible, which are particularly relevant in modern settings where selection mechanisms are increasingly complex and opaque. As a corollary of our characterization, we show that there are settings where the regression function can be identified even when the selection filter itself cannot. This observation already goes beyond the ``estimate selection filter, then debias regression'' paradigm that is followed by virtually all existing approaches. Under natural strengthenings of our identification conditions, we also establish finite-sample estimation guarantees with explicit convergence rates and provide oracle-efficient algorithms. This yields the first general-purpose estimation method for this broad class of selection problems. Finally, we explore the implications of our results for several well-studied econometric settings with complex selection mechanisms such as auctions with entry costs and labor markets.

Vikram Kher, Jane H. Lee, Anay Mehrotra +1

Yale University · Stanford University

Selection Bias
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Sep 26, 2026

Oracle Gaps in Reliability Coverage: Sampling Noise or Policy Specialization?

Policies trained from the same base model can appear to solve different problems. An oracle that chooses the best policy for each problem may therefore appear much stronger than any single policy. Selecting the largest estimated success rate also selects favorable sampling errors. We study this effect through reliability coverage, the fraction of problems whose success probability reaches a chosen threshold. Our first test redistributes stored correctness outcomes across policies within each problem. A second also preserves each policy's total successes, accounting for overall quality differences under a specified statistical model. For five training seeds of a seven-billion-parameter vision-language model, redistribution reproduces 0.096 of an estimated 0.113 oracle gap at threshold 0.10. Neither test finds significant evidence at this threshold. Small advantages remain unresolved. Mixtures, routers, voting, and weight averaging show no detectable improvement over their corresponding single-policy baselines. Training policies on different datasets shows little detectable specialization under light post-training, and no router gain. A stronger recipe does create it, both tests detect it, and a router gain appears only at the high thresholds where the specialists separate. In a control with predictable specialization, a router recovers about half the oracle gap. Coverage bounds explain why even a genuine oracle advantage need not yield a deployment gain. The tests assess apparent specialization from stored responses before investment in routing. Code: https://github.com/KurbanIntelligenceLab/oracle-gaps

Mert Onur Cakiroglu, Mehmet Dalkilic, Hasan Kurban

Luddy School of Informatics, Computing, and Engineering, Indiana University Bloomington, Bloomington, IN, USA · College of Science and Engineering, Hamad Bin Khalifa University, Doha, Qatar

LLM ReliabilitySelection Bias
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Sep 12, 2026

When Edit Localization Amplifies Relative Selection Bias: Gradient Geometry, Target Mismatch, and Importance Weighting

Human corrections identify editable spans, but the examples receiving corrections may come from a selective feedback channel. We analyze this interaction at a fixed model checkpoint by decomposing a localized gradient into edited and retained untouched components. Squared relative selection bias is a ratio of quadratics whose derivative has the sign of an explicit quadratic polynomial. Localization can increase, decrease, or nonmonotonically change this diagnostic; its direction depends on component biases and geometry. Oracle importance weighting recovers the population mean for each fixed localization objective, but these objectives have different targets. Against one common full-gradient target, we derive the finite-sample mean-squared error, an analytic optimal retention coefficient, and a fixed-clipping extension. Exact finite-population calculations and 10,000 Monte Carlo repetitions per sample size verify the identities and counterexamples. Public human-post-edit experiments use two translation directions and pretrained models, with declared synthetic selection. An English-German extension differentiates 73.89 million native parameters. In all three declared settings, hard localization has higher relative bias but lower absolute bias than full retention. Untouched-component biases are nonzero and selected component means have negative inner products, so the general criterion applies where the simple unbiased/aligned explanation fails. Output-bias diagnostics show the same endpoint ordering of relative bias across both directions, with one interior maximum. Mechanisms reuse each language's records and include a mixture; they are not independent replications. The evidence separates relative amplification from absolute gradient error and establishes estimation properties, without inferring translation-quality gains or identifying actual complaint propensities.

Shengwei Zhang, Haoda Dai, Yifei Li +1

University of Pennsylvania

Selection BiasImportance Weighting
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Sep 9, 2026

Loading history and window geometry bound compact-state slip ranking during granular shear startup

Granular slip forecasting can conflate material state, loading progress, and the geometry of event-centered sampling. We separated these contributions in slowly sheared two-dimensional frictional disks using a compact neural score of stress, pressure, coordination, non-affine motion, and force-network observables. The model was developed on 36 trajectories and frozen efore testing on 18 new trajectories under two nested stress-drop definitions. Inspection of held-out results revealed post-event sampling asymmetry; recovery-aware analyses are therefore descriptive. With trajectories weighted equally, the compact score ranked near-slip windows above both prevalence and within-trajectory circular-phase controls under both definitions (representative average precision 0.310 versus prevalence 0.173; phase-null upper bound 0.257). Loading-history coordinates ranked more strongly, reaching 0.534 for causal elapsed strain. The recovery-aware rule retained 78.4% of activity-gated events and preferentially selected longer preceding intervals; ranking by time since the previous catalogued event remained compatible with a count-conditioned geometry null. Compact observables thus contain temporally aligned slip information, but stronger loading-history baselines and window-geometry sensitivity bound that evidence. These startup data do not isolate a state-specific short-horizon precursor beyond loading history or support a renewal interpretation of elapsed-strain ranking.

Ruixin Zhou, Boliang Yu

School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China

Materials ScienceTime Series ForecastingSelection Bias
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Sep 7, 2026

Semi-Supervised Learning under Spatially Biased Sampling

Standard semi-supervised learning (SSL) typically relies on labelled and unlabelled data sharing a common marginal distribution. This assumption is often violated by biased spatial sampling mechanism, when labels are collected under spatially biased or preferential site selection. We treat this marginal mismatch, spatial autocorrelation, and spatial non-stationarity as three distinct mechanisms, varied independently via a labelled-sampling concentration parameter, a spatial length scale, and a non-stationarity strength parameter, and ask how mismatch degrades SSL, whether the cluster and manifold assumptions survive it, and how the resulting failure can be diagnosed. Using a controlled synthetic framework alongside PovertyMap-WILDS, California housing, socio-economic and US air quality monitoring datasets, we systematically vary the degree of mismatch while accounting for spatial autocorrelation and non-stationarity. Through a series of analyses including a segmented-regression changepoint, we show that in the synthetic generator, SSL performance does not degrade gradually but instead exhibits a threshold-like breakdown between approximately 0.71 and 0.77 once distribution mismatch becomes sufficiently severe. We further demonstrate that spatial non-stationarity contributes to performance loss independently of marginal mismatch and that models become increasingly overconfident outside the regions where labels are available. To support practical deployment, we evaluate several distribution-divergence measures as indicators of reliability and introduce a kernel-weighted local divergence metric that provides a more stable estimate of spatial mismatch than a naïve localised approach. These findings provide empirical evidence and diagnostic tools for better documenting the risk of incorporating unlabelled spatial data into semi-supervised learning workflows.

Bright Wiredu Nuakoh, Francky Fouedjio, Stephen Bradshaw +4

African Institute for Mathematical Sciences (AIMS), 17 KN 16 Ave, Kigali, Rwanda · Mathematical Application & Data Analytics Group, School of Science, Edith Cowan University, 270 Joondalup Drive, Joondalup, WA 6027, Australia · Data & Analytics, Rio Tinto, 152-158 St Georges Terrace, Perth, WA 6000, Australia +2

Distribution ShiftSemi-Supervised LearningSelection Bias
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Aug 23, 2026

A survey detection channel overrides the pixels in an astronomical foundation model, and biases tomographic mean redshifts

Foundation models for astronomy are trained on survey pixels together with the catalogue products derived from those pixels. Those catalogues are incomplete at a measurable rate, and a model trained on both inherits that incompleteness as a systematic. We audit AION-1, a 39-modality transformer trained on more than 200 million objects, using causal interventions on its inputs. Holding the image tokens byte-identical and editing only the survey segmentation map changes every quantity the model reports -- flux, size, ellipticity, redshift -- by 110-4400 times a matched placebo. The mechanism is detection gating, presence at the field centre (r = 0.47), not the light the mask encloses (r = 0.30); across 322 real blends the model ignores how the pipeline partitioned the light (R = -0.006). Nor is the preference specific to that channel: contradicted catalogue photometry leaves the model nine times worse than supplying no metadata at all. The Legacy Survey pipeline leaves 3.68% of targets with no segment covering their position. Propagating that rate, with a miss represented by the fields the pipeline actually returns, shifts tomographic mean redshifts by a median 0.71 times the LSST DESC requirement over 40 assignments and exceeds it in 12; observed positional errors take the worst bin to 8.3 times. Drawing the misses by their measured magnitude dependence rather than uniformly does not change it. Spectroscopy removes the effect, withholding the detection channel removes it at no measurable cost, and the effect grows with model scale. Two further limits lie in the tokeniser: its image codec resolves 28 effective states on source patches against 934 for the spectrum codec, and the redshift readout is quantisation-limited. Sparse dictionaries are unreliable causal handles: across 15, recovery spans 26-75% and moves up to 18 points on the seed alone.

Ihor Kendiukhov

Independent researcher

Selection BiasAI-Assisted Scientific ResearchBlack-Box Model Auditing
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Aug 13, 2026

Sampling Luck Masquerades as Allocation Gain: Auditing Test-Time Budget Allocation for Neural Combinatorial Optimization

Neural combinatorial optimization (NCO) solvers report the best of many sampled solutions per instance, and the sample count is, by convention, identical for every instance. Whether a non-uniform allocation of a fixed total budget would buy anything has not been measured. We measure it, and we audit the measurement itself. First, on in-distribution workloads the allocation headroom is not detectable. Across three pretrained solvers (POMO, AM, SymNCO) on uniform TSP-100, an oracle allocation computed and evaluated on the same stored samples reports a 2.2-2.6% gain with intervals excluding zero; measured out of sample the same gain is indistinguishable from zero (0.457, 0.015, -0.512 percent). Following the customary in-sample procedure, all three solvers would have supported a published 2%-level gain that does not exist. We calibrate this bias against an instance-wise null in which the true gain is zero by construction; over the ranges we test it does not shrink with more samples or more instances. Second, the same correction that removes the phantom gains preserves a real one. Under distribution shift (a workload mixing uniform and clustered instances), a pre-registered confirmatory experiment finds that allocation guided by held-out sample statistics improves best-of-k by 11.5% (AM, primary endpoint; 95% CI [7.4, 19.7]) and 12.0% (SymNCO, replication) at equal evaluation budget, with the signal-acquisition cost not charged; a pre-registered negative control (POMO, an order of magnitude more robust to shift) shows -0.3% [-0.7, 0.24]. The gain exceeds a frozen distribution-label baseline by 4.2 points [1.9, 7.7]. An exploratory policy charging a 20-sample probe against the same budget retains 3.4% (AM) and 4.6% (SymNCO). We give a correction procedure and a reporting checklist, and release all data, code, and the pre-registration record.

Jinhyung Bae

Department of Industrial and Management Engineering and the AI Data Convergence program, Hankuk University of Foreign Studies, Yongin, Republic of Korea

Algorithmic AuditingInference-Time Compute AllocationSelection BiasNeural Combinatorial Optimization
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Aug 5, 2026

Automatic Statistical Test for Rationally Expressible Algorithms by Selective Inference, with Applications to Feature Selection

Selective inference (SI) provides statistically valid pp-values for hypotheses selected by applying an algorithm to the data, correcting for the bias that arises when the same data are used both to select and to test a hypothesis. Developing an SI procedure for a new algorithm, however, has required an expert to derive, and then implement, the selection event, i.e., the conditions under which the hypothesis is selected. Repeating this specialized effort for every new algorithm is why exact SI has so far been available for only a narrow class. We propose AutoSI, a framework that removes this barrier in two ways. First, AutoSI constructs the selection event automatically from the algorithm's individual operations, so the user only writes the algorithm as ordinary NumPy-like code and derives nothing by hand. Second, AutoSI broadens the class of selection events SI can handle: existing exact methods are limited to selection events characterized by linear or quadratic inequalities in the data, whereas AutoSI covers any algorithm expressible through rational functions of the data (ratios of polynomials). We prove that the pp-values computed by AutoSI are exactly valid in finite samples. We demonstrate AutoSI on three feature-selection methods, each written in a few dozen lines of code. One of these methods, the lasso with its tuning parameter selected by cross-validated R2R^2, cannot be handled within existing exact SI frameworks and is made possible by AutoSI. Experiments on synthetic and real datasets show that the resulting pp-values control the type I error rate (i.e., the false positive rate) at the nominal level while retaining high power.

Teruyuki Katsuoka, Tomohiro Shiraishi, Shuichi Nishino +1

Nagoya University · RIKEN

Selective InferenceSelection BiasStatistical Hypothesis Testing
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Aug 2, 2026

When May a Model Replace the Experiment? Audits, Licenses, and the Price of Trust in Surrogate-Driven Design

Design campaigns in chemistry, materials science, and machine learning share a bottleneck: determining how good a candidate truly is requires an expensive evaluation - an experiment, a first-principles simulation, or a full training run. Machine-learning surrogates that predict these outcomes are increasingly used not only to propose candidates but to grade them, and even to feed their own predictions back into the search as though they were measurements. Through mathematical analysis validated on three exhaustively ground-truthed design tasks, we establish when this practice is safe, what any certificate of safety must cost, and when the substitution provably pays. Predictive accuracy cannot anchor trust: near-perfect R^2 is compatible with worst-possible selections, and screening N candidates inflates the over-prediction at the selected candidate by a quantifiable "selection tax" with matching upper and lower bounds. Safety follows instead from an architectural rule - predictions may propose and train without restriction, but every certified conclusion must rest on true evaluations - which is sufficient with no assumptions on the surrogate, and necessary, since admitting predictions into certification with the standing of measurements opens a deterministic self-confirmation failure mode. We derive the minimal criterion under which a model may act as an oracle (rank preservation, not accuracy), show that trust must be purchased through selection-aware audits that are optimal in query complexity, and prove a dichotomy fixing when audited surrogates cut certified evaluation cost. Across 432 surrogate fits over six task-regime conditions, the audit statistic tracks deployed search performance at Spearman rank correlation 0.80-0.99, while the rank correlation of R^2 with deployed regret falls as low as 0.33; audited screening reduces certified oracle cost by a measured factor of 25.

Shuangxiu, Ma, Wenhe +1

Max · William G. Lowrie Department of Chemical and Biomolecular Engineering, The Ohio State University, Columbus, Ohio 43210, United States · Zachary +1

Surrogate ModelingSurrogate-Assisted OptimizationSelection BiasBlack-Box Model Auditing
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Jul 21, 2026

Selection Shapes the Boundary: A Replication of Monotonicity and Label Agreement in Unselected NLI Populations

Prior work on human label variation (HLV) in natural language inference (NLI) has often relied on re-annotation resources that select items by disagreement level. An earlier study (Choi, 2026, arXiv:2607.15870) found that hypotheses containing non-upward monotonicity operators showed somewhat higher label entropy in ChaosNLI (Cliff's delta = -0.284), a difference that study reports as sensitive to tagger error. In its SNLI and MultiNLI portions, ChaosNLI re-annotates only items whose majority label carries exactly three of five votes. We replicate this boundary in the unselected populations that ChaosNLI was drawn from. We use the SNLI and MultiNLI development sets with the same operator tagger and a four-level ordinal agreement outcome, under a plan frozen in our working repository before analysis. The planned prediction fails. All seven contrasts return a positive Cliff's delta (non-upward items agree slightly more, not less), the only significant confirmatory contrast has the opposite sign to the planned direction, and every effect is far below our smallest effect size of interest (0.10). Robustness checks support the measurement: simulated tagger misclassification shrinks the effects rather than manufacturing them, and a manual re-tagging audit reaches four-class agreement of 0.875 on a fresh 200-item sample. We conclude that the earlier negative boundary is plausibly a structure conditional on low-agreement selection rather than a population-level property, and that HLV structure claims built on selected re-annotation resources should state their selection conditional explicitly.

Haram Choi

University of Bremen

Annotator DisagreementSelection BiasNatural Language Inference
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Jul 20, 2026

The Curvature Shadow: An Apparent Failure of Maximum-Entropy Equilibrium Selection is a Removable Artifact

In two-player zero-sum games whose Nash equilibria form a convex set, regularized solvers such as Regularized Nash Dynamics (R-NaD) empirically select the maximum-entropy member: the information projection (I-projection) of a uniform reference onto the Nash set. On a panel of small games this match is exact, with one apparent exception: in Kuhn poker R-NaD lands at bluff coordinate 0.180 while the maximum-entropy member sits at 0.201, a coordinate gap of about 0.021, even though R-NaD attains 99.7 percent of the maximum entropy. We ask whether this gap is a genuine selection bias or an artifact, and answer it quantitatively. We show that for selection on a one-dimensional Nash manifold the coordinate gap factorizes as gap≈2δ/κ\mathrm{gap} \approx \sqrt{2δ/κ}, where δδ is the entropy shortfall of the solver and κκ is the curvature of the entropy landscape at its peak. Across five games this relation holds to within 2×10−42 \times 10^{-4} (under 1 percent relative error). The four matrix games have δ≈0δ\approx 0 (R-NaD reaches the maximum-entropy member exactly) and therefore no gap regardless of curvature; only the sequential game (Kuhn) has δ>0δ> 0. A causal sweep of the magnet strength drives δ→0δ\to 0 and the gap toward zero along the predicted curve (fitted scaling exponent 0.50, R2>0.999999R^2 > 0.999999, against the exact prediction of 1/2), until the dynamics destabilize at a stability floor: behavior consistent with a removable shortfall and inconsistent with a fixed bias. We quantify the curvature half of the law from measured curvatures and flag a moving-target pitfall in the natural Tsallis-entropy experiment. The Kuhn gap is thus the curvature shadow of a small, removable entropy shortfall on an unusually flat peak; the I-projection account is upheld up to a flatness-limited residual.

Luis Leal

Nash EquilibriumImperfect-Information GamesZero-Sum GamesSelection Bias
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Jul 7, 2026

K-ABENA: K-Adaptive Backpropagation with Error-based N-exclusion Algorithm : (Compensated Loss-Based Sample Exclusion with Unbiased Gradient Estimation)

We present K-ABENA (K-Adaptive Backpropagation with Error-based N-exclusion Algorithm), a selective gradient computation framework that reduces per-iteration training cost by excluding a fraction of low-loss ("minor") observations from the backward pass. Its canonical form (v3) combines a defensive-mixture sampling design over the minor set with Horvitz-Thompson inverse-probability reweighting, yielding a design-unbiased Horvitz-Thompson gradient estimator (Lemma 2) and whose self-normalized practical variant carries a bias of order O(1/m) with an explicit constant (Lemma 3). We prove an O(1/sqrt(T)) non-convex convergence guarantee for SGD under the estimator, with an additive term that quantifies the residual bias (Theorem 1). We further prove that uncompensated loss-based selection - a family that includes OHEM, SBP, and the two earlier K-ABENA variants - admits no stationary point at any minimizer where its selection bias is bounded away from zero (Proposition 2), and we quantify this failure empirically: at 0.17% class imbalance, uncompensated variants reach test AUC 0.53-0.62 versus 0.9998 for full-batch SGD, while the compensated estimator attains 0.9991 at identical 28.4% compute savings. On real datasets (Breast Cancer, Digits, Wine, Diabetes) the compensated estimator is statistically indistinguishable from full-batch SGD (paired permutation tests, p >= 0.5; Section 7) while saving 28-54% of per-epoch gradient computation. A biased "regularized mode" (the earlier half-domain variant) is retained as an option with a proven exact bias decomposition (Lemma 5) and quantified contraindications: it collapses to 0.386 accuracy under 40% label noise (baseline: 0.832) and to 0.53 AUC under extreme imbalance. Every advantage and every limitation reported in this paper is either proved or measured; all experiments are CPU-scale (NumPy/scikit-learn) and their scope is stated explicitly.

Jean-Francois Bonbhel

NeuroSoft IA, Qu´ebec City, Canada · YekoElite University, Brazzaville, Republic of Congo

BackpropagationNeural Network OptimizationImportance SamplingNonconvex Stochastic OptimizationAdaptive SamplingSelection Bias+1
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Jul 7, 2026

Heckman-Corrected Epistemic Uncertainty: Selection on Unobservables Defeats Importance Weighting

Training data for machine learning is routinely collected by a selection process the model never sees: loans are observed only when granted, outcomes only when a test was ordered. The standard fixes -- importance weighting, covariate-shift correction, MAR imputation -- assume selection is ignorable given observables. Econometrics solved the harder case in 1979: Heckman's two-equation model jointly fits a probit selection equation and an outcome equation linked through correlated errors, and the inverse-Mills-ratio term corrects for selection on unobservables, where importance weighting is structurally helpless. We instantiate this for deep epistemic uncertainty: a deep outcome network, a linear selection head, and a joint bivariate-normal likelihood over all units, ensembled for predictive variance. In a controlled generator where sampling probability depends on an unobservable correlated (rho up to 0.9) with the outcome noise, deep ensembles, MC dropout, and GP baselines are overconfident exactly where data was avoided: coverage of nominal-90% intervals falls to 64.4% at rho=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,selected] != E[y|x]. The Heckman correction restores coverage (88.9%) when the selection equation has an instrument -- a variable affecting selection but not the outcome -- and degrades measurably without one (40.3%); we chart this honesty curve rather than hide it. On real tabular data with induced MNAR selection, the corrected intervals are the best-calibrated (lowest region-ECE) non-oracle method in selected-against regions; baselines matching its raw coverage do so only by over-widening everywhere. Our estimators reproduce classic Stata output to seven digits. We state which identification regime a practitioner is in, and release the code.

Gunner Levi Howe

Independent Researcher

Selection BiasUncertainty CalibrationRegression Prediction IntervalsEpistemic Uncertainty
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Jun 17, 2026

Identifying Structural Biases from Causal Mechanism Shifts

Causal discovery methods commonly assume that all data is independently and identically distributed (i.i.d.) and that there are no unmeasured variables affecting the system. In practice, these assumptions are often violated, leading to inaccurate inference. In this paper, we study how to identify hidden confounding and selection biases from causal mechanism shifts. In particular, we show that structural biases lead to dependent mechanism shifts. That is, by considering for which variables the mechanisms change given data from different environments, we can tell which variables are unbiased, which are subject to hidden confounding, and which are undergoing selection bias. We formalize this into an empirically testable criterion based on mutual information, and show under which conditions it identifies structural biases. To tell which nodes are subject to what kind of bias, we introduce the StruBI algorithm. Experiments on synthetic and real-world data show that StruBI works well in practice, accurately recovering affected variable sets and types of biases, outperforming the state-of-the-art by a wide margin.

Praharsh Nanavati, Jilles Vreeken, David Kaltenpoth

CISPA Helmholtz Center for Information Security

Structural Causal ModelsCausal DiscoveryCausal InferenceSelection BiasCausal Discovery with Latent Confounding
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Jun 16, 2026

The Illusion of Improvement: Reject Inference Strategies in Credit Scoring

Reject inference methods are widely used to mitigate survival bias in credit scoring, yet their effectiveness remains poorly understood. We systematically evaluate several such methods and uncover a structural failure mode: in a natural retraining cycle, models whose accuracy improves while recall collapses create an illusion of improvement that leads practitioners to believe the system is getting better when, in fact, its rejection quality -- the ability to correctly screen out defaulters -- is deteriorating. We then propose a controlled exploration strategy that breaks the feedback loop without statistical assumptions: the lender deliberately approves a fraction of rejected applicants and observes their true outcomes. We show that accuracy and rejection quality give opposite recommendations on whether to explore: accuracy favors no exploration, while rejection quality improves with it, confirming that standard evaluation metrics are misleading under selection bias. Even minimal exploration rates (2--5%) prove sufficient in our experiments to diagnose the severity of the feedback loop at near-zero cost. Our findings are consistent across two machine learning methods and three real-world datasets, and suggest that standard evaluation protocols are inadequate for assessing models trained under survival bias.

Bruno Scarone, Ricardo Baeza-Yates

Northeastern University, Boston, MA, USA · KTH Royal Institute of Technology, Stockholm, Sweden

Credit ScoringSelection BiasSelective Labels
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Jun 12, 2026

Beyond the Training Distribution: Evaluating Predictions Under Distribution Shift and Selection Bias

Understanding how a prediction model will perform in a new environment before deployment is essential to preventing harm when algorithms inform decision-making. Two common sources of model performance degradation are (i) covariate shift, where the target covariate distribution differs from the source, and (ii) selective labels, where the observability of outcomes depends on historical decisions. We study pre-deployment model evaluation under the joint presence of covariate shift and labeling of outcomes selectively based on observed features. In particular, we present a double machine learning procedure for estimating the target risk of an arbitrary black-box prediction model under a general loss function. We show identification of this estimand under standard assumptions and derive a bias-corrected estimator based on the influence function of the target risk. Finally, we evaluate our estimator through experiments using the eICU electronic health records database, showing that it tracks the true target risk more accurately than methods that address either selective labels or covariate shift alone, as well as baselines that combine standard plug-in approaches.

Annie Ulichney, Amanda Coston

Department of Statistics, University of California, Berkeley

Double MLDistribution Shift RobustnessDistribution ShiftCovariate ShiftSelection BiasDoubly Robust Estimation+1
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Jun 11, 2026

When Sample Selection Bias Precipitates Model Collapse

The proliferation of recursive training on synthetic data can alleviate data scarcity but risks model collapse, where repeated training erodes distributional tails and homogenizes outputs. Data selection is widely viewed as a remedy, yet its reliability depends critically on the reference distribution used by the verifier. We show that in low-resource verification regimes, where each verifier observes only a small, fragmented, and biased slice of the target manifold, selection itself becomes biased. This situation naturally arises in low-resource data silos such as healthcare consortia or proprietary financial institutions, where raw data cannot be pooled and local references are inherently incomplete. As a result, selection preferentially retains samples aligned with the local manifold while pruning globally relevant tail modes, turning from a safeguard against collapse into a mechanism that precipitates it. We theoretically prove that such siloed selection accelerates collapse and induces power-law diversity decay. As an initial mitigation, we construct Wasserstein proxy references from multiple silos without sharing raw data. Empirical results confirm that local-reference selection fails on skewed distributions, whereas collaborative proxy references mitigate diversity degradation, suggesting that recursive synthetic-data pipelines require particular caution when real-data coverage is fragmented or scarce.

Xinbao Qiao, Xianglong Du, Wei Liu +4

National University of Singapore (Chongqing) Research Institute · Chongqing Key Laboratory of Trusted Perception and Interaction Technology for Intelligent and Connected Vehicles, Chongqing, China · The Chinese University of Hong Kong +4

Synthetic Data PretrainingModel CollapseTraining Data SelectionSelection BiasSynthetic Data Selection
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Jun 3, 2026

When Can You Trust Your Synthetic Users? Diagnostics and Corrections for LLM Consumer Panels

Large language models are increasingly used to simulate consumers, yet agreement with aggregate survey outcomes can conceal errors in the subgroup estimates that guide decisions. We develop a framework for deciding when to trust, correct, or abandon a synthetic consumer panel by distinguishing population mismatch from differences in conditional responses. The framework combines diagnostics for covariate overlap, conditional calibration, and stability across models with an augmented inverse probability weighting estimator that treats LLM predictions as auxiliary information. Correction requires a complete invitation frame, response indicators for everyone invited, and human outcomes for respondents, together with assumptions of missing at random and positivity. We evaluate the framework using simulations and controlled nonresponse experiments constructed from paired human and LLM responses in ANES and Twin-2K-500. In identified simulation regimes, point bias remains small when either the response model or the outcome model is correct, but nominal 95% confidence intervals cover only 88--94% in some regimes. When nonresponse depends on missing human outcomes, substantial bias persists and coverage approaches zero. Controlled masking of the paired datasets reproduces this contrast between successful point correction under imposed missing at random and failure under nonignorable nonresponse. These findings show why validation must address the intended population and task, and why the scope for correcting synthetic estimates depends on the available human data and the assumptions that identify the target.

Robson Tigre, Hugo Gobato Souto

Recast · Dell

Synthetic Data EvaluationUser SimulationLarge Language Model-Based Social SimulationSelection BiasLanguage Model Calibration
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May 30, 2026

A Practical Upper Bound on Selection Bias Effects in Medical Prediction Models

Selection bias is a common and often unavoidable aspect of real-world data that challenges the generalizability of machine learning models. When models trained on biased data are deployed in the broader target population, poor model generalization may lead to real harm, particularly in high-risk settings such as healthcare. This risk highlights the need for practitioners to reliably assess model generalizability prior to deployment. However, existing methods for predicting model performance rely on unrealistic access to the target distribution or knowledge of the selection mechanism causing bias. To address these limitations, we propose a novel upper bound on the worst-case model performance on the target population under the realistic setting where the selection mechanism and the target population data are only partially observed. We demonstrate the validity and practical utility of our method through experiments on fully synthetic data, semi-synthetic data derived from the All of Us Research Program, and real-world selection bias in MIMIC-IV. Our work offers a principled and practical tool to estimate the impact of selection bias in an otherwise intractable setting, thereby enabling practitioners to build safer and more generalizable models in healthcare and beyond.

Kara Liu, Maggie Wang, Russ B. Altman

Stanford University · Stanford, California, USA

OOD GeneralizationSelection BiasGeneralization Bounds
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