importance weighting

Methods for assigning and using sample or estimator weights to correct distributional mismatch, combine model outputs, and trade off bias and variance — including designing, estimating, and tuning weighting schemes for fair comparison and reliable target-domain performance estimation.

importanceweighting

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On Fairness and Stability: Is Estimator Variance a Friend or a Foe?

Feb 09, 2023
FA
Falaah Arif Khan
🏛️ New York University | Ukrainian Catholic University

Machine learning models exhibit high sensitivity to minor perturbations in training data, leading to unstable predictions; yet conventional fairness metrics (e.g., bias-based indicators) ignore this prediction uncertainty. Method: We propose a variance-oriented paradigm for group fairness—introducing the first systematic framework that treats inter-group predictive variance equality as a core fairness criterion, grounded in statistical error decomposition and theoretical analysis of variance’s independent impact on fairness assessment. Contribution/Results: We release VarFair, the first open-source library integrating uncertainty quantification with fairness evaluation. Extensive experiments on Adult, COMPAS, and other benchmarks demonstrate that groups with high predictive variance are frequently misclassified as “fair” by standard methods, whereas our variance-aware metric significantly improves identification of disadvantaged groups and enhances assessment robustness under data perturbations.

Decompose ML model arbitrariness into epistemic and aleatoric componentsEvaluate data and model impact on epistemic and aleatoric instabilityPropose stable model selection with epistemic and aleatoric criteria

A Bilevel Optimization Framework for Imbalanced Data Classification

Oct 15, 2024
KM
Karen Medlin
🏛️ University of North Carolina at Chapel Hill | Argonne National Laboratory

Conventional resampling methods for class-imbalanced classification suffer from inherent limitations—oversampling introduces noise and boundary ambiguity, while undersampling discards informative majority-class samples, leading to information loss and underfitting. Method: This paper proposes an intelligent majority-class sample selection mechanism guided by model loss improvement. Its core innovation is a novel gradient-driven, differentiable bilevel optimization framework: the upper-level objective maximizes generalization performance, while the lower-level optimizes a differentiable loss improvement metric, enabling end-to-end, deterministic undersampling. Contribution/Results: By directly selecting discriminative majority-class instances—without synthesizing noisy minority samples—the method preserves data fidelity and decision boundary clarity. Evaluated on multiple benchmark datasets, it achieves up to a 10% absolute improvement in F1-score over state-of-the-art methods, significantly enhancing minority-class detection while maintaining majority-class accuracy.

Formulates bilevel optimization for optimal training subsetOptimizes majority data selection by improving model lossProposes undersampling method to avoid noise from synthetic data

Auditing Fairness by Betting

May 27, 2023
BC
Ben Chugg
🏛️ Carnegie Mellon University

To address the challenge of sustaining fairness auditing for deployed models under data policy drift, subgroup heterogeneity, and dynamic distributional shifts, this paper proposes the first dynamic fairness auditing framework tailored for streaming data. Methodologically, it innovatively adapts “testing by betting”—a game-theoretic statistical paradigm—into fairness monitoring, integrating anytime-valid inference with nonparametric, sample-size-agnostic sequential testing that adapts to time-varying sampling strategies. Unlike conventional batch-based approaches, our framework enables real-time, continuous fairness assessment without requiring prior knowledge of data distribution or fixed sample sizes. Experiments on three benchmark datasets demonstrate that the method achieves high detection sensitivity, low false positive rate, and strong robustness against concept drift and subgroup imbalance. These properties collectively enhance the practicality, timeliness, and deployability of fairness monitoring in real-world operational environments.

Audit fairness under probabilistic and changing data policiesDevelop sequential methods for continuous fairness monitoringHandle distribution shifts in model or population

Achieving fairness with a simple ridge penalty

May 18, 2021
MS
M. Scutari
🏛️ Istituto Dalle Molle di Studi sull’Intelligenza Artificiale (IDSIA) | London School of Economics | University of Oxford | UBS

This work addresses the problem of user-controllable fairness tuning in regression models. We propose a general fairness framework built upon ridge regression penalization. Its core innovation lies in explicitly incorporating fairness constraints into the ridge parameter selection process—achieving an adjustable trade-off between fairness and predictive performance via regularization with respect to sensitive attributes—and deriving partial closed-form solutions. The method supports multiple fairness definitions (e.g., demographic parity, equalized odds), extends to generalized linear models and kernelized settings, and corrects systematic experimental biases present in prior studies. Extensive experiments on six benchmark datasets demonstrate that, at comparable fairness levels, our approach significantly outperforms mainstream baselines—including Komiyama et al. and Zafar et al.—while simultaneously improving both goodness-of-fit and prediction accuracy.

Controlling sensitive attribute effects using ridge penalty selectionEstimating regression models with user-defined fairness levelsExtending fair regression to various models and fairness definitions

Adapting to Misspecification

May 23, 2023
TB
Timothy B. Armstrong
🏛️ USC | UC Berkeley | NBER | UCL | CEMFI

This paper addresses the trade-off between robustness and efficiency under model misspecification, proposing an adaptive estimation framework that does not require a pre-specified upper bound on bias. The core challenge is to construct an estimator whose worst-case risk—relative to an oracle knowing the true bias bound—is minimized. Methodologically, we formulate an adaptive shrinkage estimator via weighted convex minimax optimization, calibrated against the oracle risk, and develop a lookup-table-based fast algorithm. Theoretically, our approach departs from conventional hypothesis-testing paradigms and achieves, for the first time, direct adaptation to the degree of misspecification. Empirically, the method substantially improves estimation accuracy and robustness across multiple canonical studies, offering both strong theoretical guarantees and practical computational efficiency.

Adapting to unknown bias bounds in restricted estimatorsBalancing robustness and efficiency in parameter estimationSolving weighted convex minimax for adaptive estimation

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Evolved SampleWeights for Bias Mitigation: Effectiveness Depends on Optimization Objectives

Nov 25, 2025
AK
Anil K. Saini
🏛️ Cedars-Sinai Medical Center | University of California, Los Angeles

This paper addresses the problem of biased predictions by machine learning models against marginalized groups in real-world data. To jointly optimize predictive accuracy and fairness, we propose a genetic algorithm-based sample weighting method that evolves instance-level weights through multi-objective optimization. Unlike conventional uniform or feature-driven weighting schemes, our approach simultaneously optimizes accuracy, AUC, demographic parity difference, and subgroup false negative rate. Extensive experiments on 11 publicly available datasets—including two healthcare benchmarks—demonstrate that the evolved weights substantially improve the fairness–performance trade-off. The most significant gains are achieved when jointly optimizing for accuracy and demographic parity difference, confirming the method’s effectiveness and generalizability in practical, high-stakes domains.

Comparing evolved vs computed sample weights for bias reductionEvaluating fairness-performance tradeoffs across eleven public datasetsMitigating biased predictions in ML models affecting marginalized communities

This work addresses the apparent trade-off between prediction accuracy and group fairness commonly observed in existing literature, which often stems from distorted subgroup proportions in training data and leads to misleading assessments of fairness interventions. The authors propose a two-stage paradigm under settings where subgroup distributions are stable but their prevalence is shifted: first, apply a finite-sample optimal shrinkage reweighting method to correct representation bias, then evaluate fairness interventions. This approach integrates importance weighting with shrinkage estimation to decouple spurious trade-offs from genuine ones. Experiments on real-world benchmarks such as Adult and COMPAS, as well as synthetic datasets, validate the theoretical claims and accurately recover the true Pareto frontier between fairness and utility.

fairness-accuracy tradeofffinite-sample correctiongroup fairness

Weight a Minute: Understanding Variability in PATE Estimates Across Target Populations

Nov 30, 2025
WS
William Stewart
🏛️ Duke University School of Medicine | Johns Hopkins Bloomberg School of Public Health

Clinical studies often exhibit systematic discrepancies between the sample and the target population, inducing extrapolation bias. This paper investigates the robustness of inverse probability sampling weighting (IPSW) under misspecified target populations: even with correctly specified models, IPSW yields systematic bias if the selected target population fails to represent the actual inferential population. Through simulation experiments across diverse real-world covariate distributions and selection mechanisms, we quantify how deviation of the target population from representativeness affects the estimation of the population average treatment effect (PATE). Results demonstrate that bias increases monotonically with the degree of target-population mismatch—and in severe cases, IPSW performs worse than unweighted estimation. To our knowledge, this is the first systematic study revealing that target-population selection constitutes a foundational design decision in causal extrapolation, whose impact can surpass that of model misspecification—providing a critical methodological warning for causal inference beyond the study sample.

Evaluates bias in PATE estimates when target populations differ from inference populations.Highlights critical need for appropriate target population selection to ensure valid generalization.Simulates IPSW performance across varying population representativeness and effect modification.

This work addresses the challenge that existing model evaluation methods often fail to reliably assess estimator quality in low-variance settings due to confounding between bias and variance or excessive sensitivity of statistical tests. To overcome this limitation, the authors propose a fault-tolerant evaluation framework that unifies bias and variance modeling through an adjustable tolerance parameter ε, enabling robust assessment of sample-efficient performance estimators within practically acceptable error margins. The framework integrates bias-variance analysis, fault-tolerant evaluation theory, and an adaptive ε-optimization algorithm, making it particularly well-suited for scenarios with low annotation costs. Experimental results demonstrate that the proposed approach provides a more comprehensive and reliable characterization of estimator behavior, significantly enhancing both the practical utility and stability of performance evaluation.

bias-variance tradeofffault-tolerant evaluationmodel performance estimation

This study addresses the interpretational ambiguity of weighted estimators when treatment effects are heterogeneous, as their validity hinges critically on the choice of weights. To tackle this issue, the authors propose an estimator that minimizes worst-case bias and construct confidence intervals that are uniformly valid over a broad class of weighting schemes. Their approach integrates minimax bias reduction, bounds from heterogeneity-robust sensitivity analysis, and theoretical characterizations of discrepancies among weighted estimators, thereby enabling inference robust to weight uncertainty. Empirical applications illustrate the method’s utility: in Lakdawala et al.’s event study, findings remain robust across a wide range of weights, whereas in the Project STAR experiment, conclusions prove sensitive even to minor perturbations of baseline weights.

effect heterogeneityinferencepolicy interpretation

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