train with sampling weights

This study investigates how to achieve valid statistical inference when combining machine learning predictions with a small number of gold-standard labels, and clarifies its connections to classical survey sampling methods. Through theoretical analysis, it establishes for the first time the algebraic equivalence between the core estimator in prediction-powered inference (PPI) and model-assisted estimators from the 1970s—such as difference and generalized regression (GREG) estimators. The work systematically compares these approaches in terms of inferential paradigms, use of unlabeled data, and subgroup estimation error, delineating which aspects of PPI are inherited versus novel. It further proposes directions for integrating insights from both fields. These results ground PPI in classical survey sampling theory while simultaneously expanding the toolkit available for modern, nonstandard estimators within the survey sampling framework.

To address nonignorable nonresponse in sample surveys, this paper extends model-assisted estimation to the missing-at-random (MAR) framework. We propose a calibratable inverse-probability weighting (IPW) method that reweights sampled units in a second stage to compensate for nonrespondents, and systematically construct a Horvitz–Thompson-type adjusted estimator. Theoretically, we establish its asymptotic design-unbiasedness and design-consistency, derive a closed-form asymptotic variance expression, and provide a consistent variance estimator. Monte Carlo simulations demonstrate that the proposed estimator significantly outperforms the conventional Horvitz–Thompson estimator under diverse nonresponse mechanisms. Our key contributions are: (i) the first systematic adaptation of model-assisted estimation to the MAR setting; and (ii) a novel IPW weighting scheme that simultaneously satisfies calibration constraints and enjoys rigorous asymptotic properties—namely, design-consistency, asymptotic normality, and consistent variance estimation.

This study addresses the challenge of achieving safe and efficient unbiased estimation using non-probability data in the absence of a controlled selection mechanism. The authors propose Model-Assisted Data Integration (MADI), a sampling strategy that integrates non-probability data with carefully designed probability samples and leverages arbitrary machine learning models to construct design-unbiased point estimators alongside corresponding unbiased variance estimators. MADI establishes, for the first time, a general framework for design-unbiased inference based on any machine learning model, offering both theoretical rigor and practical feasibility—particularly suited for high-frequency production environments in official statistics. Empirical results demonstrate that MADI substantially reduces estimation variance compared to traditional survey estimators, confirming its effectiveness and superiority.

This paper addresses the “weak paradox” of inverse probability weighting (IPW) estimators—highlighted by Basu (1988) and Wasserman (2004)—in survey sampling, causal inference, and Bayesian evidence estimation. We propose two Bayesian remedies: an IPW correction framework based on Bayesian sieves (binning plus nonparametric smoothing) and one built upon conjugate hierarchical models. We provide the first systematic theoretical comparison, proving posterior consistency for both under MCAR, with substantially weaker assumptions on inclusion probabilities than classical IPW. Monte Carlo simulations demonstrate that both estimators drastically reduce mean squared error in Wasserman’s counterexample. Our results extend IPW robustness to Bayesian evidence estimation and average treatment effect evaluation, offering a novel paradigm for weighted inference in high-dimensional, sparse, or non-regular settings.

This work addresses the challenge of risk prediction when acquiring true outcomes is prohibitively expensive, allowing labels for only a subset of samples. The authors propose a surrogate-assisted optimal sampling framework that, under a fixed annotation budget, leverages covariates, surrogate variables, and an initial estimator to construct a sampling strategy minimizing the expected out-of-sample cross-entropy loss. Coupled with an inverse probability weighted cross-entropy estimator for model training, this approach achieves—without requiring access to true responses during design—theoretically optimal sampling. It uniquely guarantees predictive optimality, robustness to surrogate misspecification, and stability in settings with rare outcomes. Both theoretical analysis and empirical experiments demonstrate that the method significantly outperforms existing approaches, particularly when the surrogate is imperfect or the event of interest is rare.

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.

This study addresses the issue of variance inflation in regression models under complex survey designs, which often arises from unnecessary variability in sampling weights. The authors propose a novel approach that, for the first time, integrates stabilized weights with generalized raking within a two-stage sampling framework, leveraging auxiliary covariate information to effectively reduce extraneous weight variation. This method substantially enhances the efficiency of design-based estimators while remaining compatible with standard statistical software. Simulation studies demonstrate that, under typical two-stage survey designs, the proposed estimator achieves markedly higher precision compared to existing methods. The approach has been successfully applied to a large-scale multinational study of Kaposi’s sarcoma, illustrating its practical utility and robustness in real-world settings.