missing-data imputation

This study addresses the challenge of partially missing data following intercurrent events in clinical trials, where conventional methods such as last observation carried forward yield large standard errors and convergence difficulties, while reference-based imputation relies on strong assumptions that may introduce bias. The authors propose the first extension of Bayesian causal models (BCM) to this setting, leveraging a fully Bayesian framework that integrates observed data with flexible prior information to achieve robust imputation. A key innovation is the introduction of an adjustable prior variance, which enhances estimation stability—particularly under data sparsity—and demonstrably outperforms existing approaches. Simulation studies show that, compared to traditional strategies, the proposed method substantially reduces standard errors and yields more stable estimates of treatment effects, especially when data are scarce.

Missing data pose a shared challenge in signal processing (SP) and machine learning (ML), yet existing approaches lack a unified treatment across imputation, parameter estimation under missingness, and prediction with incomplete data. Method: We propose the first integrated framework for SP/ML fusion, structured around a novel “task-driven—missingness mechanism modeling—method coordination” paradigm. It explicitly models informative missingness (MNAR) and synergistically unifies statistical imputation, matrix/tensor completion, probabilistic graphical models, deep generative models, and robust optimization. Contribution/Results: Evaluated on diverse real-world datasets spanning multiple domains, our framework yields a reusable conceptual architecture and practical guidelines. It achieves statistically significant improvements over state-of-the-art methods in accuracy, robustness to missingness patterns, and interpretability—particularly under MNAR—thereby advancing principled, generalizable missing-data handling in SP and ML.

Current evaluation of medical time-series imputation models relies heavily on the random missingness assumption, overlooking clinically prevalent non-random, structured missingness patterns—leading to assessments that poorly reflect real-world clinical utility. Method: Leveraging the PhysioNet Challenge 2012 dataset, we systematically benchmark 11 state-of-the-art imputation methods—including RNN-, GAN-, and Transformer-based approaches—and introduce a clinically informed masking strategy to jointly evaluate imputation accuracy and downstream mortality prediction performance. Contributions/Results: (1) We provide the first empirical evidence that imputation accuracy does not necessarily correlate with clinical prediction AUC; several high-accuracy models fail to improve—or even degrade—mortality prediction; (2) RNN-based models demonstrate superior robustness under structured missingness; (3) Optimized clinical masking improves mortality prediction AUC by up to 3.2%. This work shifts imputation evaluation from a purely technical paradigm toward one grounded in clinical utility.

This work addresses the lack of a unified theoretical framework for handling missing data, particularly under missing-not-at-random (MNAR) mechanisms where existing methods often fail to ensure consistent prediction. The authors propose a novel framework that explicitly distinguishes between two prediction objectives—depending on whether the observation indicators of variables are utilized—and introduces a fine-grained classification of missingness mechanisms accordingly. Building on this distinction, they establish conditions weaker than missing-at-random (MAR) under which consistent prediction remains achievable. By integrating probabilistic modeling, pattern-wise submodeling, and unconditional imputation, the framework supports a comprehensive prediction theory spanning model development, validation, and deployment. Empirical evaluations on both synthetic data and a real-world emergency trauma prediction task demonstrate that the proposed approach consistently achieves optimal predictive performance across diverse missingness mechanisms, thereby overcoming the limitations of conventional methods reliant on the MAR assumption.

Existing variable selection methods struggle to control the false discovery rate (FDR) under missing data, while model-X knockoffs—though theoretically guaranteed to control FDR—cannot directly accommodate missing values. This work establishes, for the first time, the theoretical FDR controllability of knockoffs in the presence of missing data. We propose three novel paradigms: (i) posterior sampling-based imputation and knockoff reuse, (ii) knockoff generation restricted to observed variables only, and (iii) joint latent-variable imputation and knockoff construction. Our approaches integrate Bayesian posterior sampling, univariate imputation, and latent-variable modeling, and we rigorously prove that they satisfy FDR ≤ α under standard assumptions. Extensive experiments demonstrate precise FDR control across diverse missingness mechanisms (MCAR, MAR, MNAR), variable correlation structures, and sample sizes, while achieving high statistical power and substantially reduced computational complexity compared to existing alternatives.

This work addresses the degradation of model generalization caused by partially observed data, such as missing features or modalities. From the perspective of neural network distance, it provides a theoretical analysis of Measure Consistency Regularization (MCR), for the first time revealing the mechanism by which MCR enhances both data imputation quality and generalization performance. The study rigorously establishes the conditions under which MCR’s generalization advantage holds. Building on these insights, the authors propose a duality-gap-based early stopping strategy that preserves MCR’s benefits while mitigating overfitting. Extensive experiments across diverse real-world multimodal datasets and network architectures demonstrate the effectiveness and broad applicability of the proposed approach.

This work addresses semi-supervised classification under informative label missingness—where the missingness mechanism depends on features or class labels. To overcome the limitation of conventional semi-supervised learning (SSL) methods, which ignore information embedded in the missingness mechanism, we propose a likelihood-based framework grounded in finite mixture models that explicitly models the label missingness process and jointly optimizes labeled and unlabeled data via the EM algorithm. Theoretical analysis shows that, under informative missingness, our approach achieves lower asymptotic expected error than supervised learning using only fully labeled data. Empirical results demonstrate substantial accuracy gains in settings with moderate class overlap and sparse labeling. To our knowledge, this is the first work to systematically reveal and exploit the statistical information carried by the missingness indicator within a unified likelihood inference framework, thereby bridging statistical missing-data modeling and semi-supervised learning.

This study systematically investigates how missingness mechanisms, missing rates, missingness locations, and sample sizes jointly affect the accuracy and identifiability of average treatment effect (ATE) estimation under time-varying confounding. Through simulation, it compares the performance of complete-case analysis, stratified hot-deck imputation, single-model imputation, and multiple imputation by chained equations (MICE) combined with propensity score weighting, offering the first comprehensive assessment of their interactive effects. The results demonstrate that multiple imputation substantially reduces bias and improves confidence interval coverage across most scenarios. Crucially, the missingness mechanism emerges as a key determinant of estimator performance: missing not at random (MNAR) conditions, high missing rates, or small sample sizes frequently violate the positivity assumption, thereby undermining estimation validity.

This work addresses the systematic gradient bias induced by imputation in stochastic gradient descent (SGD) when covariates are missing, which compromises both optimization and estimation accuracy. The authors propose a debiased SGD method based on Richardson extrapolation that deliberately introduces controlled missingness into the originally incomplete data and combines stochastic gradients computed under multiple missingness levels to cancel the leading bias term. Innovatively “adding missingness to reduce bias,” this approach is the first to apply Richardson extrapolation to SGD under missing data, offering model-agnosticism and computational efficiency. Theoretically, a single-step extrapolation reduces the gradient bias from O(|p|) to O(|p|²), where p denotes the missingness mechanism. Experiments demonstrate substantial improvements in optimization and estimation performance across various generalized linear models, with compatibility to mainstream imputation methods such as MICE.

This paper studies the online linear contextual bandit problem under partial context observability and proposes PULSE-UCB, the first algorithm to leverage surrogate features from large-scale pretrained models for missing-feature imputation. The method integrates pretrained-feature imputation, UCB-style online decision-making, and error analysis under a Hölder smoothness assumption. Theoretical contributions include: (1) a precise decomposition of the regret bound into a standard linear bandit term and an additional term governed by pretrained model quality; (2) attainment of a near-optimal regret upper bound under i.i.d. contexts, accompanied by a matching lower bound; and (3) quantification of how prediction uncertainty impacts decision performance, explicitly characterizing the auxiliary data scale required to improve downstream learning. Experiments demonstrate the efficacy of pretrained priors in nonstationary, partially observable settings.