Learning with Missing Data

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Overview

The field studies how to use incomplete observations without introducing misleading estimates or discarding useful examples, especially when the chance of missingness depends on the data itself. Approaches range from likelihood-based methods, EM, and multiple imputation to Bayesian and diffusion generative models, masked transformers, and predictors that encode missingness patterns directly. Work spans tabular data, irregular time series, clinical records, graphs, and multimodal settings, with theory addressing identifiability, sample complexity, and uncertainty under MCAR, MAR, and MNAR mechanisms. A central tension is that missingness can be both a useful signal and a source of bias: methods must match the missingness process and downstream task, while evaluations increasingly test realistic patterns and train–test shifts rather than reconstruction error alone.

Latest papers

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120 papers22 papers in the last four weeks, up 22% on the four weeks before. 0.1% of all new papers.

Apr 13, 2026

Cost-optimal Sequential Testing via Doubly Robust Q-learning

Clinical decision-making often involves selecting tests that are costly, invasive, or time-consuming, motivating individualized, sequential strategies for what to measure and when to stop ascertaining. We study the problem of learning cost-optimal sequential decision policies from retrospective data, where test availability depends on prior results, inducing informative missingness. Under a sequential missing-at-random mechanism, we develop a doubly robust Q-learning framework for estimating optimal policies. The method introduces path-specific inverse probability weights that account for heterogeneous test trajectories and satisfy a normalization property conditional on the observed history. By combining these weights with auxiliary contrast models, we construct orthogonal pseudo-outcomes that enable unbiased policy learning when either the acquisition model or the contrast model is correctly specified. We establish oracle inequalities for the stage-wise contrast estimators, along with convergence rates, regret bounds, and misclassification rates for the learned policy. Simulations demonstrate improved cost-adjusted performance over weighted and complete-case baselines, and an application to a prostate cancer cohort study illustrates how the method reduces testing cost without compromising predictive accuracy.

Doudou Zhou, Yiran Zhang, Dian Jin +3

Department of Statistics and Data Science, National University of Singapore · Public Health Sciences Division, Fred Hutch · Department of Biomedical Data Science, Stanford University School of Medicine +1

Q-LearningCost-Sensitive LearningLearning with Missing DataDoubly Robust Estimation
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Apr 6, 2026

Generative Modeling under Non-Monotone MAR Missingness via Approximate Wasserstein Gradient Flows

The prevalence of missing values in data science poses a substantial risk to any further analyses. Despite a wealth of research, principled nonparametric methods to deal with general non-monotone missingness are still scarce. Instead, ad-hoc imputation methods are often used, for which it remains unclear whether the correct distribution can be recovered. In this paper, we propose FLOWGEM, a principled iterative method for generating a complete dataset from a dataset with values Missing at Random (MAR). Motivated by convergence results of the ignoring maximum likelihood estimator, our approach minimizes the expected Kullback-Leibler (KL) divergence between the observed data distribution and the distribution of the generated sample over different missingness patterns. To minimize the KL divergence, we employ a discretized particle evolution of the corresponding Wasserstein Gradient Flow, where the velocity field is approximated using a local linear estimator of the density ratio. This construction yields a data generation scheme that iteratively transports an initial particle ensemble toward the target distribution. Simulation studies and real-data benchmarks demonstrate that FLOWGEM achieves state-of-the-art performance across a range of settings, including the challenging case of non-monotone MAR mechanisms. Together, these results position FLOWGEM as a principled and practical alternative to existing imputation methods, and a decisive step towards closing the gap between theoretical rigor and empirical performance.

Gitte Kremling, Jeffrey Näf, Johannes Lederer

Department of Mathematics, University of Hamburg · Research Institute for Statistics and Information Science, University of Geneva

Learning with Missing DataIncomplete Data ImputationGenerative Modeling
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Apr 5, 2026

Uncertainty-Aware Foundation Models for Clinical Data

Healthcare foundation models have largely followed paradigms from natural language processing and computer vision, emphasizing large scale pretraining and deterministic representations over heterogeneous clinical data. However, clinical observations are inherently incomplete, reflecting sparse, irregular, and modality dependent measurements of an underlying physiologic state. In this work, we propose a framework for uncertainty aware foundation modeling that represents each patient not as a point embedding, but as a distribution over plausible latent states. By learning set valued representations and enforcing consistency across partial views of the same patient, the model captures what is invariantly inferable while explicitly encoding epistemic uncertainty. We integrate this formulation with multimodal encoders and scalable self supervised objectives, combining reconstruction, contrastive alignment, and distributional regularization. Across diverse clinical tasks, our approach improves predictive performance, robustness under missing data, and uncertainty calibration relative to strong baselines. These results suggest that modeling what is not observed rather than only what is constitutes a critical inductive bias for healthcare foundation models.

Qian Zhou, Yuanyun Zhang, Shi Li

University of the Chinese Academy of Sciences · Columbia University

Epistemic UncertaintyMultimodal Foundation ModelsLearning with Missing DataUncertainty CalibrationUncertainty-Aware Multimodal Fusion
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Apr 5, 2026

Incomplete Multi-View Multi-Label Classification via Shared Codebook and Fused-Teacher Self-Distillation

Although multi-view multi-label learning has been extensively studied, research on the dual-missing scenario, where both views and labels are incomplete, remains largely unexplored. Existing methods mainly rely on contrastive learning or information bottleneck theory to learn consistent representations under missing-view conditions, but loss-based alignment without explicit structural constraints limits the ability to capture stable and discriminative shared semantics. To address this issue, we introduce a more structured mechanism for consistent representation learning: we learn discrete consistent representations through a multi-view shared codebook and cross-view reconstruction, which naturally align different views within the limited shared codebook embeddings and reduce feature redundancy. At the decision level, we design a weight estimation method that evaluates the ability of each view to preserve label correlation structures, assigning weights accordingly to enhance the quality of the fused prediction. In addition, we introduce a fused-teacher self-distillation framework, where the fused prediction guides the training of view-specific classifiers and feeds the global knowledge back into the single-view branches, thereby enhancing the generalization ability of the model under missing-label conditions. The effectiveness of our proposed method is thoroughly demonstrated through extensive comparative experiments with advanced methods on five benchmark datasets. Code is available at https://github.com/xuy11/SCSD.

Xu Yan, Jun Yin, Shiliang Sun +1

College of Information Engineering, Shanghai Maritime University · School of Automation and Intelligent Sensing, Shanghai Jiao Tong University

Multi-Label ClassificationMulti-View LearningLearning with Missing DataMulti-View Consistency
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Mar 31, 2026

DiSGMM: A Method for Time-varying Microscopic Weight Completion on Road Networks

Microscopic road-network weights represent fine-grained, time-varying traffic conditions obtained from individual vehicles. An example is travel speeds associated with road segments as vehicles traverse them. These weights support tasks including traffic microsimulation and vehicle routing with reliability guarantees. We study the problem of time-varying microscopic weight completion. During a time slot, the available weights typically cover only some road segments. Weight completion recovers distributions for the weights of every road segment at the current time slot. This problem involves two challenges: (i) contending with two layers of sparsity, where weights are missing at both the network layer (many road segments lack weights) and the segment layer (a segment may have insufficient weights to enable accurate distribution estimation); and (ii) achieving a weight distribution representation that is closed-form and can capture complex conditions flexibly, including heavy tails and multiple clusters. To address these challenges, we propose DiSGMM that combines sparsity-aware embeddings with spatiotemporal modeling to leverage sparse known weights alongside learned segment properties and long-range correlations for distribution estimation. DiSGMM represents distributions of microscopic weights as learnable Gaussian mixture models, providing closed-form distributions capable of capturing complex conditions flexibly. Experiments on two real-world datasets show that DiSGMM can outperform state-of-the-art methods.

Yan Lin, Jilin Hu, Shengnan Guo +3

Aalborg University · East China Normal University · Beijing Jiaotong University

Learning with Missing DataConditional Distribution EstimationTraffic Flow Estimation
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Mar 22, 2026

Amortized Variational Inference for Logistic Regression with Missing Covariates

Missing covariate data pose a significant challenge to statistical inference and machine learning, particularly for classification tasks like logistic regression. Classical iterative approaches (EM, multiple imputation) are often computationally intensive, sensitive to high missingness rates, and limited in uncertainty propagation. Recent deep generative models based on VAEs show promise but rely on complex latent representations. We propose Amortized Variational Inference for Logistic Regression (AV-LR), a unified end-to-end framework for binary logistic regression with missing covariates. AV-LR integrates a probabilistic generative model with a simple amortized inference network, trained jointly by maximizing the evidence lower bound. Unlike competing methods, AV-LR performs inference directly in the space of missing data without additional latent variables, using a single inference network and a linear layer that jointly estimate regression parameters and the missingness mechanism. AV-LR achieves estimation accuracy comparable to or better than state-of-the-art EM-like algorithms, with significantly lower computational cost. It naturally extends to missing-not-at-random settings by explicitly modeling the missingness mechanism. Empirical results on synthetic and real-world datasets confirm its effectiveness and efficiency across various missing-data scenarios.

M. Cherifi, Aude Sportisse, Xujia Zhu +2

Lab. Traitement du signal, Ecole Militaire Polytechnique, BP 17 Bordj El Bahri, Algeria · Lab. d’Informatique de Grenoble, CNRS, France · University of Paris Saclay, CNRS, CentraleSupelec, Laboratoire des signaux et systèmes, 91190, Gif-sur-Yvette, France

Learning with Missing DataLogistic RegressionVariational InferenceIncomplete Data ImputationAmortized Inference
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Mar 17, 2026

High-dimensional estimation with missing data: Statistical and computational limits

We consider computationally-efficient estimation of population parameters when observations are subject to missing data. In particular, we consider estimation under the realizable contamination model of missing data in which an εε fraction of the observations are subject to an arbitrary (and unknown) missing not at random (MNAR) mechanism. When the true data is Gaussian, we provide evidence towards statistical-computational gaps in several problems. For mean estimation in ℓ2\ell_2 norm, we show that in order to obtain error at most ρρ, for any constant contamination ε∈(0,1)ε\in (0, 1), (roughly) n≳de1/ρ2n \gtrsim d e^{1/ρ^2} samples are necessary and that there is a computationally-inefficient algorithm which achieves this error. On the other hand, we show that any computationally-efficient method within certain popular families of algorithms requires a much larger sample complexity of (roughly) n≳d1/ρ2n \gtrsim d^{1/ρ^2} and that there exists a polynomial time algorithm based on sum-of-squares which (nearly) achieves this lower bound. For covariance estimation in relative operator norm, we show that a parallel development holds. Finally, we turn to linear regression with missing observations and show that such a gap does not persist. Indeed, in this setting we show that minimizing a simple, strongly convex empirical risk nearly achieves the information-theoretic lower bound in polynomial time.

Kabir Aladin Verchand, Ankit Pensia, Saminul Haque +1

Department of Data Sciences and Operations, University of Southern California · Department of Statistics and Data Science, Carnegie Mellon University · Department of Computer Science, Stanford University

Learning with Missing DataCovariance EstimationLinear Regression
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Mar 16, 2026

Predictive Uncertainty in Short-Term PV Forecasting under Missing Data: A Multiple Imputation Approach

Missing values are common in photovoltaic (PV) power data, yet the uncertainty they induce is not propagated into predictive distributions. We develop a framework that incorporates missing-data uncertainty into short-term PV forecasting by combining stochastic multiple imputation with Rubin's rule. The approach is model-agnostic and can be integrated with standard machine-learning predictors. Empirical results show that ignoring missing-data uncertainty leads to overly narrow prediction intervals. Accounting for this uncertainty improves interval calibration while maintaining comparable point prediction accuracy. These results demonstrate the importance of propagating imputation uncertainty in data-driven PV forecasting.

Parastoo Pashmchi, Jérôme Benoit, Motonobu Kanagawa

SAP Labs France, Mougins, France · EURECOM, Biot, France

Solar Power ForecastingUncertainty PropagationUncertainty CalibrationProbabilistic ForecastingLearning with Missing Data
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Mar 16, 2026

Learning from Limited and Incomplete Data: A Multimodal Framework for Predicting Pathological Response in NSCLC

Major pathological response (pR) following neoadjuvant therapy is a clinically meaningful endpoint in non-small cell lung cancer, strongly associated with improved survival. However, accurate preoperative prediction of pR remains challenging, particularly in real-world clinical settings characterized by limited data availability and incomplete clinical profiles. In this study, we propose a multimodal deep learning framework designed to address these constraints by integrating foundation model-based CT feature extraction with a missing-aware architecture for clinical variables. This approach enables robust learning from small cohorts while explicitly modeling missing clinical information, without relying on conventional imputation strategies. A weighted fusion mechanism is employed to leverage the complementary contributions of imaging and clinical modalities, yielding a multimodal model that consistently outperforms both unimodal imaging and clinical baselines. These findings underscore the added value of integrating heterogeneous data sources and highlight the potential of multimodal, missing-aware systems to support pR prediction under realistic clinical conditions.

Alice Natalina Caragliano, Giulia Farina, Fatih Aksu +10

Unit of Artificial Intelligence and Computer Systems, Department of Engineering, Università Campus Bio-Medico di Roma, Rome, Italy · Fondazione Policlinico Universitario Campus Bio-Medico, Rome, Italy · Department of Medicine and Surgery, Università Campus Bio-Medico di Roma, Rome, Italy +1

Clinical Outcome PredictionClinical PredictionMultimodal LearningLearning with Missing Data
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Mar 12, 2026

Multi-Station WiFi CSI Sensing Framework Robust to Station-wise Feature Missingness and Limited Labeled Data

We propose a WiFi Channel State Information (CSI) sensing framework for multi-station deployments that addresses two fundamental challenges in practical CSI sensing: station-wise feature missingness and limited labeled data. Feature missingness is commonly handled by resampling unevenly spaced CSI measurements or by reconstructing missing samples, while label scarcity is mitigated by data augmentation or self-supervised representation learning. However, these techniques are typically developed in isolation and do not jointly address long-term, structured station unavailability together with label scarcity. To bridge this gap, we explicitly incorporate station unavailability into both representation learning and downstream model training. Specifically, we adapt cross-modal self-supervised learning (CroSSL), a representation learning framework originally designed for time-series sensory data, to multi-station CSI sensing in order to learn representations that are inherently invariant to station-wise feature missingness from unlabeled data. Furthermore, we introduce Station-wise Masking Augmentation (SMA) during downstream model training, which exposes the model to realistic station unavailability patterns under limited labeled data. Our experiments show that neither missingness-invariant pre-training nor station-wise augmentation alone is sufficient; their combination is essential to achieve robust performance under both station-wise feature missingness and label scarcity. The proposed framework provides a practical and robust foundation for multi-station WiFi CSI sensing in real-world deployments.

Keita Kayano, Takayuki Nishio, Daiki Yoda +2

School of Engineering, Institute of Science Tokyo, 2-12-1 Ookayama, Tokyo, 152-8550, Japan · Wireless Systems R&D Department, Infrastructure Systems R&D Center, Corporate Laboratory, Toshiba Corporation, 1, Komukai Toshiba-cho, Saiwai-ku, Kawasaki 212-8582, JAPAN

Wi-Fi SensingLearning with Missing DataSelf-Supervised Time Series Representation LearningSelf-Supervised Learning
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Mar 11, 2026

Spatially Robust Inference with Predicted and Missing at Random Labels

When outcome data are expensive or onerous to collect, scientists increasingly substitute predictions from machine learning and AI models for unlabeled cases, a process which has consequences for downstream statistical inference. While recent methods provide valid uncertainty quantification under independent sampling, real-world applications involve missing at random (MAR) labeling and spatial dependence. For inference in this setting, we propose a doubly robust estimator with cross-fit nuisances. We show that cross-fitting induces fold-level correlation that distorts spatial variance estimators, producing unstable or overly conservative confidence intervals. To address this, we propose a jackknife spatial heteroscedasticity and autocorrelation consistent (HAC) variance correction that separates spatial dependence from fold-induced noise. Under standard identification and dependence conditions, the resulting intervals are asymptotically valid. Simulations and benchmark datasets show substantial improvement in finite-sample calibration, particularly under MAR labeling and clustered sampling.

Stephen Salerno, Zhenke Wu, Tyler McCormick

Fred Hutch Cancer Center · University of Michigan · University of Washington

Confidence Region EstimationLearning with Missing DataSemiparametric InferenceDoubly Robust Estimation
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Mar 5, 2026

Uniform Inductive Spatio-Temporal Kriging

Inductive spatio-temporal kriging infers signals at unobserved locations from observed sensors, but real-world observations are often incomplete and exhibit block-wise missingness caused by failures, interruptions, or maintenance. A common impute-then-krige pipeline suffers from objective mismatch: better reconstruction on observed sensors does not necessarily improve downstream kriging, and value-dependent imputation bias can be propagated to unobserved nodes. We propose UniSTOK, a plug-and-play framework for inductive spatio-temporal kriging under incomplete observations. We first introduce Reliability-guided Signal Regulation (RSR), which estimates entry-wise reliability from temporal continuity and spatial support, and uses it to regulate the input signals so that reliable observations are emphasized while long-gap or weakly supported entries are suppressed before spatial propagation. We further introduce Residual Bias Calibration (RBC), which estimates value-conditioned residual prototypes after the main predictor converges and learns context-correction amplitudes to adaptively calibrate systematic over- or under-estimation in final kriging predictions. Extensive experiments on real-world datasets show that UniSTOK consistently improves multiple kriging backbones.

Lewei Xie, Haoyu Zhang, Yulong Chen +3

City University of Hong Kong (Dongguan) · City University of Hong Kong

Spatiotemporal ForecastingLearning with Missing Data
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Mar 4, 2026

Mask-aware inference with State-Space Models

Many real-world computer vision tasks, such as depth completion, must handle inputs with arbitrarily shaped regions of missing or invalid data. For Convolutional Neural Networks (CNNs), Partial Convolutions solved this by a mask-aware re-normalization conditioned only on valid pixels. Recently, State Space Models (SSMs) like Mamba have emerged, offering high performance with linear complexity. However, these architectures lack an inherent mechanism for handling such arbitrarily shaped invalid data at inference time. To bridge this gap, we introduce Partial Vision Mamba (PVM), a novel architectural component that ports the principles of partial operations to the Mamba backbone. We also define a series of rules to design architectures using PVM. We show the efficacy and generalizability of our approach in the tasks of depth completion, image inpainting, and classification with invalid data.

Ignasi Mas, Ramon Morros, Javier-Ruiz Hidalgo +1

Visual SSMsState Space ModelsLearning with Missing Data
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Mar 2, 2026

MIRAGE: Knowledge Graph-Guided Cross-Cohort MRI Synthesis for Alzheimer's Disease Prediction

Reliable Alzheimer's disease (AD) diagnosis increasingly relies on multimodal assessments combining structural Magnetic Resonance Imaging (MRI) and Electronic Health Records (EHR). However, deploying these models is bottlenecked by modality missingness, as MRI scans are expensive and frequently unavailable in many patient cohorts. Furthermore, synthesizing de novo 3D anatomical scans from sparse, high-dimensional tabular records is technically challenging and poses severe clinical risks. To address this, we introduce MIRAGE, a novel framework that reframes the missing-MRI problem as an anatomy-guided cross-modal latent distillation task. First, MIRAGE leverages a Biomedical Knowledge Graph (KG) and Graph Attention Networks to map heterogeneous EHR variables into a unified embedding space that can be propagated from cohorts with real MRIs to cohorts without them. To bridge the semantic gap and enforce physical spatial awareness, we employ a frozen pre-trained 3D U-Net decoder strictly as an auxiliary regularization engine. Supported by a novel cohort-aggregated skip feature compensation strategy, this decoder acts as a rigorous structural penalty, forcing 1D latent representations to encode biologically plausible, macro-level pathological semantics. By exclusively utilizing this distilled "diagnostic-surrogate" representation during inference, MIRAGE completely bypasses computationally expensive 3D voxel reconstruction. Experiments demonstrate that our framework successfully bridges the missing-modality gap, improving the AD classification rate by 13% compared to unimodal baselines in cohorts without real MRIs.

Guanchen Wu, Zhe Huang, Yuzhang Xie +6

Emory University, Atlanta, USA · Cornell University, New York, USA

Alzheimer's Disease ClassificationLearning with Missing DataCross-Modal Representation LearningCross-Modal Knowledge Distillation
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Feb 26, 2026

Active Value Querying to Minimize Additive Error in Subadditive Set Function Learning

Subadditive set functions play a pivotal role in computational economics (especially in combinatorial auctions), combinatorial optimization or artificial intelligence applications such as interpretable machine learning. However, specifying a set function requires assigning values to an exponentially large number of subsets in general, a task that is often resource-intensive in practice, particularly when the values derive from external sources such as retraining of machine learning models. A~simple omission of certain values introduces ambiguity that becomes even more significant when the incomplete set function has to be further optimized over. Motivated by the well-known result about inapproximability of subadditive functions using deterministic value queries with respect to a multiplicative error, we study a problem of approximating an unknown subadditive (or a subclass of thereof) set function with respect to an additive error -- i. e., we aim to efficiently close the distance between minimal and maximal completions. Our contributions are threefold: (i) a thorough exploration of minimal and maximal completions of different classes of set functions with missing values and an analysis of their resulting distance; (ii) the development of methods to minimize this distance over classes of set functions with a known prior, achieved by disclosing values of additional subsets in both offline and online manner; and (iii) empirical demonstrations of the algorithms' performance in practical scenarios.

Martin Černý, David Sychrovský, Filip Úradník +1

Charles University, Prague, Czechia · Columbia University, New York, USA

Learning with Missing DataActive Learning
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Feb 26, 2026

Robust Human Trajectory Prediction via Self-Supervised Skeleton Representation Learning

Human trajectory prediction plays a crucial role in applications such as autonomous navigation and video surveillance. While recent works have explored the integration of human skeleton sequences to complement trajectory information, skeleton data in real-world environments often suffer from missing joints caused by occlusions. These disturbances significantly degrade prediction accuracy, indicating the need for more robust skeleton representations. We propose a robust trajectory prediction method that incorporates a self-supervised skeleton representation model pretrained with masked autoencoding. Experimental results in occlusion-prone scenarios show that our method improves robustness to missing skeletal data without sacrificing prediction accuracy, and consistently outperforms baseline models in clean-to-moderate missingness regimes.

Taishu Arashima, Hiroshi Kera, Kazuhiko Kawamoto

Chiba University

Human Trajectory PredictionTrajectory PredictionLearning with Missing DataRepresentation Learning
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Feb 24, 2026

T1: One-to-One Channel-Head Binding for Multivariate Time-Series Imputation

Imputing missing values in multivariate time series remains challenging, especially under diverse missing patterns and heavy missingness. Existing methods suffer from suboptimal performance as corrupted temporal features hinder effective cross-variable information transfer, amplifying reconstruction errors. Robust imputation requires both extracting temporal patterns from sparse observations within each variable and selectively transferring information across variables--yet current approaches excel at one while compromising the other. We introduce T1 (Time series imputation with 1-to-1 channel-head binding), a CNN-Transformer hybrid architecture that achieves robust imputation through Channel-Head Binding--a mechanism creating one-to-one correspondence between CNN channels and attention heads. This design enables selective information transfer: when missingness corrupts certain temporal patterns, their corresponding attention pathways adaptively down-weight based on remaining observable patterns while preserving reliable cross-variable connections through unaffected channels. Experiments on 11 benchmark datasets demonstrate that T1 achieves state-of-the-art performance, reducing MSE by 46% on average compared to the second-best baseline, with particularly strong gains under extreme sparsity (70% missing ratio). The model generalizes to unseen missing patterns without retraining and uses a consistent hyperparameter configuration across all datasets. The code is available at https://github.com/Oppenheimerdinger/T1.

Dongik Park, Hyunwoo Ryu, Suahn Bae +2

Graduate School of Data Science, Seoul National University

Time Series ImputationLearning with Missing Data
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Feb 24, 2026

Amortized Bayesian inference for actigraph time sheet data from mobile devices

Mobile data technologies use ``actigraphs'' to furnish information on health variables as a function of a subject's movement. The advent of wearable devices and related technologies has propelled the creation of health databases consisting of human movement data to conduct research on mobility patterns and health outcomes. Statistical methods for analyzing high-resolution actigraph data depend on the specific inferential context, but the advent of Artificial Intelligence (AI) frameworks require that the methods be congruent to transfer learning and amortization. This article devises amortized Bayesian inference for actigraph time sheets. We pursue a Bayesian approach to ensure full propagation of uncertainty and its quantification using a hierarchical dynamic linear model. We build our analysis around actigraph data from the Physical Activity through Sustainable Transport Approaches in Los Angeles (PASTA-LA) study conducted by the Fielding School of Public Health in the University of California, Los Angeles. Apart from achieving probabilistic imputation of actigraph time sheets, we are also able to statistically learn about the time-varying impact of explanatory variables on the magnitude of acceleration (MAG) for a cohort of subjects.

Daniel Zhou, Sudipto Banerjee

UCLA DEPARTMENT OF BIOSTATISTICS, 650 CHARLES E. YOUNG DRIVE, LOS ANGELES, 90095-1772.

Amortized InferenceWearable Health MonitoringLearning with Missing Data
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Feb 24, 2026

Imputation of Unknown Missingness in Sparse Electronic Health Records

Machine learning holds great promise for advancing the field of medicine, with electronic health records (EHRs) serving as a primary data source. However, EHRs are often sparse and contain missing data due to various challenges and limitations in data collection and sharing between healthcare providers. Existing techniques for imputing missing values predominantly focus on known unknowns, such as missing or unavailable values of lab test results; most do not explicitly address situations where it is difficult to distinguish what is missing. For instance, a missing diagnosis code in an EHR could signify either that the patient has not been diagnosed with the condition or that a diagnosis was made, but not shared by a provider. Such situations fall into the paradigm of unknown unknowns. To address this challenge, we develop a general purpose algorithm for denoising data to recover unknown missing values in binary EHRs. We design a transformer-based denoising neural network where the output is thresholded adaptively to recover values in cases where we predict data are missing. Our results demonstrate improved accuracy in denoising medical codes within a real EHR dataset compared to existing imputation approaches and leads to increased performance on downstream tasks using the denoised data. In particular, when applying our method to a real world application, predicting hospital readmission from EHRs, our method achieves statistically significant improvement over all existing baselines.

Jun Han, Josue Nassar, Sanjit Singh Batra +3

Optum AI

Incomplete Data ImputationLearning with Missing DataElectronic Health Records
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Feb 23, 2026

A Statistical Approach for Modeling Irregular Multivariate Time Series with Missing Observations

Irregular multivariate time series with missing values present significant challenges for predictive modeling in domains such as healthcare. While deep learning approaches often focus on temporal interpolation or complex architectures to handle irregularities, we propose a simpler yet effective alternative: extracting time-agnostic summary statistics to eliminate the temporal axis. Our method computes four key features per variable-mean and standard deviation of observed values, as well as the mean and variability of changes between consecutive observations to create a fixed-dimensional representation. These features are then utilized with standard classifiers, such as logistic regression and XGBoost. Evaluated on four biomedical datasets (PhysioNet Challenge 2012, 2019, PAMAP2, and MIMIC-III), our approach achieves state-of-the-art performance, surpassing recent transformer and graph-based models by 0.5-1.7% in AUROC/AUPRC and 1.1-1.7% in accuracy/F1-score, while reducing computational complexity. Ablation studies demonstrate that feature extraction-not classifier choice-drives performance gains, and our summary statistics outperform raw/imputed input in most benchmarks. In particular, we identify scenarios where missing patterns themselves encode predictive signals, as in sepsis prediction (PhysioNet, 2019), where missing indicators alone can achieve 94.2% AUROC with XGBoost, only 1.6% lower than using original raw data as input. Our results challenge the necessity of complex temporal modeling when task objectives permit time-agnostic representations, providing an efficient and interpretable solution for irregular time series classification.

Dingyi Nie, Yixing Wu, C. -C. Jay Kuo

University of Southern California

Irregular Time-Series ModelingMultivariate Time Series ClassificationLearning with Missing Data
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Feb 20, 2026

Exploiting Completeness Perception with Diffusion Transformer for Unified 3D MRI Synthesis

Missing data problems, such as missing modalities in multi-modal brain MRI and missing slices in cardiac MRI, pose significant challenges in clinical practice. Existing methods rely on external guidance to supply detailed missing-state information for instructing generative models to synthesize missing MRIs. However, manual indicators are not always available or reliable in real-world scenarios due to the unpredictable nature of clinical environments. Moreover, these explicit masks are not informative enough to provide guidance for improving semantic consistency. In this work, we argue that generative models should infer and recognize missing states in a self-perceptive manner, enabling them to better capture subtle anatomical and pathological variations. Towards this goal, we propose CoPeDiT, a shared completeness-perception framework for 3D MRI synthesis, following a common conditioning strategy with task-specific instantiations for different missing-data scenarios. Specifically, we incorporate dedicated pretext tasks into our tokenizer, CoPeVAE, empowering it to learn completeness-aware discriminative prompt tokens, and design MDiT3D, a specialized diffusion transformer architecture for 3D MRI synthesis that effectively uses the completeness-aware prompt tokens as guidance to enhance semantic consistency in 3D space. Comprehensive evaluations on three large-scale MRI datasets demonstrate that CoPeDiT consistently improves upon state-of-the-art methods across diverse missing patterns, yielding high-fidelity and structurally consistent MRI synthesis. Our code is available at https://github.com/JK-Liu7/CoPeDiT.

Junkai Liu, Nay Aung, Theodoros N. Arvanitis +3

School of Engineering, University of Birmingham, UK · William Harvey Research Institute, Queen Mary University London, UK · Barts Heart Centre, St Bartholomew’s Hospital, Barts Health NHS Trust, UK +1

Medical Image Synthesis3D Medical ImagingLearning with Missing DataDiffusion Transformer
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Feb 19, 2026

A feature-stable and explainable machine learning framework for trustworthy decision-making under incomplete clinical data

Machine learning models are increasingly applied to biomedical data, yet their adoption in high stakes domains remains limited by poor robustness, limited interpretability, and instability of learned features under realistic data perturbations, such as missingness. In particular, models that achieve high predictive performance may still fail to inspire trust if their key features fluctuate when data completeness changes, undermining reproducibility and downstream decision-making. Here, we present CACTUS (Comprehensive Abstraction and Classification Tool for Uncovering Structures), an explainable machine learning framework explicitly designed to address these challenges in small, heterogeneous, and incomplete clinical datasets. CACTUS integrates feature abstraction, interpretable classification, and systematic feature stability analysis to quantify how consistently informative features are preserved as data quality degrades. Using a real-world haematuria cohort comprising 568 patients evaluated for bladder cancer, we benchmark CACTUS against widely used machine learning approaches, including random forests and gradient boosting methods, under controlled levels of randomly introduced missing data. We demonstrate that CACTUS achieves competitive or superior predictive performance while maintaining markedly higher stability of top-ranked features as missingness increases, including in sex-stratified analyses. Our results show that feature stability provides information complementary to conventional performance metrics and is essential for assessing the trustworthiness of machine learning models applied to biomedical data. By explicitly quantifying robustness to missing data and prioritising interpretable, stable features, CACTUS offers a generalizable framework for trustworthy data-driven decision support.

Justyna Andrys-Olek, Paulina Tworek, Luca Gherardini +4

Computational Intelligence, Sano Centre for Computational Personalised Medicine, Krakow, Poland · Clinical Studies Group, Randox Laboratories Ltd., Co., Antrim, United Kingdom

Interpretable MLLearning with Missing DataExplainability EvaluationClinical Outcome Prediction
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Feb 18, 2026

What is the Value of Censored Data? An Exact Analysis for the Data-driven Newsvendor

We study the offline data-driven newsvendor problem when historical demand is censored by past inventory levels. We introduce a class of policies for which worst-case expected regret over all bounded demand distributions admits an exact finite-dimensional characterization, valid for any sample size and historical inventory design. The dimension depends on the number of distinct inventory levels, rather than the number of observations. This framework yields exact analyses of the sales-as-demand heuristic, the Kaplan-Meier policy, and recent policies from the censored-newsvendor literature. We leverage this reduction to derive sharp insights on the achievable performance of standard inventory policies under demand censoring. In particular, our analysis of the Kaplan-Meier policy shows that while demand censoring fundamentally limits what can be learned from passive sales data, just a small amount of targeted exploration at high inventory levels can substantially improve worst-case guarantees. Finally, we further leverage our reduction to design new policies that push the frontier and substantially improve upon the worst-case regret of known policies, reducing it by up to 40%.

Rachitesh Kumar, Omar Mouchtaki

Carnegie Mellon University · New York University

Inventory ControlMinimax RegretLearning with Missing Data
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Feb 17, 2026

AI-Generated Measurements for Identification and Inference with Missing Data: A Weak Shadow Variable Approach

Across business and social science applications, outcomes are often missing in ways that depend on the unobserved outcomes themselves. In service systems, for example, whether a customer submits a rating depends on the rating they would have provided. Such missing-not-at-random (MNAR) mechanisms make population quantities difficult to identify without strong assumptions on the observation process. Meanwhile, rich unstructured data, such as customer interaction histories, are increasingly available and can be used to construct structured measurements using tools such as large language models (LLMs). In this work, we develop an assumption-lean partial identification framework that uses such measurements as weak shadow variables, defined as outcome-informative proxies that are conditionally independent of missingness given the true outcome and observed covariates. Importantly, they need not accurately predict missing outcomes or satisfy the completeness requirement in the classical shadow variable literature. For identification, we characterize sharp bounds on population quantities through a pair of linear programs. For estimation and inference, we propose a localized penalized estimator that remains feasible under sampling error, and a subsampling algorithm for constructing confidence intervals. In semi-synthetic experiments using real customer-service dialogues, weak-shadow-variable intervals are about 89% narrower than those without auxiliary information, while their midpoints have around 41% lower estimation error than classical MNAR methods.

Hongyu Chen, David Simchi-Levi, Ruoxuan Xiong

Massachusetts Institute of Technology, Cambridge, MA 02139 · Emory University, Atlanta, GA 30322

Learning with Missing DataPartial Identification
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Feb 17, 2026

The Stationarity Bias: Stratified Stress-Testing for Time-Series Imputation in Regulated Dynamical Systems

Time-series imputation benchmarks employ uniform random masking and shape-agnostic metrics (MSE, RMSE), implicitly weighting evaluation by regime prevalence. In systems with a dominant attractor -- homeostatic physiology, nominal industrial operation, stable network traffic -- this creates a systematic Stationarity Bias: simple methods appear superior because the benchmark predominantly samples the easy, low-entropy regime where they trivially succeed. We formalize this bias and propose a Stratified Stress-Test that partitions evaluation into Stationary and Transient regimes. Using Continuous Glucose Monitoring (CGM) as a testbed -- chosen for its rigorous ground-truth forcing functions (meals, insulin) that enable precise regime identification -- we establish three findings with broad implications:(i)~Stationary Efficiency: Linear interpolation achieves state-of-the-art reconstruction during stable intervals, confirming that complex architectures are computationally wasteful in low-entropy regimes.(ii)~Transient Fidelity: During critical transients (post-prandial peaks, hypoglycemic events), linear methods exhibit drastically degraded morphological fidelity (DTW), disproportionate to their RMSE -- a phenomenon we term the RMSE Mirage, where low pointwise error masks the destruction of signal shape.(iii)~Regime-Conditional Model Selection: Deep learning models preserve both pointwise accuracy and morphological integrity during transients, making them essential for safety-critical downstream tasks. We further derive empirical missingness distributions from clinical trials and impose them on complete training data, preventing models from exploiting unrealistically clean observations and encouraging robustness under real-world missingness. This framework generalizes to any regulated system where routine stationarity dominates critical transients.

Amirreza Dolatpour Fathkouhi, Alireza Namazi, Heman Shakeri

Department of Computer Science Center for Diabetes Technology University of Virginia Charlottesville, Virginia, USA · School of Data Science Center for Diabetes Technology University of Virginia Charlottesville, Virginia, USA

Continuous Glucose MonitoringTime Series ImputationLearning with Missing DataNon-Stationary Time Series
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Feb 16, 2026

Learning Representations from Incomplete EHR Data with Dual-Masked Autoencoding

Electronic health records (EHR) arrive masked. Clinicians order measurements selectively, and any patient table thus contains only a subset of the values that characterize the underlying physiological state. Prior masked modeling approaches on EHR data either impute the table before learning, represent missingness through a dedicated placeholder signal, or optimize solely for imputation, which limits the representations they learn for downstream clinical tasks and carries every unobserved entry through the encoder. We introduce AID-MAE, an Augmented-Intrinsic Dual-Masked Autoencoder that learns directly from incomplete tables by combining the intrinsic mask the record already carries with an augmented mask that hides a subset of observed values for reconstruction during pretraining. Neither type of masked entry enters the encoder, so attention operates only over what was observed. AID-MAE achieves consistent improvements over strong baselines across multiple clinical tasks on two datasets. Across experiments, we discuss that recovering the missing entries is not a prerequisite for learning and show that the representations learned carry clinical structure without supervision.

Xiao Xiang, David Restrepo, Hyewon Jeong +2

Massachusetts Institute of Technology · École Polytechnique Fédérale de Lausanne · Harvard University +1

Learning with Missing DataMasked AutoencodersTabular Representation LearningElectronic Health Records
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Feb 1, 2026

Theoretical Analysis of Measure Consistency Regularization for Partially Observed Data

The problem of corrupted data, missing features, or missing modalities continues to plague the modern machine learning landscape. To address this issue, a class of regularization methods that enforce consistency between imputed and fully observed data has emerged as a promising approach for improving model generalization, particularly in partially observed settings. We refer to this class of methods as Measure Consistency Regularization (MCR). Despite its empirical success in various applications, such as image inpainting, data imputation and semi-supervised learning, a fundamental understanding of the theoretical underpinnings of MCR remains limited. This paper bridges this gap by offering theoretical insights into when MCR yields a more favorable finite-sample estimation-error upper bound, viewed through the lens of neural network distance. Under ideal interpolation and compatibility conditions, we show that the MCR estimation-error upper bound is no larger than vanilla supervised training and becomes strictly smaller when the mixed-sample alternative is favorable. We then extend the analysis to the non-ideal regime, where optimization and compatibility residuals can potentially offset this finite-sample advantage. Guided by these insights, we propose a novel practical diagnostic that leverages the duality gap and a calibrated drift estimator to infer the potential benefit of MCR training. We present detailed empirical evidence to support our theoretical claims and to show the effectiveness and accuracy of our practical diagnostic. We further provide simulations on real-world datasets to show the versatility of MCR under different model architectures designed for different data sources.

Yinsong Wang, Shahin Shahrampour

University of Nevada Reno, Reno, NV 89557 USA · Department of Mechanical and Industrial Engineering at Northeastern University, Boston, MA 02115 USA

Neural Network GeneralizationLearning with Missing DataStatistical Learning TheoryConsistency Regularization
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Sep 23, 2025

Linear Regression under Missing or Corrupted Coordinates

We study multivariate linear regression under Gaussian covariates in two settings, where data may be erased or corrupted by an adversary under a coordinate-wise budget. In the incomplete data setting, an adversary may inspect the dataset and delete entries in up to an ηη-fraction of samples per coordinate; a strong form of the Missing Not At Random model. In the corrupted data setting, the adversary instead replaces values arbitrarily, and the corruption locations are unknown to the learner. Despite substantial work on missing data, linear regression under such adversarial missingness remains poorly understood, even information-theoretically. Unlike the clean setting, where estimation error vanishes with more samples, here the optimal error remains a positive function of the problem parameters. Our main contribution is to characterize this error up to constant factors across essentially the entire parameter range. Specifically, we establish novel information-theoretic lower bounds on the achievable error that match the error of (computationally efficient) algorithms. A key implication is that, perhaps surprisingly, the optimal error in the missing data setting matches that in the corruption setting-so knowing the corruption locations offers no general advantage.

Ilias Diakonikolas, Jelena Diakonikolas, Daniel M. Kane +2

University of Wisconsin-Madison · University of California, San Diego · University of California, Davis

Robust RegressionLearning with Missing DataCorruption RobustnessLinear RegressionStatistical Learning Theory
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Aug 15, 2025

No Data Wasted: A Semi-supervised Generative Model for Incomplete Multi-view Data Integration with Missing Labels

Multi-view learning is widely applied to real-life datasets, but it often suffers from both missing views and missing labels. Prior probabilistic approaches addressed the missing view problem by using a product-of-experts scheme to aggregate representations from present views and achieved superior performance over deterministic classifiers, using the information bottleneck (IB) principle. However, the IB framework is inherently fully supervised and cannot leverage unlabeled data. In this work, we propose a semi-supervised generative model that utilizes both labeled and unlabeled samples in a unified framework. Our method maximizes the likelihood of unlabeled samples to learn a latent space shared with the IB on labeled data. We also include modality-specific information in likelihood modeling and perform cross-view mutual information maximization in the shared latent space to enhance the extraction of shared information across views. Compared to existing approaches, our model achieves better predictive and generation performance on complex datasets with missing views and limited labeled samples.

Yiyang Shen, Weiran Wang

Department of Computer Science, University of Iowa, Iowa City, Iowa, USA

Learning with Missing DataMulti-View LearningGenerative ModelingSemi-Supervised Learning
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Apr 21, 2025

Deep learning with missing data

In the context of multivariate nonparametric regression with missing covariates, we propose Pattern Embedded Neural Networks (PENNs), which can be applied in conjunction with any existing imputation technique. In addition to a neural network trained on the imputed data, PENNs pass the vectors of observation indicators through a second neural network to provide a compact representation. The outputs are then combined in a third neural network to produce final predictions. Our main theoretical result exploits an assumption that the observation patterns can be partitioned into cells on which the Bayes regression function behaves similarly, and belongs to a compositional Hölder class. It provides a finite-sample excess risk bound that holds for an arbitrary missingness mechanism, and in combination with a complementary minimax lower bound, demonstrates that our PENN estimator attains in typical cases the minimax rate of convergence as if the cells of the partition were known in advance, up to a poly-logarithmic factor in the sample size. Numerical experiments on simulated, semi-synthetic and real data confirm that the PENN estimator consistently improves, often dramatically, on standard neural networks without pattern embedding. Code to reproduce our experiments, as well as a tutorial on how to apply our method, is publicly available.

Tianyi Ma, Tengyao Wang, Richard J. Samworth

Statistical Laboratory, University of Cambridge · Department of Statistics, London School of Economics

Neural Network GeneralizationLearning with Missing DataNonparametric Regression
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