Learning with Missing Data

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12 papers in the last four weeks, up 33% on the four weeks before. 0.1% of all new papers.

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Latest papers 68

Oct 5, 2026stat.ML

Assumption-lean logistic regression with missing covariates

Missing covariates are frequently encountered in supervised learning problems, and classical methods for estimation using such data use carefully chosen imputation schemes for missing data, or likelihood approximations that lead to nonconvex

M

-estimation problems. These methods and their relatives are suitable for scenarios in which the covariate distribution is known, and more broadly, have enjoyed tremendous success in linear models. But even in basic nonlinear problems such as logistic regression in moderate dimensions, such methods can experience drastic failure modes when the covariate distribution is unknown. Motivated by the need for reliable alternatives, we consider the problem of parameter estimation in logistic regression with missing covariates. Crucially, we operate in the assumption-lean setting where the covariate distribution is unknown (but bounded). We design a stochastic approximation method that is based on

Z

-estimation with a novel monotone operator, and establish that our algorithm is computationally efficient and achieves provable signal recovery at parametric rates under the hypothesis that covariates are missing completely at random. Our theory sharply characterizes the

\ell_2^2

risk of the estimator in terms of the missingness profile, accommodating heterogeneous observation probabilities. Importantly, it shows that our method always outperforms the de facto ``complete-case'' estimator that ignores observations with any missing data. Even in the setting with homogeneous missingness (in which each covariate is observed independently with probability

q

), our bounds exhibit intricate and nonstandard dependence on

q

that can yield significant improvements over using only complete cases. We complement our upper bounds with new information-theoretic lower bounds that show that this intricate dependence on

q

is fundamental in a minimax sense.

Jyotishka Ray Choudhury, Kabir Aladin Verchand, Richard J. Samworth +1

School of Industrial and Systems Engineering, Georgia Institute of Technology · Department of Data Sciences and Operations, University of Southern California · Statistical Laboratory, University of Cambridge +1

Logistic Regression Learning with Missing Data Minimax Estimation

Oct 5, 2026cs.LG

ARO: Aligned Representation learning for multi-Omics data

The high cost of functional molecular assays, and prevalence of missing modalities and unmatched samples in computational biology, create significant barriers to comprehensive multi-omic profiling, essential for capturing and reasoning over molecules, cells, tissues, and organisms. This work proposes a model that learns meaningful representations from multi-omics cancer data supporting the reconstruction of missing and unpaired modalities. Contrary to increasingly complex, larger models, e.g. Foundation Models (FMs), ARO prioritizes practical applicability in limited or incomplete data settings. ARO optimally reconstructs missing modalities (MSE of

0.15

on the validation and test data in the Unmasked settings), with its learned latent embeddings enabling a downstream cancer classification task. Our findings indicate that analyzing diverse molecular layers as a single integrated system offers a reliable and cost-efficient approach, reducing dependence on large-scale experimental testing, while still supporting multi-omic exploration in limited data settings.

Amogh Singh, Yash Shah, Chiara D'Ercoli +4

Department of Computer Science, University of Cambridge, Cambridge, UK · DIAG, University of Rome “Sapienza”, Rome, Italy · Max Planck Institute for Intelligent Systems

Missing-Modality Learning Learning with Missing Data Molecular Representation Learning

Oct 4, 2026cs.AI

Learning Field Reconstruction from Incomplete Data by Globally Correcting Local Estimates

Reconstructing physical fields from training samples that are always incomplete requires learning spatial structure from fragmented observations. Existing context--query work establishes how held-out observations provide valid training targets, but this does not make the complete-field distribution identifiable when every training field is incomplete. With finite data, weak evidence of sharp transitions and localized variations can further favor averaged predictions that attenuate local detail. A structural prior is therefore needed to favor plausible completions; local spatial relationships offer one grounded in the observations. We propose a locally constructed, globally revisable estimator that explicitly learns local field estimates and subsequently corrects them using full-domain observations. A shared coordinate-conditioned predictor learns from incomplete patches, allowing relatively well-observed neighborhoods to provide direct supervision of local structure. Its overlapping predictions are reconciled into an observation-conditioned consensus field. A full-domain estimator retains the original observations and learns a residual correction around this frozen field estimate, allowing locally constructed structure to be revised by broader evidence. The local estimate serves as both an explicit input, accompanied by its discrepancies with the observations, and a prediction starting point that the global model can revise. On three real-world ocean datasets with authentic observation gaps, our estimator achieves the lowest MSE and highest PSNR on withheld source-supported values, reducing MSE by 28.9%--34.5% against the strongest external baseline.

Renhao Zhong, Zihan Zhou, Chiyuan Ma +1

The Chinese University of Hong Kong, Shenzhen · Shanghai Artificial Intelligence Laboratory

Incomplete Data Imputation Learning with Missing Data

Oct 4, 2026cs.LG

The Effect of Missingness-Pattern Mismatch on Method Selection for Time-Series Classification: A Controlled Empirical Study

Classifiers for time-series classification are commonly selected on validation data, but the temporal pattern of missing observations at deployment may differ from the pattern seen during validation. We examine whether such a mismatch affects validation-based classifier selection. In a controlled

2 \times 2

design, validation and test sets of 64 univariate UCR datasets were masked with either random point missingness or circular block missingness at six rates from 5% to 30%, imputed by linear interpolation, and used to select among three prespecified candidates: 1NN-DTW, MiniRocket with a Ridge classifier, and a statistical-feature Random Forest. Training data remained complete, and selections made under matched and mismatched validation patterns were compared on the same masked test sets. Mismatched validation reduced the test balanced accuracy of the selected classifier by 1.14 percentage points on average (95% CI 0.79 to 1.51), with losses on 49 of the 64 datasets. The loss was negligible at 5% missingness and increased to 2.46 percentage points at 30%. It was concentrated in point-masked deployment (1.84 percentage points), where block-masked validation shifted selection away from the usually best candidate, while the effect for block-masked deployment was small and not significant. Mismatch changed the selected classifier in 35.5% of paired comparisons, but a changed selection did not always reduce performance. A supplementary analysis with non-wrapping linear blocks reproduced these findings with a larger effect (1.67 percentage points). Matching the missingness pattern of validation data to the expected deployment pattern is therefore a simple safeguard for method selection, particularly at higher missingness rates.

Ruiqi Zhao, Zishun Yuan, Zhentao Wang +3

The University of Tokyo, Tokyo, Japan · Stony Brook University, SUNY Korea, Incheon, South Korea · Fuyao University of Science and Technology, Fujian, China +3

Model Selection Time Series Classification Learning with Missing Data

Sep 30, 2026stat.ML

Towards Optimal Inventory Control under Censored Demand: A Biased Sample-Average Approximation Approach

We study data-driven multi-period lost-sales inventory control under censored demand, where a stockout reveals only that demand exceeded the stocking level. We develop a unified, model-based framework for policy learning from censored data, built on a new cost decomposition for base-stock policies and a biased sample-average approximation (SAA) approach. The cost decomposition allows us to propose a new coverage condition under which censored observations are informative enough for sample-efficient policy learning. Guided by this coverage condition, we design two biased SAA algorithms: an upper-biased one that achieves near-optimal sample complexity under the offline coverage condition, and a lower-biased one that actively generates the required coverage and achieves near-optimal regret online. More broadly, this biased SAA approach provides a general principle for implementing pessimism and optimism under censored feedback, which may be of independent interest.

Yuxuan Han, Xiaoyu Fan, Jiawei Zhang +1

Stern School of Business, New York University

Inventory Control Learning with Missing Data Data-Driven Control

Sep 28, 2026cs.LG

MASCIT: A Mask-Aware State Space Classifier for Naturally Irregular Time Series

Naturally irregular time series combine asynchronous observations, missing values, unequal lengths, and nonuniform sampling, while dense adapters can discard temporal structure. We propose a mask-aware state space classifier for irregular time series (MASCIT), which supplies observation masks to the encoder and excludes invalid steps from gated temporal aggregation. Across 34 irregular time series datasets, MASCIT yielded the strongest aggregate point estimate and was the only evaluated neural model with three-seed results on every dataset. MASCIT retained the lowest point rank across six overlapping irregularity indicators, while factorial ablations favored partial over full selectivity. These results support selective state space models as effective, executable backbones for naturally irregular time series classification.

Yoo-Min Jung, Hyeon-Gi Kim, Jonghun Park

Department of Industrial Engineering Seoul National University, Seoul, Republic of Korea

Irregular Time-Series Modeling Selective SSMs Time Series Classification Learning with Missing Data

Sep 28, 2026cs.CL

Unknown is not normal: separating language-model extraction from rule-based decision logic for clinical risk scores

Large language models (LLMs) are increasingly used to compute clinical risk scores from free-text notes. Notes are often incomplete, and treating undocumented findings as normal can silently misclassify patients. We test whether separating three-state extraction (present, absent or unknown, by an LLM) from decision logic (deterministic code computing score bounds over unknown inputs) lets a system ask only questions that can change the decision. On 1,200 synthetic emergency cases across six calculators (HEART, CURB-65, qSOFA, PERC, Wells, Cockcroft-Gault), with a simulated clinician answering questions, we compared this bounds policy with asking for every missing input, a missing-equals-normal schema, and an end-to-end LLM agent (Claude Opus 5.5). With Claude Haiku 4.5 as extractor, the bounds policy matched ask-all accuracy (99.4% vs 99.4%) with half the questions (0.92 vs 1.78 per case) and no irrelevant ones. Treating missing as normal dropped accuracy to 91.2% and under-triaged 8.5% of patients (95% CI 7.1-10.2), and under-triage persisted under messy notes and a noisy clinician. The agent was equally accurate under ideal conditions (99.6%) but 9.5% of its questions were irrelevant; with a noisy clinician it was less accurate than the bounds policy (83.5% vs 87.0%, p<0.001) and committed prematurely in 2.7% of cases (bounds: 0%). A 9B local model as extractor reached oracle-level accuracy (99.8%). In 584 real case reports from MedCalc-Bench, only 52% contained enough information to determine the category (HEART 13%). Routing decisions through code that reasons explicitly about unknowns avoids premature commitment and irrelevant questions, halves the questions asked, and works with small local models.

Nicolás Vera Zúñiga

Independent Researcher, Chile

Clinical Decision Support Learning with Missing Data Clinical Information Extraction Classification Clinical Risk Prediction

Sep 23, 2026cs.LG

Fed-ReMasker: Federated Tabular Imputation under Feature-Level Missingness

Multi-center clinical studies and biomedical research collaborations increasingly seek to utilize data across centers to build models that generalize beyond any single center. This creates two distinct challenges: data protection regulations may restrict the sharing of raw patient data across institutions, while centers may collect only partially overlapping sets of features under different protocols. Federated learning enables collaborative model training without centralizing raw data. However, existing federated imputation methods rarely evaluate feature-level missingness, in which entire features are unobserved at some centers. To address this setting, we adapt the ReMasker masked autoencoder to federated learning (Fed-ReMasker), enabling centers to impute features never observed locally by leveraging knowledge learned across collaborating centers. We evaluate Fed-ReMasker in a benchmark spanning synthetic datasets with linear and nonlinear relationships and real-world tabular datasets, including clinical data. The benchmark varies the number of centers, the missingness ratios, and client heterogeneity. Fed-ReMasker achieves the lowest imputation error in 93.2% of value-level and 96.7% of feature-level scenarios in the homogeneous benchmark. It also remains robust to client heterogeneity using simple federated averaging, outperforming all baselines in all 36 value-level scenarios and each baseline in at least 35 of 36 feature-level scenarios, and comes within 3.0% on average of a centralized model trained on the pooled data.

Ioannis Papathanail, Rooholla Poursoleymani, Lubnaa Abdur Rahman +1

ARTORG Center for Biomedical Engineering Research University of Bern, Bern, Switzerland · Graduate School for Cellular and Biomedical Sciences University of Bern, Bern, Switzerland

Incomplete Data Imputation Masked Autoencoders Learning with Missing Data Federated Learning

Sep 22, 2026stat.ME

Optimal Sequential Annotations for Off-Policy Evaluation

Offline reinforcement learning and off-policy evaluation evaluates dynamic treatment rules based on retrospectively collected data prior to deployment. In recent AI applications, state and reward information is recorded as complex text or image, which recent AI advancements such as LLM-as-a-judge can label with unknown bias. Expert annotation may be available but at a higher cost. For example, safety classification via cheap but imperfect classifiers vs. expensive expert review. We show how a limited budget for ground-truth data-annotation can be used via doubly-robust OPE with missing rewards, and we optimize variance-optimal annotation probabilities for sequential off-policy evaluation, where the target policy value is estimated from annotated data. We characterize the optimal annotation probabilities for sequential forward-monotone annotation protocols, and provide a feasible batch-adaptive implementation. Our work is motivated by a collaboration with a homelessness services nonprofit that writes casenotes for individuals over time. Our method can be used to unlock trustworthy inference from casenote data and answer new inferential questions such as: how does expanding outreach effort over time affect progress towards a housing application and improvement in housing placement? In simulations and on two real datasets - casenotes from the nonprofit and human-preference votes from LMArena - we see reductions in RMSE of 34-65% for housing placement and 17-68% for progress towards a housing application at budgets of 40% of full annotation and above, and by 55-62% at every budget on LMArena.

Woojin Chae, Ezinne Nwankwo, Haitong Qin +1

University of Southern California · University of California, Berkeley · University of Washington, Seattle

Off-Policy Evaluation Learning with Missing Data Human-in-the-Loop Annotation

Sep 22, 2026stat.ML

Conditional Tensor Diffusion: Distributional Counterfactual Learning and Inference

Causal inference guides operational and managerial decisions but remains challenging in high-dimensional panel or tensor settings, where decisions may depend on the joint conditional distribution of missing control outcomes. We develop \emph{Counterfactual Tucker Diffusion} (\CFTDiff), which integrates the treatment mask and latent Tucker structure into conditional diffusion to recover this distribution given observed control outcomes through efficient nonlinear score learning in a low-dimensional core. The masked Tucker score preserves dependence across tensor modes while reducing the dimension of nonlinear score learning from the product of mode dimensions to the much smaller product of Tucker ranks. We establish high-probability error bounds for conditional score estimation that depend on the Tucker ranks, largest mode dimension, and the factor-strength-adjusted number of missing outcomes, and show how these bounds translate into recovery guaranties for the conditional distribution of the missing control outcomes. Across missing rates, simulations show more accurate point recovery than common causal panel and matrix/tensor completion methods; comparisons with nested diffusion specifications further demonstrate the gains from masked conditioning and Tucker dimension reduction. In Norway's iFlex experiment, \CFTDiff recovers missing outcomes more accurately than competing methods; when applied to causal analysis, its estimated conditional distributions yield counterfactual prediction intervals and target-attainment probabilities, allowing pricing interventions to be evaluated by demand-reduction magnitude and reliability.

Xinbing Kong, Zeyu Li, Junfan Mao +1

Southeast University · University of Science and Technology of China

Causal Counterfactual Generation Low-Rank Matrix Decomposition Learning with Missing Data Conditional Distribution Estimation Conditional Diffusion Models

Sep 20, 2026cs.LG

ITSY: Causal Discovery From Irregular Time-Series Data

Structural causal models for time series recover contemporaneous and lagged effects, but most methods require complete observation windows and become misspecified when samples are missing. We introduce ITSY, the first continuous-optimization method for causal discovery from irregular time series under a linear model. ITSY reformulates the structural equation so that prediction uses the nearest available history rather than the possibly missing current slice, and jointly imputes missing values while learning both graphs. A weighted reconstruction objective corrects the noise transformation induced by this reformulation. Across synthetic regimes varying missingness, scale, graph density, and noise, and on a real world benchmark, ITSY consistently improves graph recovery over representative SCM-based baselines, demonstrating the effectiveness of the proposed method. The results establish a focused solution for irregular linear first-order dynamics and clarify the assumptions required for nonlinear or higher-order extensions.

Wenbo Xu, Yue He, Yunhai Wang +2

Renmin University of China, China · Zhejiang University, China

Irregular Time-Series Modeling Structural Causal Models Time-Series Causal Discovery Learning with Missing Data Causal Discovery

Sep 14, 2026cs.LG

Cross-Block Conditioning in Deep Boltzmann Machines for Statistical Data Fusion

Statistical data fusion combines two panels that share a block of covariates but observe disjoint outcome blocks, and in its traditional form no row observes both outcomes at once. That rules out the discriminative criterion one would rather train a Deep Boltzmann Machine with, since multi-prediction training needs ground truth for whatever it holds out. We propose observed-block multi-prediction, which restricts the multi-prediction objective to targets drawn from what each row actually observes. It is well defined for any missingness pattern and reduces to the original criterion when rows are complete. Having a discriminative criterion that survives the setting lets us ask whether the joint model is needed at all, by separating what it contributes into a representation part and an inference part. On two datasets of different kinds, a consumer purchase panel and public-domain census microdata, over grids in sample size and covariate width spanning 40 cells and 200 runs per method, almost none of the fine-tuned DBM's advantage comes from generative pre-training, which is confined to the smallest sample size on one dataset and absent on the other. It comes from conditioning on one outcome block when predicting the other. This term amounts to +0.19 and +0.36 percentage points, is positive in all 40 cells, never decays as the panels grow (it is flat on one dataset and grows on the other), and requires neither a second hidden layer nor more inference. Against baselines tuned on validation and given the same conditioning, the fine-tuned DBM is the best method in 37 of the 40 cells. The imputers that can also condition on the other outcome block mostly lose accuracy when they do, whereas the DBM gains in every cell; since fusion data cannot validate that choice, this is the property that matters.

Junichiro Niimi

Meijo University

Learning with Missing Data Conditional Distribution Estimation

Sep 14, 2026stat.ML

Shapley Value Estimation for Multi-Site Data with Blockwise-Missing Features

Shapley value (SV)-based methods are the prevailing framework for feature attribution in machine learning, yet existing population-level Shapley estimators generally assume that observations used to evaluate the coalitional game are fully observed under a common feature space. This assumption is routinely violated in multi-site studies across biomedicine, social science, and environmental monitoring, where institutions record different features under different protocols, producing systematic blockwise missingness across sources. We first show that the standard remedy of imputing missing features before computing Shapley values introduces systematic, coalition-dependent bias into the resulting attributions. We then propose \textbf{FUSHAP} (\textbf{Fu}sion \textbf{Sh}apley \textbf{A}ttribution from \textbf{P}artially-observed data), a method that leverages partially-observed auxiliary sites to reduce the variance of a preliminary single-site Shapley estimate without imputation. A permutation-based screening step detects and excludes sites whose data distributions are incompatible with the target population. In synthetic experiments, FUSHAP achieves

3

--

8\times

lower MSE than the single-site estimator and

2

--

3\times

lower MSE than imputation baselines without incurring imputation-induced bias, and the screening procedure identifies misaligned sites with

82\%

power at moderate misalignment and

100\%

for strong misalignment. On multi-site air quality and multi-center clinical data, FUSHAP reduces MSE by approximately

3

--

7\times

relative to the single-site estimator; in the clinical application, standard imputation can increase MSE above the single-site baseline.

Siqi Li, Wangxuan Fan, Yiming Li +2

Centre for Biomedical Data Science, Duke-NUS Medical School · School of Data Science, Chinese University of Hong Kong, Shenzhen · Department of Biostatistics, Columbia University +3

Feature Attribution Learning with Missing Data Shapley Value Attribution

Sep 9, 2026cs.CV

MethaneFuse: Learning from Multi-Sensor Satellite Observations for Methane Plume Detection

Methane plume detection from satellite imagery is constrained by incomplete observations: public satellites provide complementary spatial, spectral, and atmospheric evidence, but real plume cases rarely contain fully paired multi-sensor measurements because of revisit schedules, cloud coverage, acquisition quality, and the transient nature of emissions. Most learning-based detectors rely on single-sensor inputs, especially Sentinel-2 (S2), leaving many reported plume cases unusable. We construct MethaneUnion, a temporal multi-sensor dataset built from Carbon Mapper plume reports and matched S2, Landsat 8/9 (L8/9), EMIT, and Sentinel-5P (S5P) observations. Built on MethaneUnion, MethaneFuse learns from heterogeneous satellite observations under partial sensor availability without requiring complete four-sensor measurements. MethaneUnion expands usable coverage from 3,211 valid S2-matched plume cases to 8,981 reported plume cases with multi-sensor observations. At the representative 480 m setting, MethaneFuse achieves 84.87 F1 and 93.62 AUROC, improving over the strongest baseline by 5.65 F1 and 8.30 AUROC points while reducing false positives by 8.19 points. Sensor-availability experiments show that MethaneFuse improves detection when S2 is available and transfers plume knowledge to L8/9, EMIT, and S5P when S2 is unavailable. These results demonstrate the value of learning from incomplete heterogeneous sensor observations for practical methane plume detection.

Yuyao Wang, Juliana Y. Leung, Di Niu

Department of Electrical and Computer Engineering University of Alberta Edmonton, Canada · Department of Civil and Environmental Engineering University of Alberta Edmonton, Canada

Learning with Missing Data Remote Sensing Multimodal Sensor Fusion

Sep 2, 2026math.NA

Coupled Tensor-Tensor Completion Method with Applications in Drug Repurposing

Many biomedical challenges can be posed as tensor completion problems where the observed entries of a multidimensional array (a tensor) are used to impute the missing values. In such settings, incorporating side information about the modes of the tensor, such as gene-gene similarity, can significantly enhance the solutions of the completion problem. Most existing tensor completion methods can only incorporate side information in the form of matrices. In this study, we introduce a novel framework to incorporate side information in the form of tensors. Our new approach, called Coupled Tensor-Tensor Completion (CTTC), leverages the hidden connections among multimodal tensors to improve tensor completion performance. In addition to practical utility, CTTC has theoretical foundations in distance metric learning and group theory. We derive an alternating algorithm to solve the CTTC optimization problem and establish its convergence to a stationary point. Finally, we show that CTTC outperforms state-of-the-art tensor completion methods at predicting drug effects. Results: Compared with other tensor completion methods, including HaLRTC, CTRC, Cell, and NTDDR, CTTC demonstrates superior run-time and RSE tensor completion accuracy on two benchmark datasets, DTD and LINCS.

Maryam Bagherian, Albert Hung, Ivo Dinov +1

Department of Mathematics & Statistics, Idaho State University, Physical Science Complex — 921 S. 8th Ave., Stop 8085 — Pocatello, ID 83209 · Computer Science & Artificial Intelligence Laboratory, Massachusetts Institute of Technology · Department of Computational Medicine & Bioinformatics, University of Michigan, Ann Arbor +2

Tensor Completion Learning with Missing Data Tensor Decomposition

Sep 1, 2026cs.LG

Solving In-Table Prediction Problems by Deep Neural Networks with Performance Evaluation Using Synthetic Data

Tabular deep learning (TDL) leverages neural networks (NN) to extract patterns from tabular data. Traditional TDL methods follow a supervised learning paradigm, where a target feature is explicitly given. In this work, however, we explore a different approach by employing deep NNs to learn relationships among individual columns within a given table. We investigate whether NNs can predict the values of arbitrarily selected columns in a given table based on the remaining known columns. We call this problem In-Table Prediction (ITB), which is slightly different from table imputation methods and the pretraining task of TDL. Three potential usage scenarios are identified, which, to our best knowledge, have not been extensively studied in the literature. A self-supervised learning approach is applied to address this problem by randomly selecting columns to be masked out and used as learning targets. This work focuses on tabular datasets containing only continuous features. To handle missing values in continuous features, a novel neural layer is proposed to embed both numerical and empty values. Synthetic data is generated based on predefined column relationships, with empty values inserted using two distinct mechanisms. Additionally, an adapted masking strategy is employed to create test data. Performances of three NN architectures, namely MLP, Resnet and Transformer, are evaluated using the generated synthetic data. We conclude that, the attention-based structure outperforms the other two networks, when a sufficiently large number of training examples is available and a relatively large embedding length is chosen. We stress that these findings are obtained under controlled, synthetic conditions with a small number of columns and it should therefore be regarded as an initial, narrowly-scoped investigation rather than a general characterization of ITP on real-world tabular data.

Xiao Zhao, Daniela Oelke

Institute for Machine Learning and Analytics Offenburg University · Department of Electrical Engineering, Medical Engineering and Computer Science Offenburg University

Learning with Missing Data Tabular ML Tabular Prediction

Sep 1, 2026stat.ML

Semi-Supervised Classification with Informative Missing Labels in Weibull Mixture Models

We consider semi-supervised classification from a partially classified sample arising from a two-component Weibull mixture. The feature is observed for all data, whereas some class labels are missing. The probability of a missing label is modelled as a function of classification uncertainty, giving a feature-dependent missing-at-random (MAR) mechanism that shares parameters with the Weibull-mixture classifier. The missing-label indicators can therefore provide information about the classifier in addition to the observed features and available class labels. Under a common Weibull shape, a Bayes' rule has at most one positive decision boundary, which is unique when the rule is nonconstant; under unequal shapes, it can have two. We characterise these decision regions, derive the Fisher information for the classifier after adjustment for nuisance parameters in the missingness model, and obtain a decision-boundary expansion of the expected error rate of the plug-in sample rule relative to the Bayes error. The expansion yields classification-specific asymptotic relative efficiency formulas for the one- and two-boundary cases and shows that a positive-definite increase in Fisher information is sufficient, but not necessary, for a smaller first-order expected error rate. Numerical studies and a semi-synthetic analysis based on hard-drive failure data illustrate potential reductions in expected error rate and improvements in decision-boundary estimation from modelling feature-dependent label missingness.

Jinran Wu, You-Gan Wang, Geoffrey J. McLachlan

The University of Queensland, Australia

Learning with Missing Data Binary Classification Classification Semi-Supervised Learning

Aug 31, 2026cs.LG

Nonparametric Contextual Pricing and Inventory Learning under Censored Demand

In online retailing, when a product sells out, a retailer often sees only the units sold, not how many customers would have bought it had inventory been available. However, the inventory level determines how much demand is revealed, and this information can influence subsequent decisions and future profits. We study an online selling problem in which, in each round, the seller observes a market context and then makes pricing and stocking decisions based on censored sales data from previous rounds. The challenge is to learn a context-dependent pricing and stocking policy without assuming a particular formula for demand or observing realized profit. To overcome this difficulty, we propose a Mean-Calibrated Kernel UCB (MCK-UCB) algorithm that turns each incomplete sales record into a reliable guide for both inventory and price decisions, using data from past rounds with similar market conditions. This design allows us to learn while serving customers, without a separate exploration phase or the need to recover all demand hidden by stockouts. We prove the minimax optimality of the proposed algorithm, with strictly faster rates when expected profit varies more smoothly with price. Comprehensive numerical experiments have been conducted to confirm the effectiveness of the proposed algorithm.

Zean Han, Jing Liang, Ruihan Lin +2

Department of Industrial Engineering and Decision Analytics The Hong Kong University of Science and Technology

Inventory Control Learning with Missing Data Contextual Bandits

Aug 31, 2026stat.ML

Informative Label Missingness in Multiclass Classification Information Geometry and Excess Risk

Informative label missingness can change the usual efficiency ordering between completely and partially labelled classifiers because the pattern of missing labels may itself carry information about the classification model. We develop a general likelihood-based theory for this phenomenon in parametric multiclass classification. An efficient-information decomposition separates information lost through unavailable class memberships from information contributed by the missing-label mechanism. We then derive a quadratic expansion of plug-in excess risk over the active pairwise faces of the multiclass Bayes boundary, showing that classification efficiency depends on how information gains and losses align with directions that perturb the decision boundary. This yields a classification-weighted generalized-eigenvalue criterion under which informative partial classification may have smaller asymptotic classification risk without globally dominating complete classification in Fisher information. Near missing completely at random, with the marginal missing-label proportion fixed, redistribution of missing labels changes lost class-label information at first order, whereas efficient information from the missingness pattern appears only at second order. Three-class quadratic discriminant calculations, finite-sample experiments, and a semi-synthetic multiclass application illustrate the resulting regime-dependent behaviour.

Fariborz Setoudehtazang, Geoffrey J. McLachlan

Dipartimento di Scienze Statistiche, Universit`a di Padova, Padova, Italy · School of Mathematics and Physics, The University of Queensland, Australia

Information Geometry Learning with Missing Data Multiclass Classification Classification Statistical Learning Theory

Aug 30, 2026stat.ML

A Deep Latent Variable Framework for Jointly Modeling Missingness, Measurement Error, and Heterogeneity

Missing data, measurement error, and population heterogeneity are pervasive challenges in analyzing data arising from modern observational studies and machine learning applications. Although these problems frequently coexist and interact, they are often treated separately in existing works. We propose a unified probabilistic framework that jointly addresses these issues utilizing deep latent variable representation. The proposed method integrates a novel hierarchical tree-routed variational autoencoder with pattern-aware latent representations and calibration-based denoising. The framework accommodates missing data mechanisms, including MCAR, MAR, and MNAR, while simultaneously learning subgroup-specific and globally shared latent structure. The introduced reconvergent routing mechanism enables selective parameters to be shared across related subpopulations, which offers flexibility as well as improved statistical efficiency. Simulation studies demonstrate substantial improvements over existing deep generative imputation approaches under complex heterogeneous missingness and measurement-error settings. The proposed framework provides a principled approach for learning from noisy and incomplete data in modern healthcare and other high-dimensional applications.

Yasin Khadem Charvadeh, Grace Y. Yi, Mithat Gönen +1

Department of Radiology and Diagnostic Imaging, University of Alberta, Edmonton, Alberta, Canada · Department of Statistical and Actuarial Sciences, Department of Computer Science, University of Western Ontario, Ontario, Canada · Department of Epidemiology & Biostatistics, Memorial Sloan Kettering Cancer Center, New York, New York, USA +1

Variational Autoencoders Incomplete Data Imputation Latent Variable Models Learning with Missing Data

Aug 12, 2026cs.LG

Represent, Then Generate: Multimodal-Conditioned Time-Series Generation under Irregular Missingness

Continuous physiological time series underpin modern clinical monitoring, yet many of the most informative signals are invasive, expensive, or simply unavailable for a given patient. Conditional generation offers a remedy: an absent signal can be synthesized from co-recorded signals and routine clinical variables. Existing generators, however, are built around a single conditioning modality and degrade when forced to handle the heterogeneous, irregularly missing mix of time-variant signals and static covariates seen in practice. We propose ReCoGen (Represent Conditions, then Generate), a two-stage framework that decouples multimodal condition representation from target generation. Stage I trains one masked autoencoder per modality, distilling each time-variant condition into a compact and missingness-tolerant token sequence. Stage II trains a flow-matching generator that fuses these tokens with static conditions to synthesize the target signal. Across three physiological benchmarks, including continuous glucose monitoring on AI-READI and arterial blood pressure generation on MIMIC-III and MIMIC-IV, ReCoGen attains the best downstream utility on all sixteen (dataset, task, metric) settings, surpassing six representative conditional generators; on thirteen of them its utility also reaches or exceeds the utility measured on the real signal, a reference we read as an approximate anchor rather than a ceiling. Ablations trace the gains to the conditioning path: learnable cross-attention over the frozen per-modality encoders, and a dual token-plus-AdaLN route for the static conditions. ReCoGen thus turns routinely collected signals into informative surrogates for invasive or unavailable ones, a step toward less invasive, lower-cost continuous clinical monitoring.

Haochen Zhang, Jiaheng Guo, Yu-Chao Huang +2

UNITES Lab, University of North Carolina at Chapel Hill

Learning with Missing Data Time Series Generation Multimodal Generation

Aug 11, 2026cs.LG

GARLIC: Graph Attention-based Relational Learning of Multivariate Time Series in Intensive Care

Healthcare data, such as Intensive Care Unit (ICU) records, comprise heterogeneous multivariate time series sampled at irregular intervals with pervasive missingness. However, clinical applications demand predictive models that are both accurate and interpretable. We present our Graph Attention-based Relational Learning for Intensive Care (GARLIC) model, a novel neural network architecture that imputes missing data through a learnable exponential-decay encoder, captures inter-sensor dependencies via time-lagged summary graphs, and fuses global patterns with cross-dimensional sequential attention. All attention weights and graph edges are learned end-to-end to serve as built-in observation-, signal-, and edge-level explanations. To reconcile auxiliary reconstruction and primary classification objectives, we developed an alternating decoupled optimization scheme that stabilizes training. On three ICU benchmarks (PhysioNet 2012 & 2019, MIMIC-III), GARLIC sets the new state of the art in outcome prediction, significantly improving AUROC and AUPRC over best-performing baselines at comparable computational cost. Ablation studies confirm the contribution of each module, and feature-removal trials validate the fidelity of importance attribution through a monotonic performance drop (full > top 50% > random 50% > bottom 50%). Real-time case studies demonstrate actionable risk warnings with transparent explanations, marking a significant advance toward accurate, explainable deep learning for irregularly sampled ICU time series data. Moreover, we demonstrated \proposed{}'s superiority in data imputation and classification on various time-series datasets beyond the ICU domain, showing its generalizability and applicability to broader tasks.

Ruirui Wang, Yanke Li, Manuel Günther +1

Department of Informatics University of Zürich · SCAI Lab, D-HEST ETH Zürich & SPF

Irregular Time-Series Modeling Graph Attention Networks Time Series Imputation Learning with Missing Data Clinical Outcome Prediction

Aug 10, 2026eess.SY

Closing the loop in learning with missing data

What should a machine learning model learn when data is missing during training? We look at the learning process from a dynamical systems perspective, cast data missingness as a structured loss of actuation that limits controllability of the parameter error dynamics, and ultimately derive adaptation mechanisms with Lyapunov stability characteristics that throttle model updates in ways that preserve learning coherence under partial, intermittent observability. Under recurrent excitation, our analysis provides ISS-type residual-to-state bounds with respect to a bounded closed-loop mismatch between the loss residual and the preconditioned update geometry. We evaluate the efficacy of our directional observability-aware adaptive learning approach on multimodal contexts, reinforcing its premise in promoting learning coherence and stability even in pathologically sparse domains and problems.

Dimitrios Pylorof, Humberto E. Garcia

U.S. Department of Energy Idaho National Laboratory

Learning with Missing Data Adaptive Learning

Aug 6, 2026stat.ML

Handling Missing Data in Probabilistic Regression Trees

Probabilistic Regression Trees (PRTrees) are a smooth and consistent alternative to classical regression trees, producing continuous predictions through probabilistic split assignments. This paper extends the PRTree framework to accommodate missing predictor values directly during tree construction, eliminating the need for prior imputation. Three strategies are proposed, each exploiting the available information differently: a uniform-probability approach, a partial-observation approach, and a dimension-reduced smoothing approach. These modifications are defined to preserve the fundamental probabilistic properties of the original methodology, including probability conservation and marginal compatibility, under arbitrary patterns of missing covariate values. The proposed methods are evaluated on several real-world datasets exhibiting different levels of missingness and are compared with classical regression trees. The results show that the effectiveness of probabilistic tree construction depends strongly on the treatment of missing observations. Across the considered datasets, the fill strategy emerged as the dominant modeling component, often exerting a larger influence on predictive performance than either the smoothing distribution or the proxy-selection criterion. In datasets where a substantial proportion of observations contained missing predictor values, the proposed methods frequently outperformed CART, while maintaining the interpretability and flexibility of tree-based models.

Taiane Schaedler Prass, Alisson Silva Neimaier, Guilherme Pumi

a Graduate Program in Statistics - Universidade Federal do Rio Grande do Sul.

Learning with Missing Data Decision Tree Learning Tabular Regression

Aug 6, 2026stat.ML

Deep Generalised Mixed Models: a Novel Neural Network Structure for Analysing Hierarchical Data

The experience sampling method (ESM) is a longitudinal research design where participants report their thoughts, emotional states and behaviours multiple times a day. Our work is motivated by such data collected by the GrowIt! app, which was released to investigate daily emotions among adolescents during the COVID-19 pandemic. Current procedures to analyse ESM data face various challenges. While standard statistical techniques may not scale well to a high-dimensional setting, machine learning procedures can give biased results due to selection bias introduced by missingness. In our motivating dataset, adolescents dropped out due to previous strong feelings of negative emotions. Hence, the implied missing data are of the missing-at-random type that standard machine learning procedures cannot accommodate. We develop a novel neural network architecture that generalises mixed effects models to deep learning to overcome these challenges. It allows semi-parametric and flexible modelling of data's mean and correlation structure through fixed and random effects. For estimation, we use an adaptation of variational auto-encoders and a Bayesian data augmentation algorithm. Through this approach, the model can accommodate longitudinal outcomes following generic distributions, scale well to high-dimensional settings and provide valid inference when data are missing-at-random. We applied the Deep Generalised Mixed Model to the GrowIt! study and various simulations. The results show potential for the Deep Generalised Mixed Model, yet suboptimal performance due to model instability.

Nina van Gerwen, Dimitris Rizopoulos, Manon Hillegers +2

Department of Biostatistics, Erasmus University Medical Center, the Netherlands · Department of Epidemiology, Erasmus University Medical Center, the Netherlands · Department of Child Psychiatry, Erasmus University Medical Center, the Netherlands +1

Learning with Missing Data Mixed-Effects Models

Aug 4, 2026cs.LG

CRS-Triage: Confidence- and Reliability-Aware Selective Triage under Incomplete Clinical Evidence

Emergency triage requires reliable decisions within a short time period. However, the available electronic health record (EHR) data, including structured data and clinical text, are often incomplete, unreliable, and inconsistent. This makes machine learning (ML)-based triage prediction more challenging, as existing ML models typically rely on complete and reliable EHR data to accurately predict patients' acuity levels. To address this, we propose confidence- and reliability-aware selective triage (CRS-Triage) to predict patients' acuity levels with a confidence score. By comparing the confidence score with a predefined threshold, CRS-Triage can selectively determine whether the model should make the decision or defer the case. Specifically, CRS-Triage separately evaluates the reliability of structured data and clinical text and then jointly considers the consistency between the two modalities to estimate the confidence of each prediction. Moreover, to reduce the risk of missing high-acuity patients, namely under-triage, CRS-Triage prefers to assign patients slightly higher acuity levels, namely over-triage, by penalizing under-triage errors. Experiments on the MIMIC-IV-ED dataset show that CRS-Triage achieves strong predictive performance. It also provides a better risk-coverage trade-off and remains reliable when the available EHR data are incomplete, degraded, or inconsistent across modalities.

Guan Qiang, Yushen Chen, Tianlong Liu +3

Western University, London, Ontario, Canada · Centre for Addiction and Mental Health, Toronto, Ontario, Canada

Selective Prediction Clinical Triage Learning with Missing Data Electronic Health Records

Aug 3, 2026cs.LG

From fragmented data to actionable design: Physics-calibrated learning for plastic upcycling

Thermochemical upgrading of plastic waste is a key upcycling pathway, yet the experimental literature is fragmented by heterogeneous conditions and incomplete reporting. Complete-case learning would retain only 10.99% of the curated experiments, while target imputation can introduce biased supervision. Here we develop a Physics-Calibrated, Missingness-Gated, and Load-Balanced Mixture-of-Experts (PC-MG-MoE) framework that converts structured missingness into an informative learning signal. PC-MG-MoE learns directly from partially observed experiments without target imputation, reconstructs physically consistent product distributions, accommodates cross-laboratory heterogeneity, and provides interpretable model behaviour rather than black-box prediction alone. Under stringent source-grouped validation, it achieved the lowest aggregate absolute error among the evaluated models, supporting engineering screening under cross-laboratory heterogeneity. Wet-lab experiments provide an external comparison, showing key composition-dependent trends. Implemented as an interactive web-based workflow, PC-MG-MoE enables forward screening, physics-grounded constrained inverse design, targeted experimental planning that supports reduced experimental workload and trial-and-error, and laboratory-specific adaptation with new platform-specific data. This work establishes a transferable framework for converting fragmented literature data into experimentally actionable guidance for model-guided plastic upcycling and broader thermochemical systems.

Jingyang Bai, Zijia Wang, Xiangyi Long +3

Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK · Department of Electrical and Electronic Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK · Interdisciplinary Research Center for Refining and Advanced Chemicals, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia +4

Mixture of Experts Learning with Missing Data Physics-Informed ML

Aug 3, 2026cs.LG

GLAIM: Learning Global and Local Adaptive Inter-Variable Dependency for Multivariate Time Series Imputation

Multivariate time series imputation is fundamental to downstream analysis, yet modeling inter-variable dependencies with incomplete observations remains challenging. Existing methods learn global dependencies across samples or dynamic local dependencies per sample. Global dependencies are stable but adapt poorly to sample variations and temporal non-stationarity, whereas local dependencies are adaptive yet unreliable when observations are insufficient, causing erroneous information propagation. To address these limitations, we propose GLAIM, a Global-Local Adaptive Inter-variable Dependency Modeling framework for multivariate time series imputation. GLAIM comprises two complementary components. The Stable Global Dependency Constructor derives robust global inter-variable dependencies from complementary temporal representations, providing a stable backbone less affected by sample-specific missingness and noise. The Sample-Conditioned Dependency Refiner adapts this backbone to each sample and time step using its temporal state and available observations, enabling reliable local refinement under incomplete observations. Extensive experiments on nine real-world datasets demonstrate that GLAIM achieves state-of-the-art performance under random and block missingness, remains robust to missing-rate shifts, and benefits from its complementary global and local components. Code is available at https://github.com/LuRenjias/GLAIM.

Mingyang Wang, Rongwen Li, Xiao Wang +1

College of Computer Science and Electronic Engineering, Hunan University, Changsha, Hunan, China

Time Series Imputation Learning with Missing Data

Jul 30, 2026cs.LG

Flow Matching with Missing Data

Flow matching assumes fully observed training data, which many real-world applications rarely provide. We propose Missing-Data Flow Matching, which treats the missing coordinates of training samples as latent variables and averages the flow matching loss over the values they could take. We first prove the correction is exact rather than approximate. Under missing completely at random with true completions, the incomplete-data objective equals the complete-data objective, so missingness changes nothing about what flow matching learns and the entire difficulty relocates to the completion model. Our finite-sample analysis then answers design questions that the algorithm leaves open, and the answers are not the ones intuition suggests. Missingness transfers estimator variance rather than adding it, one completion per example already matches complete-data variance exactly, and under a fixed evaluation budget one completion is optimal. A learned completion model contributes a single irreducible bias, which we bound by its expected conditional Wasserstein distance to the true completion law. Experiments numerically validate the theoretical predictions, show that deterministic rather than frozen imputation is what collapses the generated distribution, and place our method alongside strong classical and deep imputation baselines on real tabular data.

Fairoz Nower Khan, Nabuat Zaman Nahim, Peizhong Ju

Department of Computer Science, University of Kentucky

Flow Matching Incomplete Data Imputation Learning with Missing Data

Jul 28, 2026cs.LG

Mind the Missing Split: Resolving Feature Heterogeneity in Swarm Learning with Random Forests

Swarm Learning is a decentralized collaborative learning mechanism that allows multiple organizations to train a shared model without central coordination or direct data sharing. In typical horizontal Swarm Learning, datasets across sites are usually assumed to share the same feature set. However, in real-world applications, sites often have partially overlapping features because measurements, protocols, and available covariates differ across sites. This feature heterogeneity creates a practical issue for machine learning algorithms such as Random Forests. Specifically, when decision trees are pooled into a global Random Forest, inference at a given site can become ill-defined if a traversal encounters a split on a feature that is not available locally, often forcing organizations to discard site-specific variables upfront. In this paper, we address feature heterogeneity in Swarm Learning with Random Forests under partially overlapping feature spaces. We propose several deterministic and probabilistic inference-time strategies that resolve such missing splits without restricting training to the intersection of features. We evaluate the methods on nine datasets and demonstrate that they outperform both the intersection baseline and locally trained models across a broad range of scenarios.

Mohammad Tajabadi, Dominik Heider

Institute of Medical Informatics, University of Münster, Münster, Germany

Learning with Missing Data Decentralized Learning Decision Tree Learning Random Forest Heterogeneous Federated Learning

Jul 25, 2026cs.LG

FILLER: Feature Imputation via Latent Location Exploration and Retrieval

In real-world machine learning applications, incomplete observations create a fundamental challenge. Researchers have come up with several ideas to address this crucial problem. However, current models still face challenges in balancing scalability and structural consistency. This study proposes a feature imputation method, called FILLER, that deliberately searches the two-dimensional latent space produced by a generative model and fills the missing values with appropriate entries. The generative model is trained on fully observed data to generate samples from the latent space, and FILLER uses this trained model to impute the values missing in the corrupted test samples. In this study, G-NeuroDAVIS serves the purpose of the generative model. This work also presents a mathematical proof on the convergence of the iterative search. Finally, FILLER has been evaluated on several image datasets under random and structured missingness patterns with varying levels of imputation complexities. In order to justify the efficacy of FILLER, it has been compared against existing state-of-the-art solution strategies in terms of RMSE, PSNR, and SSIM. In addition, Wilcoxon signed-rank test has been carried out to validate statistical significance. Moreover, downstream analyses (classification and clustering) have also established the quality of imputation in terms of standard metrics.

Santu Mondal, Chayan Maitra, Rajat K. De

Machine Intelligence Unit Indian Statistical Institute 203 Barrackpore Trunk Road Kolkata 700108

Incomplete Data Imputation Learning with Missing Data Image Inpainting Latent Space Optimization

Jul 24, 2026cs.LG

MissHyper: Restoring Clinical Synchronicity in Missingness-Guided Hypergraph Forecasting

Clinical irregular multivariate time series are shaped not only by physiological dynamics but also by the measurement process that determines when and what to observe. In event-centric models, however, co-timestamp structure can be flattened too early: measurements acquired at the same timestamp are embedded as isolated nodes, leaving local patient-state context unavailable until later message-passing layers. We study this pre-propagation representation bottleneck and address it by restoring co-timestamp context before message passing begins. We propose MissHyper, a missingness-guided hypergraph forecasting model with pre-propagation synchronicity restoration. MissHyper augments each event with a local support-density cue, aggregates co-timestamp records to recover patient-state context, and uses a missingness-guided gate to adaptively fuse node-specific evidence with the recovered context. Across PhysioNet 2012, MIMIC-III, and MIMIC-IV, MissHyper achieves consistent gains in multi-step forecasting and outperforms a strong hypergraph baseline. These results suggest that improving event initialization can benefit sparse clinical forecasting without requiring a redesigned downstream propagation architecture. Ablations indicate that snapshot restoration, adaptive fusion, and support-density encoding all contribute, pointing to event initialization as a critical design axis for sparse clinical forecasting.

Mingyi Ma, Qingxiong Tan

Academy of Advanced Interdisciplinary Studies Wuhan University · Institute for Mathematics & Artificial Intelligence Wuhan University

Irregular Time-Series Modeling Multivariate Time Series Forecasting Learning with Missing Data Hypergraph Neural Networks Longitudinal EHR Modeling

Jul 21, 2026cs.LG

Incomplete Observations Boost Evolutionary Performance in Ocean Modeling

Data-driven methods have revolutionized ocean modeling, yet current approaches rely heavily on complete reanalysis datasets, imposing computational constraints and limiting model performance to that of the training data. Here, we present a generative state-space model and an optimization framework that enable learning directly from sparse and noisy observations. The model is essentially a hidden Markov model with a continuous state space, where oceanic physical quantities are treated as hidden states and measurements as observations, enabling a unified representation of ocean fields and observational data. Both the initial-state and state-transition modules are implemented as neural networks to capture the complexity and temporal evolution of ocean states, while the emission module is formulated as a masked Gaussian distribution. To train the model from sparse observations, we derive an optimization framework based on the expectation-maximization (EM) algorithm. The framework alternately reconstructs high-fidelity ocean fields via Langevin dynamics and optimizes deep neural networks to capture temporal evolution. Theoretical analysis shows that the framework maximizes the likelihood of observations under the generative model. For efficiency, we assume that ocean-state evolution follows a stationary, ergodic, and Markovian stochastic process and adopt only length-two state sequences during optimization. Experiments on CMIP6 simulation data and FY-3D satellite data demonstrate high-fidelity reconstruction and accurate prediction, showing that sparse observations can directly improve the model's representation of ocean-state dynamics. This work offers a scalable pathway for next-generation Earth system models to learn directly from sparse, incomplete real-world observations.

Yangyang Kong, Yutong Jiang, Yanhai Gan +3

State Key Laboratory of Physical Oceanography, Ocean University of China, Qingdao, China · School of Computer Science and Technology, Ocean University of China, Qingdao, China

Learning with Missing Data Data Assimilation Hidden Markov Models State Space Models

Jul 15, 2026cs.LG

Learning Who to Treat When Treatment is Missing

Policy learning methods are increasingly used to inform treatment allocation under budget constraints. Most proposed methods assume complete treatment data, yet applications frequently suffer from missingness that can bias estimates and lead to suboptimal policies. We address this gap by extending efficient estimators for average treatment effect (ATE) estimation to policy value and conditional average treatment effect (CATE) estimation under missing at random (MAR) and missing completely conditionally at random (MCCAR) treatment data. Through asymptotic efficiency analysis, we prove that the MAR estimator, which leverages partially-observed units, is both valid and more efficient than the MCCAR estimator when MCCAR assumptions hold. This result provides formal justification for preferring MAR-based estimation in policy learning under both missing data settings. Our comprehensive experiments using synthetic and semi-synthetic datasets confirm that correctly specifying the missingness mechanism is crucial: misspecified estimators remain biased regardless of sample size, while our estimators achieve near-oracle performance when assumptions are satisfied. Our work provides practitioners with theoretically grounded, empirically validated tools for robust policy learning in the presence of missing treatment data.

Johnna Sundberg, Rayid Ghani, Eli Ben-Michael +1

Carnegie Mellon University, Pittsburgh, Pennsylvania

Causal Effect Estimation Conditional Average Treatment Effect Estimation Learning with Missing Data Policy Optimization

Jul 13, 2026q-bio.NC

Imputation-free transformer learning enables robust Alzheimer's disease prediction and calibrated uncertainty quantification across heterogeneous clinical cohorts

Accurate diagnostic classification and disease-severity prediction for Alzheimer's disease are hampered by the incompleteness and heterogeneity of real-world clinical data. Left unaddressed, these barriers prevent reliable disease modelling and hinder effective clinical evaluation. Conventional imputation strategies introduce systematic bias, distort inter-feature relationships, and yield overconfident predictions, limitations especially consequential in diagnostic settings. Here, we propose NITROGEN, an imputation-free transformer that jointly models within-patient feature dependencies and between-patient relational structure through masked and intersample attention, enabling robust multimodal learning directly from partially observed records. We trained NITROGEN on ADNI (N=7858 scans), and evaluated it on two independent cohorts: OASIS-3 (N=2675 scans) and AIBL (N=1286 scans). Across cohorts and diagnostic and cognitive score prediction tasks, NITROGEN showed robust calibration and uncertainty quantification advantages over tree-based ensemble methods, while maintaining competitive discriminative performance. Cross-cohort and cross-method analyses identified cortical thickness in the temporal pole, age, and APOE genotype as important, though not individually sufficient, features for AD classification. We further introduced a modality-aware uncertainty adjustment that augments predictive uncertainty proportionally to the importance of absent modalities, enabling calibrated confidence when diagnostic information is unavailable. Together, our results show that imputation-free attention learning preserved meaningful discrimination under cohort shift, revealing expected degradation on more distributionally different cohorts, and demonstrate that evaluating models along calibration, interpretability, and cross-cohort reliability, not accuracy alone, is essential for clinical deployment.

Christelle Schneuwly Diaz, Narmina Baghirova, Duy-Thanh Vu +4

Platform of Bioinformatics, Lausanne University Hospital. · Faculty of Biology and Medicine, University of Lausanne. · 3Leenaards Memory Centre, Lausanne University Hospital. +1

Missing-Modality Learning Learning with Missing Data Clinical Outcome Prediction Alzheimer's Disease Classification Neuroimaging Alzheimer's Disease Progression Prediction+1

Jul 10, 2026cs.LG

A Personalized Computational Framework for Assessing the Sufficiency of Partially Observed Data in Healthcare AI models

Achieving early and timely diagnosis and treatment for disease is a major challenge. Recent applications of machine learning (ML) algorithms trained on patient data have shown promise in many different settings for predicting the patient health state. A challenge often faced when applying these ML algorithms is that at any given time, not all clinical variables (features) needed as input to perform prediction tasks are available. We define the concept of full-feature-capacity (FFC) to refer to prediction performance when such algorithms make use of all features on which they were trained. We then introduce Feature Sufficiency Analysis (FSA) - an analysis for determining whether a subset of all clinical features needed by an AI model is sufficient to achieve FFC. FSA estimates the underlying distributions of missing variables conditioned on features that are available. FSA provides a patient-specific assessment of whether the existing set of measured features achieves FFC. If yes, then there is no need to acquire further inputs and a ML-based prediction. We provide two case studies: prediction of need for postoperative prolonged ventilation in patients recovering from heart surgery; 10-year mortality prediction in an outpatient cohort. We also demonstrate that FSA also provides a clinically interpretable feature-ranking methodology based on prediction sufficiency, identifies intrinsically hard-to-predict patient populations, and has the potential to perform cost-aware optimization for clinical data acquisition. FSA provides a generic computational approach for determining whether incomplete clinical information is sufficient to support trustworthy AI-assisted clinical decision-making, thereby facilitating the prospective deployment of healthcare AI systems across diverse clinical settings.

Qingchu Jin, Felistas Mazhude, Jamie B. Rabb +3

Roux Institute, Northeastern University, ME USA · MaineHealth Institute for Research, ME USA · MaineHealth, ME USA +3

Learning with Missing Data Clinical Outcome Prediction Clinical Decision-Making Clinical Risk Prediction

Jul 10, 2026eess.IV

Beyond Metadata: CAPRA for Hidden Subgroup Analysis under Missing Metadata in Medical Imaging

Medical imaging models are often deployed without the demographic, acquisition, and quality metadata needed for subgroup auditing. Once those metadata disappear, clinically critical failure modes can be masked by strong aggregate performance, and many robust-learning methods lose the group structure they rely on. We present CAPRA, a calibrated proxy-axis framework for hidden subgroup analysis under missing metadata. CAPRA predicts image-derived semantic axes, calibrates axis posteriors on a small metadata-labeled split via patient-level cross-fitting, and organizes those posteriors into a calibrated subgroup interface that supports both deployment-time failure analysis and downstream robust learning without requiring subgroup labels at deployment. Across fundus, dermoscopy, and chest radiography, CAPRA reveals disparity patterns missed by metadata-only slicing, remains informative under dataset shift, and produces subgroup partitions that align more closely with explicit failure axes than image-only or latent-slice baselines. The same interface can also be reused by downstream robust learners, although those gains are domain-dependent. Overall, CAPRA turns hidden subgroup analysis under missing metadata into a calibrated, interpretable, and reusable subgroup interface for deployment-time analysis and robust transfer.

Yawen Li, Yan Li, Zhe Xue +3

Beijing University of Posts and Telecommunications Beijing, China

Medical Image Analysis Learning with Missing Data

Jul 9, 2026cs.LG

Pattern-Aware Graph Neural Networks for Handling Missing Data

Missing data is ubiquitous in real-world datasets. Traditional methods either discard incomplete samples or apply imputation techniques that ignore potentially informative missingness patterns, implicitly assuming that missingness occurs randomly. However, missingness patterns might provide additional information. We propose pattern-aware graph neural networks that explicitly encode which features are missing alongside observed values. We used four encoding strategies -- learned embeddings, frozen random embeddings, statistical features, and hierarchical representations -- across seven UCI datasets with naturally occurring missingness. Our Pattern-aware methods achieve substantial improvements over baselines, with an average improvement of 17% in balanced accuracy and 22% in F1-macro across all datasets. The benefits vary significantly by dataset: annealing shows dramatic improvement (+80% balanced accuracy), while hepatitis and soybean show minimal gains (+4--5%). Notably, even simple random pattern embeddings perform comparably to learned embeddings (0.650 vs 0.663 balanced accuracy), suggesting that distinguishing between patterns may be more important than task-specific optimization. Our ablation study reveals that attention mechanisms, while helpful, are not critical when pattern information is available -- simple mean aggregation with pattern awareness achieves 0.640 balanced accuracy compared to 0.645 for attention-based variants.

Minett Tran, Taehee Jeong

San Jose State University

Graph Neural Networks Learning with Missing Data Tabular Classification

Jul 8, 2026cs.CV

General Incomplete Multimodal Learning via Dynamic Quality Perception

Multimodal learning robust to missing modalities is essential for real-world applications. Existing methods mainly focus on inter-modality missing, where entire modalities are absent, while overlooking intra-modality degradation, where modalities are present but severely corrupted. In practice, these two types of missing often coexist, making existing approaches ineffective. To address this limitation, we propose General Incomplete Multimodal Learning (GIML), a unified framework that simultaneously handles both inter-modality missing and intra-modality degradation through dynamic quality perception. Specifically, GIML models heterogeneous missing patterns as continuous modality information degradation, enabling degradation-aware adaptive fusion. To achieve reliable quality perception, we introduce a Noise-aware Quality Estimator that learns the mapping from corrupted features to noise intensity through controlled noise injection. Furthermore, we propose a Noise-Semantic Decoupled module that separates semantic information from noise interference. This improves robustness and generalization to unseen corruption patterns. Extensive experiments across datasets with diverse modality types demonstrate the effectiveness and generality of GIML. Code is available at: https://github.com/Yu-Five/GIML.

Xiangyu Meng, Shicai Wei

University of Electronic Science and Technology of China

Missing-Modality Learning Multimodal Robustness Learning with Missing Data Multimodal Fusion

Jul 8, 2026cs.LG

Imputation Meets Clustering: Exploiting Latent Subgroup Structure for Missing Data Recovery

Missing data is prevalent in practical applications, making effective imputation an essential preprocessing step for downstream analysis. Real-world datasets often exhibit complex latent structures composed of multiple subgroups with distinct distributions. However, existing methods often overlook such population heterogeneity. Without explicit structural guidance, these methods tend to produce generic estimates that blur subgroup boundaries and lack instance-level fidelity. While incorporating subgroup information offers a remedy, it faces a circular dependency: reliable subgroup identification requires complete data, while data completion is the imputation objective itself. To resolve this, we propose CAGI (Cluster-Aware Generative Imputation), a framework that reformulates clustering and imputation as a mutually reinforcing co-optimization process. CAGI employs a ``Partition-Guide-Restore'' strategy where dynamic cluster assignments act as local priors to condition a Generative Adversarial Network. An iterative feedback loop is established to progressively refine both cluster structures and imputed values toward faithful subgroup distributions. To ensure distributional stability, CAGI further employs a multi-level optimization objective combining instance-level reconstruction with distribution-level regularization. Extensive experiments on 14 benchmark datasets with 15 representative baselines demonstrate the superiority of CAGI. The source code is available at: https://github.com/supercocachii/CAGI

Chuyao Zhang, E Li, Taochen Chen +5

Guangdong University of Technology, Guangzhou, China · Hong Kong Baptist University, Hong Kong, China

Incomplete Data Imputation Learning with Missing Data Unsupervised Clustering

Jul 4, 2026cs.LG

SHIFT: Survival Prediction from Incomplete and Heterogeneous Genomic Data

Genomic prediction models often fail to transfer across institutions because sequencing panels differ across sites, creating structural feature missingness at deployment. Existing approaches to this challenge typically restrict analysis to genes shared across cohorts, exclude patients with incomplete profiles, or rely on test-time imputation, all of which can reduce robustness and limit the use of multi-center data. We propose Survival prediction Handling Incomplete Features using Transformer (SHIFT), a missingness-aware survival model that directly predicts from incomplete genomic inputs without test-time imputation. SHIFT represents each genomic feature separately and uses masked self-attention, along with a feature-availability mask, so that predictions are based only on observed inputs. Further, we introduce variable-rate feature masking during training to improve robustness to heterogeneous missingness patterns. We evaluate the approach on glioblastoma and lung squamous cell carcinoma with external validation across multiple cohorts, including a challenging setting with severe cross-cohort panel mismatch. Across these settings, SHIFT shows strong generalization and compares favorably with standard survival baselines and imputation-based approaches, while using a single model across differing feature sets. We also find that incorporating patients from incomplete cohorts during development can improve performance on external data, suggesting that partially observed cohorts need not be excluded from model building. These results support missingness-aware modeling as a practical strategy for multi-center survival prediction in precision oncology.

Muhammet Sami Yavuz, Ayhan Can Erdur, Sabri Mustafa Kahya +2

AI for Image-Guided Diagnosis and Therapy, School of Medicine and Health, Technical University of Munich (TUM), Munich, Germany · Munich Center for Machine Learning (MCML) · Department of Radiation Oncology, TUM University Hospital +4

Cancer Genomics Cancer Survival Prediction Transformer Survival Analysis Learning with Missing Data Oncology+2

Jul 3, 2026stat.ML

Missing Data Imputation under Manifold Hypothesis

The manifold hypothesis posits that high-dimensional data are concentrated near a low-dimensional embedded manifold. Recent advances in mixture variational autoencoders (VAEs) provide a powerful tool for extracting such underlying structure in a faithful manner. The resulting geometric structure naturally introduces local and global relationships among variables, thereby providing a systematic way of imputing missing data. We propose a model-based imputation method that enables sampling from

p(\bm{x}_{\mathrm{mis}} \mid \bm{x}_{\mathrm{obs}})

via a sampling-importance-resampling (SIR) procedure, which can be further augmented with a joint diffusion model in the latent space. Our method imputes missing data while respecting the underlying geometry, achieves competitive performance compared to state-of-the-art procedures, quantifies uncertainty in the imputations, and is model-based, thereby enabling on-the-fly imputation without rerunning the entire procedure.

Zelong Bi, Amuchechukwu Ibenegbu, Sarat Moka

Incomplete Data Imputation Learning with Missing Data

Jun 30, 2026stat.ML

MNAR- $k$ -means: A $k$ -means Clustering for Data Missing Not at Random with Magnitude-Decaying Probability

The classical

k

-means clustering, based on distances computed from all data features, cannot be directly applied to incomplete data with missing values. A natural extension of

k

-means to missing data is to involve only the observed positions in clustering, which is equivalent to imputing missing values by corresponding cluster means. However, for data missing not at random (MNAR), since missingness is related to data values, such a mean-imputation-based method may lead to the distortion of estimated cluster centers, resulting in a poor clustering result. Since MNAR mechanisms are very common in reality, it is necessary to improve the performance of

k

-means-based clustering methods for such data. In this paper, we focus on a magnitude-decaying MNAR scenario where data is more likely to be missing at positions with smaller absolute values, and we propose a novel

k

-means clustering method based on the constraint of the size of imputation values, which enjoys a good mathematical interpretation. Moreover, we establish the statistical consistency of the estimated cluster centers of the proposed method to the true cluster centers of fully observed data, and solve the optimization of the proposed loss function via an alternative minimization algorithm. Simulation experiments verify the effect of the proposed method in improving clustering results and reducing the bias of estimated cluster centers. Applications to real-world missing data further show the utility of the proposed method.

Xin Guan

Graduate School of Information Sciences Tohoku University Sendai, Miyagi 980-8579, Japan

Clustering Learning with Missing Data Unsupervised Clustering

Jun 29, 2026cs.CV

Residual-Guided Expert Specialization for Incomplete Multimodal Learning

As real-world prediction systems often face missing modalities at inference, incomplete multimodal learning (IML) remains a practical challenge. While prior methods aim to learn representations robust to missing inputs, representations from incomplete modalities inevitably deviate from their full-modality counterparts due to missing evidence. To explicitly leverage these deviations, we propose MARS (Missingness-Aware Residual-guided Specialization), a mixture-of-experts framework that guides expert specialization based on how representations are reshaped by missingness. By contrasting task representations derived from incomplete inputs with their complete counterparts during training, we derive a privileged residual signal that captures this representational gap. The residual signal guides a residual router to assign samples to experts specialized for the corresponding deviation patterns. In parallel, a feature router learns to imitate this routing behavior using only incomplete inputs, enabling deployment without access to full modalities. To mitigate this train-test router gap, we develop a discrepancy-aware noise regularization that adaptively perturbs the residual router's decisions when the feature router deviates, enhancing expert robustness under imperfect imitation. Experiments on multimodal classification (CASIA-SURF, CREMA-D, UPMC Food-101) and segmentation (MCubeS) under missing scenarios show that MARS consistently surpasses baselines while remaining efficient and extensible to diverse backbones and tasks.

Seunghun Baek, Jihwan Park, Jaeyoon Sim +3

Pohang University of Science and Technology (POSTECH), South Korea

Missing-Modality Learning Multimodal Robustness Learning with Missing Data Multimodal Classification Mixture-of-Experts Models

Jun 18, 2026stat.ML

Off-Policy Evaluation for Missingness-Aware Policies in MDPs with Rewards Missing Not at Random

In offline Reinforcement Learning, immediate rewards in logged batch data are often unobserved due to sparse or irregular record-keeping, or censored beyond certain reward values. This issue arises in practical settings, including health care and marketing. We investigate off-policy evaluation (OPE) in finite-horizon Markov decision processes when rewards are missing not at random (MNAR), which breaks ignorability and induces selection bias even after conditioning on states and actions. To address this, we formalize a reward-dependent propensity model and use future states as shadow variables to identify the full-data conditional mean reward. We further introduce a bridge function that recovers the conditional mean reward without explicitly modeling the MNAR mechanism, and estimate it via a min-max procedure to avoid double sampling. Building upon these identification results, we propose an Fitted-Q-Evaluation-style estimator that propagates the recovered rewards while allowing target policies to depend on past missingness indicators. Finally, we establish consistency and finite-sample error bounds for our OPE estimator, and show through experiments the strong performance of our method compared to existing methods on simulated and MIMIC-III Sepsis data.

Ziheng Wei, Annie Qu, Rui Miao

Department of Statistics, University of Michigan at Ann Arbor · Department of Statistics and Applied Probability, University of California at Santa Barbara · Department of Mathematical Sciences, University of Texas at Dallas

Reinforcement Learning Off-Policy Evaluation Learning with Missing Data Offline RL

Jun 14, 2026cs.LG

Unsupervised Learning for Missing Modalities in Multimodal Learning

This paper addresses the missing-modality challenge in multi-modal learning by introducing Unsupervised Learning for Missing Modalities in Multi-Modal Learning (UL4M4), a flexible framework that imputes missing feature embeddings in a task-independent manner before supervised prediction. We propose modality-specific normalization and a novel partial-modality distance metric to enable fair clustering of incomplete observations, capturing cross-modal structures while preserving scale-invariance across varying dimensionalities and modality counts. Cluster centers from this unsupervised stage guide an iterative greedy imputation process for any missing modalities during training or inference, supporting arbitrary numbers of modalities and arbitrary missing patterns per sample. The imputation module is lightweight, uses frozen encoders, and decouples from the downstream task, allowing easy integration with any fusion/prediction architecture. Extensive experiments under diverse and highly incomplete regimes demonstrate UL4M4's robustness, achieving, to the best of our knowledge, the first consistent F1-Micro scores above 0.7 on challenging missing configurations even when more than 50% of modality slots are missing. Results are also stable across cluster sizes and significantly outperform state-of-the-art baselines. Code is available here: https://github.com/h-ismkhan/Multimodal-Learning-with-Missing-Modalities-via-Unsupervised-Learning.

Hassan Ismkhan, Hamid Bouchahcia

Bournemouth University Bournemouth, UK

Missing-Modality Learning Unsupervised Learning Learning with Missing Data Multimodal Learning

Jun 8, 2026cs.CL

In-Context Learning for the Imputation of Public Opinion Data with Large Language Models

Large language models have been widely evaluated as simulators of individual survey responses. In practice, however, fully unobserved responses are rare; the dominant problem is partial non-response. Imputation aims to restore the overall structure of a survey dataset by filling in these missing values. It has its own well-defined evaluation criteria and differs fundamentally from prediction. We propose to impute missing survey data through in-context learning (ICL). We systematically evaluate ICL design choices across different missingness mechanisms (MCAR, MAR, MNAR) on 150 opinion variables spanning 15 waves of the American Trends Panel. Compared to well-established statistical methods for data imputation like MICE PMM, our ICL approach consistently reduces absolute error across all missingness mechanisms, with the largest gains under non-random missingness (MNAR). Notably, the best-performing specification (gpt-oss-120b with 100 in-context examples) achieves near-nominal aggregate coverage (approaching the 95% level) with confidence intervals two to five times narrower than MICE PMM. We publish a Python package with an sklearn-like API to enable easy deployment of our method using local and proprietary LLMs.

Tobias Holtdirk, Georg Ahnert, Joseph W Sakshaug +1

LMU Munich · Munich Center for Machine Learning · University of Mannheim +2

Incomplete Data Imputation Learning with Missing Data In-Context Learning Tabular ICL

Jun 4, 2026cs.LG

PAMF: Prior-Aware Multimodal Fusion for Incomplete Time Series Data

In healthcare, multimodal time series tasks often operate on incomplete observations in practice, for example when ECG segments are lost because electrodes detach or an entire respiratory channel is unavailable during overnight monitoring. Such missingness typically appears in two structurally distinct patterns: within-modality missing, where values are absent within an otherwise observed modality, and modality-level missing, where an entire modality is unavailable. Existing methods typically represent unobserved data implicitly through masks or missing embeddings, without learning instance-specific missing information, and most are designed for only one missingness pattern. A natural approach is to explicitly estimate the missing data; however, existing imputation methods treat missingness uniformly despite their different structural priors, and the imputation process is often isolated from downstream tasks, preventing downstream tasks from guiding imputation toward more informative representations. To address these limitations, we present PAMF, a multimodal time-series framework that explicitly handles different missingness patterns while coupling imputation with downstream prediction through prior-aware flow matching and weight sharing. Specifically, the method initializes the flow-matching source state with type-specific priors to distinguish two missing types. It further connects imputation and classification through architecturally matched encoders with weight sharing, transferring task-relevant representations into the imputation process. Experiments on multiple multimodal healthcare time-series benchmarks show that the proposed method achieves the strongest overall downstream performance across diverse datasets and missing settings compared with existing baselines.

Ziwen Kan, Wugeng Zheng, Tianlong Chen +1

Department of Computer Science, University of Central Florida · Department of Computer Science, University of North Carolina at Chapel Hill

Missing-Modality Learning Flow Matching Time Series Imputation Learning with Missing Data Multimodal Classification Multimodal Fusion

Jun 3, 2026stat.ML

TabSODA: Tabular Diffusion based Imputation with Skip Pattern Detection and Ordinal Awareness

Missing data imputation in large-scale surveys faces two challenges that are not well handled by current tabular diffusion methods. First, \emph{structural skips}, cells made inapplicable by questionnaire design, should not be imputed but are often conflated with item nonresponse. Second, \emph{ordinal} responses encode ordered categories, yet most pipelines treat them as nominal levels through one-hot or analog-bit encodings. We introduce \textbf{TabSODA} (\textbf{Tab}ular diffusion with \textbf{S}kip pattern detection and \textbf{O}r\textbf{d}inal \textbf{A}wareness), an Expectation-Maximization (EM)-based diffusion imputer built on the Elucidated Diffusion Model (EDM) framework. TabSODA propagates structural skips through the denoising loss and reverse-time sampler, and represents ordinal variables with cumulative-probit scalar latents while retaining analog-bit encodings for nominal variables. When a codebook skip mask is available, TabSODA uses it directly; otherwise, the TabSODA+SKIP variant estimates the mask from raw responses and questionnaire order using a CART-based skip-pattern miner. On Population Assessment of Tobacco and Health (PATH) study and the National Survey on Drug Use and Health (NSDUH), two nationally representative U.S.\ surveys, TabSODA reduces ordinal MACE by up to

23.7\%

and improves categorical accuracy by up to

9\%

over the strongest baseline across MCAR, MAR, and MNAR masking. The skip miner achieves near-perfect precision on both datasets, allowing TabSODA+SKIP to closely track the codebook-mask variant.

Yuyu Chen, Taehyo Kim, Hai Shu +1

Department of Biostatistics NYU School of Global Public Health

Incomplete Data Imputation Learning with Missing Data Tabular Diffusion Models Diffusion Models

Jun 3, 2026cs.LG

Learning What Not to Impute: An Uncertainty-Aware Diffusion Framework for Meaningful Missingness

Missing value imputation is a fundamental task in machine learning, with most existing methods assuming that all missing entries correspond to unobserved regular values. In many real-world datasets, however, missingness may arise from two distinct sources: some entries are meaningfully missing (intrinsically absent and semantically valid), while others are missing due to the observation process and should be imputed. We formalize this distinction as a selective imputation problem, where the goal is to jointly infer which missing entries should be preserved and which should be recovered. To address this challenge, we propose Diff-Joint, a diffusion-based framework that jointly models tabular data together with a latent missingness mask. The method alternates between conditional sampling and uncertainty-aware aggregation to iteratively refine both imputed values and missingness labels. Empirical results on synthetic and real-world datasets demonstrate that Diff-Joint effectively identifies meaningfully missing entries while achieving competitive imputation accuracy and improved downstream task performance.

Lixing Zhang, Yidong Ouyang, Weifu Li +3

University of Minnesota · University of California, Los Angeles · Carnegie Mellon University

Incomplete Data Imputation Learning with Missing Data Tabular Diffusion Models Diffusion Models

Jun 3, 2026cs.LG

Beyond Missing Rates: Rethinking Incomplete Multi-View Clustering with Protocol Divergence

Incomplete multi-view clustering (IMVC) is typically evaluated by retraining separate models under different missing-view configurations. Evaluations indexed only by nominal missing rate can overlook differences in observation structure across missing-view protocols. We show that missing-data protocols with identical nominal missing rates can induce substantially different learning regimes, differing by approximately 50-fold in the proportion of fully observed samples. We formalize this phenomenon as protocol divergence, which quantifies structural disparities among missing-view protocols beyond marginal missing rates. Furthermore, we analyze support-gated reconstruction mechanisms and show that their optimization contribution is inherently limited by the frequency of eligible observations under explicit normalization and optimization conditions. Based on these observations, we propose CRAFT (Co-occurrence-free Robust Attention-masked Fusion Transformer), a train-once framework that combines representation learning with an architecture designed to process missing-view inputs. CRAFT combines (i) per-sample forward computation using each sample's observed views and shared parameters, and (ii) mask-aware fusion over nonempty observed-view subsets. The deployment evaluation starts from training data with all views available and reuses one final checkpoint per dataset and seed across missing-view protocols without retraining. Experiments on CUB and MultiFashion show that CRAFT achieves the strongest performance in 12 out of 13 information-matched settings. Additional deployment experiments across seven benchmarks and sixteen missing configurations demonstrate substantial computational savings through checkpoint reuse while maintaining competitive clustering performance. Code and evaluation tools: https://github.com/dk23lhl/CRAFT and https://github.com/dk23lhl/imvc-audit.

Haolu Liu, Xiyue Wang, Xuanting Xie +2

Missing-Modality Learning Learning with Missing Data Multi-View Learning Multimodal Fusion

Jun 2, 2026cs.LG

AugMask: Training Diffusion Models on Incomplete Tabular Data via Stochastic Augmentation and Masking

Score-based diffusion models have emerged as prominent deep generative models; however, their application to tabular data remains challenging because their backbones assume fully specified inputs, whereas real-world tabular data often contain missing values. We propose AugMask, a plug-and-play training framework that adapts missing-unaware backbones to incomplete data by separating conditioning from supervision. AugMask 1) constructs numeric inputs via conditional stochastic augmentation using lightweight auxiliary models, and 2) applies denoising supervision only to observed coordinates. In effect, augmented missing entries serve as uncertain conditioning context rather than training targets. We connect this training rule to a Rao--Blackwellized objective and show that marginalizing missing entries yields a variance-weighted sensitivity penalty, discouraging over-reliance on uncertain completions. Across diverse datasets and missingness regimes, AugMask enables standard diffusion-based tabular generators to outperform specialized missing-aware baselines.

Jungkyu Kim, Taeyoung Park, Kibok Lee

Department of Statistics and Data Science, Yonsei University, South Korea.

Learning with Missing Data Tabular Diffusion Models Synthetic Tabular Data Generation Diffusion Models

May 27, 2026cs.LG

Latent Diffusion for Missing Data

Diffusion models have emerged as powerful generative approaches for missing-data imputation, yet most existing methods operate directly in data space and degrade when training data are heavily incomplete. We investigate whether shifting diffusion to a learned latent representation improves robustness under missing-completely-at-random (MCAR) corruption. To this end, we propose a two-stage framework: a robust VAE-based imputer first learns compact semantic features from incomplete observations, and a diffusion model is then trained in the resulting latent space. Across training missing rates, we perform a controlled comparison against pixel-space diffusion models under the same incomplete-data setting. The latent diffusion model maintains high sample quality and remains stable up to 50% missingness, while pixel-space diffusion degrades progressively as missingness increases. For downstream imputation, latent diffusion also achieves consistently better performance than pixel-space diffusion. These findings indicate that latent-space modeling mitigates artifact amplification from zero-imputed inputs and provides a more robust generative prior for incomplete-data learning. Overall, our results support latent diffusion as a strong and practically useful alternative to pixel-space diffusion for missing-data problems.

Alberte Heering Estad, Ignacio Peis, Jes Frellsen

Technical University of Denmark · Pioneer Centre for Artificial Intelligence

Incomplete Data Imputation Latent Diffusion Models Learning with Missing Data Diffusion Models

May 25, 2026cs.LG

Missing Pattern Recognized Diffusion Imputation Model for Missing Not At Random

Missing data frequently arises across diverse domains, including time-series and image domains. In the real world, missing occurrences often depend on the unobservable values themselves, which are referred to as Missing Not at Random (MNAR). In this work, we introduce the Missing Pattern Recognized Diffusion Imputation Model (PRDIM), a novel framework that explicitly captures the missing pattern and precisely imputes unobserved values. PRDIM iteratively maximizes the likelihood of the joint distribution for observed values and missing mask under an Expectation-Maximization (EM) algorithm. In this sense, we first employ a pattern recognizer, which approximates the underlying missing pattern and provides guidance during every inference toward more plausible imputations with respect to the missing information. Through extensive experiments, we demonstrate that PRDIM consistently achieves strong imputation performance under MNAR settings across multiple data modalities.

Gyuwon Sim, Sumin Lee, Heesun Bae +5

KAIST · Seoul National University

Time Series Imputation Incomplete Data Imputation Learning with Missing Data Diffusion Models

May 19, 2026stat.ML

Increasing Missingness to Reduce Bias: Richardson-SGD with Missing Data

Stochastic gradient methods are central to modern large-scale learning, but their use with incomplete covariates remains delicate since imputation schemes generally introduce systematic gradient biases, as shown for linear models. In this work, we prove that all parametric models exhibit similar gradient bias for various imputation procedures and characterize exactly the dependence on the missingness ratio vector

p

, with

O(\|p\|)

as the leading term. We exploit this analysis to propose a simple debiasing procedure for stochastic gradient descent (SGD) with missing values based on Richardson extrapolation, which leverages the exact expression of the gradient bias. The key idea is to \emph{deliberately add missingness}: from an already incomplete observation, we generate a further-thinned version at a higher, controlled missingness level, and combine the two resulting stochastic gradients to cancel the leading bias term. We prove that one Richardson step reduces the gradient bias from

O(\|p\|)

to

O(\|p\|^2)

under several missingness scenarios. Our proposed method is computationally efficient, model-agnostic and applies to any parametric loss whose stochastic gradient can be computed after imputation. Furthermore, when missing indicators are independent, the population gradient bias is a multilinear polynomial in

p

and depends only on population gradient errors induced by declaring a single coordinate missing. In this case, our method generalizes to a multi-step Richardson procedure which recursively cancels higher-order terms. Empirically, Richardson debiasing improves optimization and estimation across several generalized linear models and combines positively with widely used imputation procedures such as MICE. These results suggest that, somewhat counter-intuitively, adding controlled missingness on top of existing missing data can make stochastic learning from incomplete data more accurate.

Ferdinand Genans, Erwan Scornet

SU, LPSM · Sorbonne Université and Université Paris Cité, CNRS, Laboratoire de Probabilités, Statistique et Modélisation, LPSM, F-75005 Paris, France

Learning with Missing Data Stochastic Gradient Descent

May 17, 2026cs.LG

Learning Higher-Order Structure from Incomplete Spatiotemporal Data: Multi-Scale Hypergraph Laplacians with Neural Refinement

Sensor networks increasingly govern modern infrastructure, yet the data they lose are rarely missing in the uniform-random patterns assumed by standard imputation benchmarks. Loop detectors go offline during calibration, roadside cabinets silence clusters of nearby sensors, and newly installed instruments provide no history. Such failures create structured absences whose values are constrained by higher-order relations among groups of sensors, not merely by pairwise proximity. Existing low-rank and graph-based methods often miss this collective structure and can fail when missingness becomes coherent. We introduce Multi-Scale Hypergraph Laplacians (MSHL), a two-stage framework for learning higher-order structure from incomplete spatiotemporal observations. The Discovery stage builds a multi-scale hypergraph from complementary topology and residual-correlation evidence, with an observation-only selector that adapts to the supported interaction scale. The Refinement stage adds a small hypergraph-conditioned residual network that is safe by construction: it learns nonlinear corrections where informative residual features exist and defers to the linear estimate where they do not. We prove that MSHL represents group-conservation patterns inaccessible to pairwise graph priors, adapts to the best fixed scale up to a logarithmic factor, transfers this advantage to held-out imputation error, and admits a one-sided refinement guarantee. On two real traffic networks evaluated across scattered cell missingness, contiguous block outages, and whole-sensor blackouts at five rates, MSHL improves over a pairwise-graph baseline whenever higher-order structure is identifiable and otherwise matches it within sampling noise. The results point to a broader principle for reliable infrastructure learning: missing data should be treated not as isolated entries to fill, but as evidence of structure to discover.

Keshu Wu, Sixu Li, Zihao Li +3

Texas A&M University · University of Wisconsin-Madison

Graph Structure Learning Incomplete Data Imputation Learning with Missing Data Hypergraph Neural Networks Hypergraph Learning

May 13, 2026cs.CV

PRA-PoE: Robust Multimodal Alzheimer's Diagnosis with Arbitrary Missing Modalities

Missing modalities are prevalent in real-world Alzheimer's disease (AD) assessment and pose a significant challenge to multimodal learning, particularly when the distribution of observed modality subsets differs between training and deployment. Such missingness pattern mismatch induces a conditional representation shift across modality subsets. Existing approaches that rely on implicit imputation or modality synthesis often fail to explicitly model modality availability and uncertainty, leading to overconfident dependence on synthesized features, reduced robustness, and miscalibrated uncertainty estimates. To address these limitations, we propose PRA-PoE, an incomplete multimodal learning framework that is equipped with Prototype-anchored Representation Alignment (PRA) and an Uncertainty-aware Product of Experts (UA-PoE) fusion mechanism. First, PRA uses learnable global prototypes and availability-conditioned tokens to encode modality availability, distinguish observed from missing modalities, re-synthesize features for missing modalities, and adaptively refine observed representations to align latent spaces across modality subsets, with the goal of reducing representation shift under varying missingness patterns. Second, UA-PoE models each modality as a Gaussian expert and performs closed-form Product of Experts fusion, where experts with higher uncertainty are automatically down-weighted via lower precision, improving uncertainty reliability. We evaluate PRA-PoE under a clinically realistic protocol by training with naturally missing data and testing on all non-empty modality combinations. PRA-PoE consistently outperforms the state-of-the-art across datasets, achieving a 5.4% relative improvement in average accuracy on ADNI and a 10.9% relative gain in average F1 on OASIS-3 over the strongest baseline across all non-empty modality subsets.

Guangqian Yang, Ye Du, Wenlong Hou +2

Department of Biomedical Engineering, The Hong Kong Polytechnic University, Hong Kong SAR, China · Department of Technology Management for Innovation, The University of Tokyo,2026 Japan · Department of Data Science and Artificial Intelligence, The Hong Kong Polytechnic University, Hong Kong SAR, China

Missing-Modality Learning Alzheimer's Disease Multimodal Robustness Medical Diagnosis Cross-Modal Alignment Learning with Missing Data+1

May 12, 2026cs.AI

Missingness-MDPs: Bridging the Theory of Missing Data and POMDPs

We introduce missingness-MDPs (miss-MDPs), a novel subclass of partially observable Markov decision processes (POMDPs) that incorporates the theory of missing data. A miss-MDP is a POMDP whose observation function is a missingness function, specifying the probability that individual state features are missing (i.e., unobserved) at a time step. The literature distinguishes three canonical missingness types: missing (1) completely at random (MCAR), (2) at random (MAR), and (3) not at random (MNAR). Our planning problem is to compute near-optimal policies for a miss-MDP with an unknown missingness function, given a dataset of action-observation trajectories. Achieving such optimality guarantees for policies requires learning the missingness function from data, which is infeasible for general POMDPs. To overcome this challenge, we exploit the structural properties of different missingness types to derive probably approximately correct (PAC) algorithms for learning the missingness function. These algorithms yield an approximate but fully specified miss-MDP that we solve using off-the-shelf planning methods. We prove that, with high probability, the resulting policies are epsilon-optimal in the true miss-MDP. Empirical results confirm the theory and demonstrate superior performance of our approach over two model-free POMDP methods.

Joshua Wendland, Markel Zubia, Roman Andriushchenko +6

1Ruhr University Bochum · 2Brno University of Technology · 3Radboud University Nijmegen +2

Markov Models Learning with Missing Data Model-Based Planning Partially Observable Markov Decision Processes Decision-Making under Uncertainty

May 12, 2026cs.LG

OverNaN: NaN-Aware Oversampling for Imbalanced Learning with Meaningful Missingness

Missing values are routinely treated as defects to be eliminated through deletion or imputation prior to machine learning. In many applied domains, however, missingness itself carries information, reflecting experimental constraints, measurement choices, or systematic mechanisms tied to the data-generating process. Eliminating or masking this structure can distort class boundaries, introduce bias, and reduce generalisability; particularly in imbalanced datasets where minority classes are already under-represented. OverNaN is a lightweight, NaN-aware oversampling framework designed to address class imbalance without erasing missingness structure. It extends common synthetic oversampling methods to operate directly on incomplete feature vectors, allowing missing values to be preserved, propagated, or selectively interpolated according to explicitly defined strategies. Rather than repairing missing data, OverNaN treats missingness as part of the feature space over which synthetic samples are generated. This paper situates OverNaN within the broader landscape of imbalanced learning, missing-data handling, and NaN-tolerant algorithms. Using representative examples included with the software, we demonstrate that meaningful missingness can be retained during oversampling without introducing artificial certainty. OverNaN is intended for practitioners working with small, incomplete, and imbalanced datasets in scientific and engineering domains where missingness is unavoidable and often informative.

Amanda S Barnard

School of Computing Australian National University Acton, ACT 2601

Class-Imbalanced Learning Synthetic Data Augmentation Learning with Missing Data

May 8, 2026cs.LG

GAD in the Wild: Benchmarking Graph Anomaly Detection under Realistic Deployment Challenges

Graph Anomaly Detection (GAD) is a critical task in graph machine learning with vital applications in financial fraud detection and social platform governance. However, existing GAD benchmarks are often restricted to small-scale, curated graphs with relatively balanced anomaly ratios, leaving a substantial gap between academic evaluation and real-world deployment. To bridge this gap, we present a multi-dimensional benchmark that systematically evaluates GAD models under three deployment-relevant challenges: million-scale graphs, extreme anomaly scarcity, and missing node attributes. We derive a family of controlled benchmark variants from five diverse graphs, including two native industrial-scale datasets with over 3.7 million nodes. Our extensive evaluation of nine representative GAD models reveals three major limitations: (1) most GNN-based methods fail to scale to million-node graphs due to prohibitive memory requirements; (2) detection performance drops sharply under realistic anomaly ratios (e.g., 0.1%), often resulting in zero recall; and (3) reconstruction-based models are highly sensitive to attribute imputation strategies. Our findings suggest that strong performance in laboratory settings does not guarantee robustness in production environments. We release this benchmark and empirical evaluation as a diagnostic testbed to promote the development of robust and scalable GAD systems for large-scale, imperfect graphs encountered in practice. Code is available at https://anonymous.4open.science/r/Benchmark_GAD-E7A3.

Jingjing Zhou, Shiyu Huang, Qing Qing +7

Zhejiang Gongshang University · Jilin University · Adelaide University +2

Graph Neural Networks Graph Representation Learning Learning with Missing Data Anomaly Detection