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.

Jul 13Week of Sep 28

Latest papers 68

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