An efficient EM algorithm for both element-wise and structural missingness in matrix-variate normal mixture models

Matrix-variate data with missing entries arise frequently in applications where observations are naturally organized as two-dimensional arrays. Although the matrix normal distribution provides a parsimonious model through its Kronecker covariance structure, standard EM estimation can be computationally expensive because arbitrary missingness patterns typically destroy this separability in the E-step. In this paper, we propose an efficient partial EM algorithm for matrix-variate normal data with missing entries. The proposed method updates the conditional mean and covariance of the missing component through coordinate-wise approximations, avoiding repeated inversion of pattern-specific covariance matrices and avoiding construction of the full vectorized covariance matrix. We further develop a specialized update for submatrix missingness, where the missing-block precision retains a Kronecker product structure, and the covariance update can be carried out independently in the row and column directions. Simulation studies show that the proposed methods substantially reduce computation time compared with exact EM while preserving nearly identical observed-data likelihood across a range of dimensions and missing proportions. A real-data application to hyperspectral image patches demonstrates that the proposed imputation strategy can be embedded within a matrix-variate mixture model for simultaneous imputation and clustering.

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.

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.

When Does Self-Supervised Pretraining Help Tabular Models? A Study of Label Scarcity and Missing Data

Self-supervised learning (SSL) has emerged as a promising approach for tabular data, yet its efficacy under extreme label scarcity and test-time missingness remains under-explored. In this paper, we evaluate a mask-and-recover SSL pretraining objective against training from scratch and classical baselines across 14 diverse classification tasks. First, while SSL outperforms training from scratch on average and remains competitive with state-of-the-art tree ensembles (achieving ~0.8954 AUC vs. Random Forest's 0.9015 at 10% labels), the SSL-vs-scratch gains exhibit high inter-task variance and lack significance (p = 0.626 at both 5% and 10% labels). Second, contrary to the hypothesis that missing-value imputation objectives universally benefit datasets with native missingness, SSL yields the most reliable improvements on clean datasets, while frequently degrading performance on datasets with high inherent missingness. Third, despite this training variance, SSL-pretrained models achieve a higher average AUC than scratch-trained models under both test-time missingness completely at random (MCAR) injection (+0.0245 AUC, positive on 11 of 14 tasks) and structured missingness shifts (MNAR, +0.0418 AUC, positive on 8 of 14 tasks), though neither difference remains statistically significant after Holm-Bonferroni correction for multiple comparisons (adjusted p = 0.118 and p = 0.518, respectively). Fourth, comparing our mask-and-recover objective against three established tabular SSL baselines (VIME, SCARF, SubTab) under an identical encoder architecture, we find no significant difference from any of them (adjusted p = 0.459, p = 1.000, p = 1.000), indicating our findings reflect general properties of tabular SSL rather than idiosyncrasies of one particular pretext task.

MARCUS: Missing-Aware Region Representation with Contextual Urban Signals for Rent Prediction

Multimodal urban data has expanded the applications of urban region representation learning, such as functional zone identification and real estate appraisal, but also introduces challenges caused by data incompleteness. Existing studies usually handle missing data through imputation, treating missingness as noise while ignoring its potential semantic value. To address this issue, we propose MARCUS, a missing-aware region representation model that treats missingness as a contextual urban signal. MARCUS models missingness in three stages: Intra Learning jointly encodes observed features and missing patterns, Inter Learning estimates modality reliability to guide cross-modal interaction, and Fusion uses missing-aware and time-aware gating to generate the final region embedding. We apply MARCUS to rent prediction, a task with long-term trends and seasonal fluctuations, using real-world datasets from Sydney and New York. Experimental results show that MARCUS achieves state-of-the-art performance, reducing MAE by 51.35% on Sydney and 12.62% on New York compared with the best baselines. Additional experiments, including an imputation-based ablation study and randomized additional-missingness analysis, further demonstrate the effectiveness of the proposed method.

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.

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.

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.

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.

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.

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.

Inferring Missing Trajectory Data with Temporal Convolutional Networks

Trajectory data collected in real-world settings is frequently incomplete due to sensor failure, communication loss, or occlusion. We address the task of \emph{trajectory inpainting}: reconstructing contiguous missing segments from observed context. We propose a Temporal Convolutional Network (TCN) with symmetric dilation that relaxes the standard causality constraint, allowing each time step to draw on both past and future observations, a property that is essential for inpainting, but absent from forecasting-oriented architectures. The model is trained with a composite loss that combines weighted mean squared error, boundary--continuity penalties, and a smoothness regularizer. Trained on a synthetic dataset of $1,000$ (train), $200$ (validation), and $300$ (test) two-dimensional trajectories with randomly placed 20% masked segments, the model achieves good R$^{2}$, MSE and MAE metrics.

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.

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.

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.

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.

ImputeViz: A Visual Analytics Dashboard for Diagnosing Missing Data and Comparing Imputation Methods

Missing data is a persistent obstacle in scientific, social science, and public health research, often biasing analyses and placing accountability on analysts for how they handle missing values. We introduce ImputeViz, an integrated visual analytics dashboard that supports diagnosing missingness, configuring imputation models, and evaluating results. The system brings together widely used methods, including MICE, Random Forest, XGBoost, and kNN, within an interactive environment that makes missingness patterns explicit. To support geospatial reasoning, we introduce gKNN, a geographically informed kNN variant that blends socioeconomic and spatial distances and exposes donor contributions, enabling provenance-based visual accountability by showing which regions drive each estimate. Our primary contribution is a method-agnostic visual analytics environment that makes cross-method comparison a first-class visual task and integrates gKNN alongside standard methods. Coordinated views reveal missingness structure through heatmaps, co-missingness summaries, and distributional diagnostics that help analysts reason about missingness patterns (MCAR/MAR) and cases where missingness may be non-random (MNAR). Users can compare and tune models and interrogate results via distributional overlays, a Method Comparison Summary reporting MAE, RMSE, Delta RMSE, and runtime for each algorithm on the current target and mask, along with variable-level discrepancy views. Cached per-method results and locked axis scales reduce cognitive overhead from shifting ranges during method switching. These comparisons highlight where methods disagree, which variables are sensitive, and how imputation choices affect downstream summaries. Case studies demonstrate how ImputeViz helps analysts select effective strategies, surface sensitive variables, and assess model robustness.

Distributionally Faithful Imputation via Positive Semi-Definite Kernel Density Estimation

Missing values undermine statistical inference and machine learning pipelines, yet most imputation methods rely on heuristics or restrictive parametric assumptions that ignore the joint data distribution. We recast imputation under missing completely at random (MCAR) as density estimation from masked observations: estimate a distribution whose observed marginals exactly match those in the data. Leveraging positive semi definite (PSD) kernel densities we obtain a convex empirical risk problem with closed form marginals, solvable by a Newton interior point method. The resulting PSD Impute model yields both single and multiple imputations from the same fitted density, enjoys statistical consistency with fast adaptive excess risk beating the curse of dimensionality for very regular probabilities. Preliminary experiments on one synthetic and eleven real world datasets already indicate competitive distributional accuracy compared with popular imputation baselines, suggesting strong practical promise.

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.

Statistical Properties of $k$-means Clustering for Data Missing Completely at Random

The classical $k$-means clustering cannot be directly used to incomplete data, and existing $k$-means-based clustering for missing data primarily focus on improving the practical accuracy of clustering, whereas most of them lack theoretical guarantees in the asymptotic sense. In this paper, we investigate the statistical properties of $k$-means clustering in the presence of missing data. We first establish the $\sqrt{n}$-excess risk bound and prove the consistency of the estimated cluster centers under general missing mechanisms. For the Missing Completely at Random (MCAR) mechanism, we further derive the $\sqrt{n}$-convergence rate and asymptotic normality of the estimated cluster centers. Moreover, we study in what cases the cluster centers estimated by incomplete data converge to the true cluster centers of original fully observed data, and give a sufficient condition about the missing probability and the separation among true clusters. These results provide a theoretical guarantee for missing-data-$k$-means. Notably, our analysis reveal that under MCAR mechanism, both achieving the $\sqrt{n}$-rate and converging to the true cluster centers require $k$ true centers to be distinct in every dimension, highlighting the significant challenges of application in high-dimensional regimes. Finally, we conduct numerical simulations on synthetic incomplete datasets to support our theoretical analysis results.

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.

A GAN-Based Framework for Robust Data Synthesis in Satellite Internet Observations

Low-Earth orbit (LEO) satellite Internet has become an important infrastructure for enabling ubiquitous connectivity to align with the International Telecommunications Union vision for 6G telecommunications networks. However, current LEO satellite Internet observations often suffer from missing data, which complicates data augmentation task and limits the expansion of representative datasets. Given the complex characteristics of these datasets, generative AI (GenAI) presents a promising approach, yet its application in this domain has received little attention to date. In this paper, we propose a GenAI-based framework to synthesize high-fidelity data directly from incomplete LEO network observations. We propose the representative data missing scenarios, and evaluate the performance with the latest GAN- and VAE-based GenAI models on the recent WetLinks dataset. We design block-wise and point-wise missing scenarios to closely simulate the data loss that happens on real-world LEO satellite networks. Our results show the effectiveness of our proposed GAN-based framework and GT-GAN model exhibits the best performance among all models in both missing scenarios. Even under extreme conditions (e.g., 40% of the input data is missing), GT-GAN shows the highest robustness, consistently capturing the underlying input data distribution and being the least affected in terms of generalization. Our results shed light on future directions for GenAI-based data augmentation methods and data-driven research on satellite network measurement.

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.

Anomaly Detection for Sparse and Irregular Multivariate Time Series with Latent SDEs

Multivariate time series anomaly detection (MTSAD) is critical for a wide range of application areas, such as industrial monitoring, cybersecurity, or healthcare. Real-world data is often sparse, irregularly sampled or partially observed, yet existing methods assume uniformly sampled time series. We propose a generative approach based on Latent SDEs that projects the observed time series on a continuous-time stochastic dynamical system, directly being able to handle missing observations and irregular sampling, while also naturally capturing possible cyclic behavior that many real-world use cases inherently possess. Experiments on six anomaly benchmark datasets show that our proposed method ranks first among state-of-the-art baselines. We further demonstrate that our method remains robust under severe data sparsity, while performance significantly degrades for the tested baseline methods. These results highlight latent SDEs as a natural inductive bias for anomaly detection in multivariate time series, especially in presence of real-world irregularities.

Informative Missingness to Generate Irregular Clinical Time Series

Laboratory tests in electronic health records are collected irregularly, and the absence of a test order can be as informative as the measurement itself. Such missingness reflects clinicians' decisions and patient physiology, making it important to model it directly rather than treat it as a preprocessing artifact. Here we present a diffusion-based approach for generating clinical time series that jointly models laboratory values and their observation patterns using the public Data Analytics Challenge on Missing Data Imputation (DACMI) benchmark derived from MIMIC-III. To preserve realistic sampling, we align chart times into 4-hour intervals and segment admissions into 7-day windows, producing trajectories that pair each lab value with a corresponding observation indicator. Standard transformations and normalization are applied to stabilize training. Our method extends the TimeDiff framework to learn continuous lab values and discrete missingness patterns through complementary diffusion objectives. Experiments show that the generated data closely match real patient trajectories across individual lab distributions and joint value-missingness embeddings, demonstrating that diffusion models can capture clinically meaningful dependencies between patient physiology and clinicians' testing behavior under MNAR-like (missing-not-at-random) missingness. These preliminary results indicate that our model can serve as an initial component toward developing clinical foundation models. By producing synthetic priors that preserve key physiology-missingness relationships, this work motivates the subsequent training of Prior-Data Fitted Networks capable of leveraging informative missingness, which we will investigate in the extended work.

Existence Precedes Value: Joint Modeling of Observational Existence and Evolving States in Time Series Forecasting

Real-world time series are often highly incomplete and irregular due to sensor dormancy, transmission delays, and event-driven sampling, making reliable forecasting fundamentally challenging. Existing methods have evolved from impute-then-forecast pipelines to continuous-time models such as Neural ODEs and continuous-time graph networks. While these approaches improve the modeling of historical irregularity, they still rely on an implicit oracle assumption at inference time: the timestamps of future valid observations are presumed to be known in advance. This assumption limits practical relevance, since in many real systems the more fundamental question is not only what the future value will be, but also whether a valid observation will occur at all. In this paper, we propose Timeflies, a unified framework that reformulates forecasting as a joint problem of future observability inference and value estimation. To explicitly model the interaction between observation dynamics and state evolution, Timeflies adopts an observation stream and a value stream, coupled through three dedicated modules for reliability-aware embedding, observation-guided dependency modeling, and joint prediction. We further construct Shadow, a benchmark that combines natural missingness from public datasets with real-world industrial data, and introduce the Observation-Value Joint Entropy (OVJE) metric to comprehensively evaluate this coupled predictability. Extensive experiments show that Timeflies consistently outperforms existing methods, highlighting the importance of explicitly modeling future observability in time series forecasting with missing values. Code and dataset are available in https://github.com/ant-intl/Timeflies.

Conformal Prediction for Dyadic Regression Under Complex Missingness

We develop a framework for conformal prediction in dyadic regression problems under complex missingness mechanisms. At the theoretical level, we establish super-uniformity of conformal prediction under distributional invariance conditions weaker than exchangeability. A key result handles the case where the sample itself is a random subset of the index set, a setting not covered by existing theory, via a novel bijection argument that constructs an explicit measure-preserving correspondence between events. In addition, we propose conformal prediction procedures for jointly exchangeable arrays, including full conformal, split conformal, a row-column approach exploiting similarities within rows and columns, and a selective conformal procedure achieving mask-conditional validity. For missing elements, we establish asymptotic validity of a graphon-weighted conformal procedure under a nonparametric graphon model for the missingness mechanism. We further establish conditional validity results for both continuous and discrete responses; to the best of our knowledge, this is first formal proof of asymptotic conditional validity for weighted conformal prediction under a missing-not-at-random assumption. The proposed methods are illustrated on synthetic and real network data.

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.

Multi-FRuGaL: Multimodal Flexible Redundancy-aware Decomposed Gated Learning for Cancer Diagnosis and Prognosis

Modern medicine relies on heterogeneous data sources spanning radiology, pathology, text reports, and structured clinical information. However, real-world patient data are frequently incomplete, with missing or sparsely acquired modalities, limiting the effectiveness of standard multimodal fusion approaches. To this end, we propose the Multimodal Flexible Redundancy-aware decomposed GAted Learning (Multi-FRuGaL) framework, a decomposition-aware, adaptive gated intermediate-fusion framework that performs modality-level representation learning under missing data. Multi-FRuGaL integrates per-modality encoders with a signal decomposition layer, an input-conditioned gating network, and an information-aware fusion objective to separate redundant from modality-specific complementary signals, selectively upweighting informative modalities and suppressing redundant or noisy inputs, and remaining well-defined even when multiple modalities are absent. We evaluate Multi-FRuGaL on two multimodal head and neck cancer cohorts: the HANCOCK challenge dataset (N = 763) comprising five modalities and two prognostic endpoints (5-year survival and 2-year recurrence), and the HECKTOR challenge dataset (N = 588) comprising three modalities for human papillomavirus (HPV) status classification. Multi-FRuGaL consistently achieves higher mean performance than the evaluated baselines across multiple tasks, improving AUC from 0.601 to 0.8496 for survival, from 0.672 to 0.8102 for recurrence, and achieving 0.975 AUC for HPV prediction on HECKTOR. For survival analysis, it further achieves a concordance index of 0.6814 for overall survival, 0.7421 for recurrence-free survival, and 0.7143 for progression-free survival on HANCOCK, and 0.7203 for recurrence-free survival on HECKTOR. Qualitative analyses further show that Multi-FRuGaL learns discriminative and robust multimodal representations, even under severe missing-modality conditions.

Spatiotemporal Imputation with Graph-Informed Flow Matching

Missing data is a common challenge in spatiotemporal systems, arising in applications such as air quality monitoring and urban traffic management. Traditional machine learning approaches, like recurrent and graph neural networks, rely on iterative propagation, which tends to accumulate errors over time and space. Recent diffusion-based methods mitigate error propagation but require iterative sampling and often depend on problem-agnostic Gaussian priors, limiting both efficiency and effectiveness. To address these limitations, we propose GiFlow, a Graph-Informed Flow Matching framework for spatiotemporal imputation. GiFlow replaces the typical Gaussian prior with a graph-informed prior constructed via spatiotemporal filtering of observable signals, which better aligns the source distribution to the target and thereby simplifies the generation trajectory. The flow field is parameterized by a hybrid vector field model that integrates spatial attention, temporal attention, and spatiotemporal propagation, enabling joint modeling of spatial and temporal dependencies. Extensive experiments on both synthetic and real-world datasets demonstrate that the proposed GiFlow outperforms the state-of-the-art approaches in spatiotemporal imputation. The code is available at https://github.com/zepengzhang/GiFlow.