Missing Data

Time-series foundation models have demonstrated strong cross-domain transfer, yet their common architectural assumptions remain poorly aligned with wearable physiological signals, which are multichannel, irregularly sampled, noisy, and governed by coupled continuous-time dynamics spanning distinct spectral scales. We present SOTER, a generative foundation model for wearable physiological time series that unifies cross-channel coupling, spectrum-guided expert specialization, and continuous-time latent evolution within a single pre-training framework. SOTER combines a spatial feature-aware backbone that models inter-signal dependencies, a power spectral density (PSD)-guided mixture-of-experts layer that routes representations to experts associated with fixed spectral bands through an inspectable, non-learned rule, and a neural controlled differential equation decoder that supports prediction and imputation at arbitrary timestamps. We pre-train SOTER on 226 billion time points from five public physiological datasets and evaluate the same pre-trained model across out-of-distribution zero-shot forecasting, frozen-encoder linear-probe classification, and continuous-time imputation on wearable benchmarks. SOTER achieves the best RMSE on 4 of 6 datasets and the best MAE on 5 of 6 in zero-shot forecasting, the highest average Macro-AUROC in classification, and the lowest imputation error on all six datasets at 75% missingness. It further remains robust to additive acquisition noise, matching or surpassing baselines evaluated on clean inputs even under the strongest corruption. These results indicate that domain-specialized foundation models for wearable physiology benefit from jointly modeling channel structure, spectral scale, and continuous-time dynamics.

In order to make Reinforcement Learning algorithms applicable in real world scenarios, safety must be ensured even under adverse operating conditions. In this work, we consider the challenge of adversarial feature missingness: a scenario in which an adversary occludes features from the agent's observation in order to reduce performance as much as possible. We formally define adversarial missingness for Reinforcement Learning and compare it to the related concepts of $\ell_\infty$-norm bounded adversarial perturbations and learning with missing data. We develop an adversarial training algorithm and show its effectiveness in increasing robustness against adversarial missingness on three MuJoCo benchmark environments. Compared to a baseline trained with random uniform missingness, our method achieves better robustness on all three tasks.

Missing values are ubiquitous in heterogeneous data mining, where numerical, categorical, and binary variables often coexist. Many imputation methods, especially diffusion-based ones, treat discrete variables through continuous surrogates such as one-hot relaxations rather than modeling them natively. This creates a mismatch between the model state space and the mixed discrete and continuous structure of the data. We propose Impute-EM, an Expectation Maximization style framework that alternates between imputing missing entries with the current model and refitting a diffusion backbone on completed data. We instantiate Impute-EM with native mixed-state diffusion backbones for heterogeneous data, combining Gaussian and masked categorical components without one-hot relaxations. In exact settings, we characterize the update and show that the observed mask-indexed marginals match the targets at the limit, while making explicit that the full data distribution is generally non-identifiable from incomplete observations alone. Empirically, Impute-EM delivers the best distributional fidelity on mixed-type tabular imputation, on which downstream modeling relies, with text imputation serving as a controlled validation of the native discrete backbone.

Shapley value (SV)-based methods are the prevailing framework for feature attribution in machine learning, yet existing population-level Shapley estimators generally assume that observations used to evaluate the coalitional game are fully observed under a common feature space. This assumption is routinely violated in multi-site studies across biomedicine, social science, and environmental monitoring, where institutions record different features under different protocols, producing systematic blockwise missingness across sources. We first show that the standard remedy of imputing missing features before computing Shapley values introduces systematic, coalition-dependent bias into the resulting attributions. We then propose \textbf{FUSHAP} (\textbf{Fu}sion \textbf{Sh}apley \textbf{A}ttribution from \textbf{P}artially-observed data), a method that leverages partially-observed auxiliary sites to reduce the variance of a preliminary single-site Shapley estimate without imputation. A permutation-based screening step detects and excludes sites whose data distributions are incompatible with the target population. In synthetic experiments, FUSHAP achieves $3$--$8\times$ lower MSE than the single-site estimator and $2$--$3\times$ lower MSE than imputation baselines without incurring imputation-induced bias, and the screening procedure identifies misaligned sites with $82\%$ power at moderate misalignment and $100\%$ for strong misalignment. On multi-site air quality and multi-center clinical data, FUSHAP reduces MSE by approximately $3$--$7\times$ relative to the single-site estimator; in the clinical application, standard imputation can increase MSE above the single-site baseline.

Multivariate time series imputation (MTSI) aims to recover missing values in temporal data composed of multiple interdependent variables. This problem is central to real-world applications such as healthcare monitoring, traffic networks, and energy systems. Recent diffusion-based approaches have shown strong potential for probabilistic imputation by learning to generate missing values through iterative denoising. However, most existing approaches perform diffusion directly in the original data space, requiring the denoising network to simultaneously capture global structure, temporal dynamics, and stochastic variability. This makes the generative task unnecessarily complex, especially when modern deterministic imputers can already provide accurate initial reconstructions. To address this limitation, we propose RDDMPI, a conditional residual diffusion framework that operates directly in residual space. Instead of modeling the full missing signal directly, we reformulate probabilistic imputation as a baseline-residual decomposition, where a pretrained model captures the dominant signal and a diffusion process models the residual uncertainty. To better exploit deterministic guidance, \model{} conditions the reverse denoising process on both the baseline-completed signal and its latent representation, while a reliability-aware conditioning mechanism adaptively controls the influence of baseline information during residual generation. This formulation simplifies the diffusion learning objective, enabling it to focus on structured correction terms rather than reconstructing the full signal. Experiments on multiple benchmark datasets demonstrate that RDDMPI consistently improves both reconstruction accuracy and uncertainty quantification.

Velocity-aware pitch control is standard, but under a broadcast viewport half the players are off screen and on-screen velocities come from a drifting calibration. We ask at which layer of broadcast off-ball analysis velocity changes the answer. Inheriting our off-screen imputation protocol (three Metrica matches, 44 m viewport, block-bootstrap CIs), we score four velocity regimes -- none, viewport-legal observed, true-for-visible, true-for-all -- against a velocity-aware ground truth at three layers: imputation, the control surface, and team verdicts. Velocity is nearly useless for imputation (-0.2 pp against a 12--14 pp velocity-free surface MAE), first-order for the surface (-1.5 to -1.8 pp, 11--15% of that MAE), and ten times smaller for verdicts (-0.12 to -0.19 pp). The velocity that matters is the visible channel: perfect occluded-player velocity adds 2--6% of the visible gain, and no last-seen decay policy we tested exceeds that. Omitting velocity blurs the surface (per-frame |e| 2.2--2.6 pp) with small time-averaged bias (per cell <=0.4 pp), whereas imputation error is a structured bias against the defending team's deep zone (5--9 pp). At a fixed velocity window, a noise ladder of eleven jitter settings, including sigma_v-matched pairs, is ordered to first order by one velocity-noise axis sigma_v with break-even ~1 m/s; eleven SoccerNet-GSR clips from one match through our pipeline measure sigma_v=1.65 m/s yet recover 24--36% of the benefit: 43% of the variance is frame-common, which the surface tolerates, and the residual is heavy-tailed and clustered, which Gaussian controls matched on component RMS do not reproduce (+0.03 vs. +0.36). The share of velocity-free error that velocity removes grows with viewport width (7% at 36 m, 21% at 60 m): fix imputation on tight shots, velocity on wide ones. Code and logs are released.

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

Depression and anxiety in older adults with Mild Cognitive Impairment (MCI) are frequently underdiagnosed due to limited access to care. Multimodal analysis of remote clinical interviews is a scalable screening approach, but existing methods have three limitations. First, they do not correct temporal misalignment across multimodal features extracted at different resolutions, inducing spurious cross-modal associations. Second, remote recordings exhibit uneven modality dropout, but missing values are often zero-filled, making them indistinguishable from valid near-zero measurements. Finally, they do not jointly attribute predictions to modalities, questions, and interview moments, limiting fine-grained clinical interpretation. We propose a Temporally-Aligned, Missingness-Aware, Interpretable (TAMI) multimodal fusion framework. TAMI aligns speech, language, facial, and physiological features within question-answer segments on a shared timeline, encodes modality-level missingness over time, and conditions fusion on question context. In interviews with 49 older adults with MCI, TAMI achieved area under the receiver operating characteristic curve (AUROC) scores of 0.68 (depression) and 0.69 (anxiety). Fine-grained temporal alignment of multimodal features produced the largest performance gain ($Δ{\geq}0.1$). Multi-level interpretability analysis revealed that depression classification relied on eyegaze and open-ended questions, while anxiety classification depended on eyegaze and head pose, with attribution uniformly distributed across questions. Using only responses to the open-ended questions (5.1min), the depression model achieved an AUROC score of 0.67, which was not significantly different from using the full interview (19min) ($p>0.05$). Our findings support designing interview protocols centered on open-ended questions for depression screening in older adults with MCI.

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.

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.

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

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

Probabilistic coastal hazard assessments require accurate characterization of tropical cyclone (TC) parameters, yet datasets often contain missing records for the radius of maximum winds (Rmax), a key variable in Joint Probability Method analyses. This study evaluates data-driven approaches for Rmax imputation, including one-dimensional Convolutional Neural Networks (1DCNNs), Long Short-Term Memory (LSTM) networks, and conventional machine learning models. We examine physics-informed input augmentation, temporal modeling, and transfer learning using synthetic RAFT and STORM datasets for pre-training and observational IBTrACS data for fine-tuning. Including the radius of 34-knot winds (R34) substantially improves performance across all model types. Temporal models achieve higher average correlations than non-temporal models despite using approximately an order of magnitude fewer samples, indicating better preservation of relative Rmax variability across storms. This advantage is more pronounced when R34 is unavailable, suggesting temporal information can partially compensate for missing storm-size predictors. Transfer learning does not improve performance, likely because synthetic datasets have lower and less variable Rmax distributions than IBTrACS. These findings demonstrate the potential of temporal deep learning for reconstructing incomplete TC records and highlight the importance of physics-informed inputs, observational data availability, and distributional consistency in coastal hazard assessment.

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.

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.

Task-specific fine-tuning can improve the performance of large language models (LLMs) on downstream tasks. However, our study reveals that task-specific fine-tuning can also weaken the safety guardrails of aligned LLMs. A widely adopted strategy for preserving safety during fine-tuning is to incorporate safety data. Although previous studies have shown that randomly mixing safety data can alleviate safety degradation, the underlying principle determining why some safety examples are more effective than others still remains unclear. In this paper, we propose DataRx, a missingness-aware sampling method for selecting safety-critical examples. DataRx is based on the hypothesis that a safety sample is more effective when the selected examples provide safety signals that fill the missing parts of LLMs' safety capabilities. DataRx's key insight is leveraging high-dimensional hidden representations rather than discrete tokens to quantify the safety signal gap between the target model's native response and the safety reference response. The results show that, with only 1% additional safety samples from BeaverTails, DataRx reduces the average attack success rate of Llama3-8B-Instruct across seven downstream tasks from 59.23% under random sampling to 13.70%. In addition, DataRx can be combined with the existing safety data synthesis method to further enhance safety defenses during fine-tuning. We hope that DataRx will inspire more data-centric defense research.

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.

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.

Utility data (e.g., electricity, water, and gas consumption), collected by ubiquitous sensors and embedded devices, often contains substantial missing values due to various factors such as device failures and data transmission issues. The data missingness can severely impact utility billing accuracy, hinder demand forecasting, and disrupt efficient utility supply management. As a result, utility data imputation has attracted much interest from both industry and academia. While many studies have attempted to address this issue, most of them rely on aggregated datasets for training, overlooking rich user behavior information, which could provide valuable insights for more accurate imputation. However, learning comprehensive user behavior from long-term, diverse, and incomplete utility data remains a significant challenge. Moreover, leveraging user behavior information to guide imputation is nontrivial due to the indirect nature of the correlations. To address these challenges, we propose MBDiff, a Multi-view Behavior-aware Diffusion Model for Probabilistic Utility Data Imputation. MBDiff incorporates two key technical components: (i) a multi-view User Behavior Extraction module that learns comprehensive user behavior from multiple perspectives, including global, local, and instance-level views; and (ii) a behavior-aware conditional diffusion model consisting of a reference selection module and a conditional attentional denoising network to impute utility data in a computationally efficient manner. We implement and evaluate MBDiff by collaborating with one of the largest municipal utility providers in Florida. Experimental results demonstrate our proposed MBDiff effectively outperforms state-of-the-art baselines, e.g., it improves 7.04% and 29.1% on the electricity and water usage datasets for block missingness imputation, respectively.

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.

Internet of Things (IoT) applications generate vast amounts of Correlated Time Series (CTS) data that often contain missing values and require imputation. Existing methods emphasize accuracy but often lack adaptability to changing IoT environments: they are vulnerable to sensor failures, cannot selectively impute only incomplete sensors, and use static architectures that do not adapt to resource availability. To address these limitations, we propose AdaCTSi, an adaptive CTS imputer for changing environments. AdaCTSi combines a One-shot Temporal Convolutional Network with a Learned Time-Sensor Index Table to extract and decouple complex spatio-temporal features into sensor-wise embeddings, enabling adaptation to varying sensor subsets. Sparse Spatial Attention efficiently extracts dynamic spatial correlations, while Correlation-Weighted Sensor Selection selects informative sensors to provide sufficient spatial context. Experiments with twelve baseline methods, three adaptability scenarios, and five benchmark datasets covering traffic, air quality, and trajectory data show that AdaCTSi reduces MAE by an average of 33.1% relative to the strongest baseline on each dataset. A single trained model supports sensor-subset and resource-adaptive inference, and its modest memory footprint enables deployment on commodity computing devices, including MCUs.

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.

The modeling of hydrometeorological time series with limited observations is a key challenge in the monitoring of hydro-systems and water resources, as well as for flood or drought risk assessment. Due to the high variability of the underlying processes and the sparsity of available measurements, traditional statistical approaches often struggle to accurately represent their dynamics. In this context, recent advances in deep learning offer a promising direction for improving the representation and generation of complex temporal processes sampled at several observation sites. This study investigates the application of transformer-based diffusion models to the simulation and reconstruction of hydrological time series. The proposed framework is applied to the joint modeling of water quantity and quality at six sites spread across three adjacent headwater catchments located in North-East France on a limestone plateau covered by forests and field crops. The model is calibrated and validated using available observational data, which has been quality controlled and corrected for sensor drift and malfunction through collaborative efforts by LNE metrology expertise and Andra monthly quality control over more than 15 years. Its performance is compared with several established baseline approaches commonly used for time series modeling. Quantitative evaluation metrics are employed to assess the ability of the proposed method to reproduce key temporal characteristics of the observed signals in two settings: the imputation of incomplete time series and the forecasting of upcoming hydrological conditions. Results support the effectiveness of the transformer-based approach and highlight its capacity to capture and simulate the complex patterns present in hydrological data. In particular, the results indicate that diffusion models can efficiently sample realistic time series distributions under observation settings with variable missing data for both forecasting and imputation.

Predicting missing cell values in tabular data is a fundamental problem in data cleaning. While state-of-the-art reasoning models show great promise in predicting missing values in tables, by reasoning holistically across rows and columns, they are costly to deploy at scale and tend to be overconfident, often generating hallucinated or false-positive predictions. In this paper, we observe that achieving high-precision missing-value prediction in tables requires a distinct combination of three capabilities: (1) world knowledge, (2) text-based reasoning, and (3) code-based reasoning. We systematically explore design choices for combining these capabilities, and propose an Auto-Fill approach that post-trains three specialist small language models (SLMs), each optimized for one capability. We develop a calibrated ensemble mechanism that either dynamically selects the most confident specialist or abstains, ensuring high accuracy. Extensive experiments on 11 benchmarks with 2200 real tables drawn from diverse domains show that Auto-Fill achieves superior accuracy compared to state-of-the-art reasoning models (e.g., o3-pro, Gemini 3 Pro, and DeepSeek R1), while operating at a fraction (less than 1%) of the cost of these frontier models. Our results highlight the effectiveness of specialization and calibrated abstention in the important domain of tabular data. Auto-Fill is publicly available at https://github.com/lyrain2001/auto-fill.

We describe DS@GT's submission to the eRisk 2026 Task 1 challenge on conversational depression screening, in which systems interview LLM personas that simulate individuals with varying depression profiles and produce a Beck Depression Inventory II (BDI-II) score plus four key symptoms per persona, without directly asking sensitive mental health questions. Our pipeline evolved through three stages: a monolithic single-model prototype to start off, a baseline multi-agent architecture that separates conversational interviewing from BDI-II scoring under a coordinating orchestration layer, and a final hybrid configuration that replaces the paid GPT-5-nano interviewer with the open-source Gemma 27B. To offset the model's weaker reasoning and instruction-following, the hybrid adds three algorithmic components: a precomputed dialogue tree that standardizes interview openers and follow-ups, a reliability-weighted consensus aggregation inspired by the Weaver framework, and a cluster-based imputation step for unprobed symptoms. We submitted three fully automated runs across all 20 personas, with Run 1 from the paid baseline and Runs 2 and 3 from the hybrid. Hybrid Run 3 achieved an ADODL of 0.9063, ranking 3rd among all complete-submission runs and placing DS@GT 2nd among the 21 teams overall, while outperforming our paid baseline Run 1 (0.8841) at roughly one-quarter of the per-persona API cost. These results support our central hypothesis that with sufficient algorithmic supervision, a weaker open-source model can compete with a stronger proprietary model in the conversational interviewer role. Our source code is available at https://github.com/dsgt-arc/erisk-task1-2026.

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.

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.

Spatial football metrics such as pitch control assume access to the positions of all 22 players, yet the most widely available source of positional data -- the broadcast main camera -- shows only 10-16 of them at any moment. We quantify the resulting distortion with an open, reproducible benchmark: a simulated broadcast viewport applied to open full-pitch tracking data (Metrica Sports; three matches, one held out from method development). Ignoring off-screen players -- the visible-only baseline implied whenever a video-based game-state-reconstruction (GSR) pipeline adds no imputation layer -- inflates hidden-zone pitch-control error to 25.1-26.9 percentage points and a mean absolute control-share error of 11.1-13.4 points across the three matches. We then evaluate a ladder of training-free, online imputation baselines that use only observations from the match being analysed. The best overall on these decision-relevant metrics, role-anchored centroid voting (each visible player votes for the full-team centroid by subtracting its running role offset, attenuating the viewport-induced subset bias), roughly halves hidden-zone error (to 12.2-13.8 points) and cuts control-share error to 28-48% of the ignore policy at every viewport width from 36 m to 60 m in all three matches. For occlusions <=9.6 s -- the regime of the closest learned prior work -- it reaches binwise median position errors of 3.3-8.9 m; but 50-57% of hidden-player observations lie beyond that regime. Integrated end-to-end into a broadcast-video GSR pipeline, imputation moves a downstream possession-quality score (Space-Creation Index) by 15.6 and 17.2 points on two real World Cup broadcast windows, flipping the verdict class in one.

Prototype-based Incomplete Multi-view Clustering has recently attracted increasing attention by exploiting prototypes as semantic anchors for missing-view imputation. However, existing approaches are still limited in three aspects. First, they typically focus on enforcing cross-view prototype consistency, while ignoring view-specific information embedded in prototypes, thus limiting multi-view expressiveness. Second, most methods rely on instance-level contrastive learning that only aligns paired samples across views, failing to preserve cluster-level relational structures. Third, missing-view imputation is usually performed using global prototypes alone, without considering local geometric neighborhood structures, leading to inaccurate recovery of missing representations. To address these limitations, we propose a novel framework termed Structure-aware PrOtotype disentanglement foR incomplete multi-view clusTering (SPORT), which explicitly disentangles shared and view-specific components of prototypes while preserving cluster-level relational structures. Specifically, we decouple prototypes into orthogonal shared and view-specific components, aligning only shared components to capture consensus semantics while de-correlating view-specific components to preserve complementary information. Meanwhile, a structure-aware contrastive learning mechanism is incorporated to explicitly model cluster-level relationships during cross-view representation learning. Furthermore, a hybrid imputation strategy integrates global prototype matching with local neighborhood matching, enabling joint exploitation of semantic prototypes and manifold structures for missing-view recovery. Extensive experiments on six benchmark datasets show that SPORT achieves superior performance over state-of-the-art methods under various missing rates.

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.

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.

Deep learning has significantly advanced time series imputation, yet most existing architectures primarily rely on localized temporal context within the corrupted input sequence. This reliance can be limiting in real-world scenarios, where time series often exhibit non-stationary dynamics, weak temporal correlations, and infrequent patterns that are difficult to reconstruct from nearby observations alone. In this paper, we propose ALER-TI, Aligned Latent Embedding Retrieval for Time Series Imputation, a retrieval-augmented framework that explicitly leverages historical patterns to supplement degraded local context for more reliable missing-value reconstruction. The core of ALER-TI is Latent Embedding Alignment (LEA), which mitigates the representation mismatch between corrupted queries and complete historical candidates. By applying post-hoc masking in the latent space, LEA aligns candidates with the query's missingness pattern while allowing historical embeddings to be pre-computed and cached for efficient retrieval. ALER-TI is model-agnostic and can be integrated with various imputation backbones through a lightweight adaptation module. Extensive experiments on six real-world datasets under different missing rates demonstrate that ALER-TI consistently improves strong baseline models and enhances robustness across diverse imputation settings.

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.

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

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.

Clinical time series prediction in intensive care units remains challenging due to heterogeneous physiological variables and informative missingness. The presence or absence of a measurement can reflect clinical decisions and patient severity, and thus missingness can serve as a predictive signal rather than a simple data artifact. This work presents CISM, a Channel-Independent Spectrogram framework with a Missingness stream for clinical multivariate time series prediction. CISM converts each clinical variable into a variable-wise time-frequency spectrogram, preserves variable identity through variable-aligned encoding, and aligns an explicit missingness stream with the spectrogram representation. Experiments on an in-hospital mortality task derived from MIMIC-IV show that CISM achieves the highest mean AUROC (0.7225), AUPRC (0.3308), and F1 (0.3808) among the compared time series, missingness-aware, vision, and time-frequency baselines. Ablation studies further show that observation patterns provide a meaningful informative signal. Pixel-level mask injection improves performance over plain spectrogram inputs and recovers much of this predictive value. The aligned missingness stream contributes a further, complementary gain in both AUROC and AUPRC. These results highlight the importance of modeling observation patterns as structured signals in clinical time series prediction.

Alzheimers disease (AD) is a brain disorder that develops slowly and mainly affects memory, thinking, language, and daily activities. It is one of the most common causes of dementia and creates many difficulties for patients as well as their families. In the early stage, the symptoms are often mild and may look like normal ageing. For this reason, many people are diagnosed late, when the disease has already progressed. At present, there is no complete cure for AD. Still, early detection can help doctors manage the condition better and take suitable steps at the right time. In this study, a machine learning model is proposed to detect the early stages of Alzheimers disease using clinical details, neuropsychological test scores, and neuroimaging-related measures. The data used in this work is collected from the Alzheimers Disease Neuroimaging Initiative (ADNI). As the dataset has missing values, iterative imputation is applied to fill them. The dataset also has class imbalance, which is handled using Borderline SVM-SMOTE. After that, feature selection is carried out using wrapper-based and embedded methods so that only important features are used for training. The selected features are divided into training and testing sets, and feature scaling is applied. A stacking ensemble model is developed using Logistic Regression, Extra Trees, Bagging KNN, and LightGBM as base classifiers. Along with this, an artificial neural network is also trained on the same dataset. The performance of these models is compared using precision, recall, F1-score, and AUC-ROC. This study aims to find the best classifier and also identify important biomarkers that may help in the early diagnosis of Alzheimers disease.

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.

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.

Tabular foundation models (TFMs) achieve strong performance on microbiome abundance data, yet their robustness under realistic distribution shift remains poorly characterized. We introduce a benchmark that evaluates the robustness of TFMs to biologically inspired perturbations across six gut microbiome datasets spanning four disease contexts. In this in-context learning setting, models receive unperturbed support sets as context and are evaluated on perturbed query samples. To isolate robustness beyond "shortcut" features, we preserve the most discriminative taxa and apply three controlled perturbation strategies: (i) removal of high-abundance (uninformative) taxa, (ii) sparsification via increased zero-inflation, and (iii) zero-imputation via spurious non-zero injections. Our results show that protecting discriminative features is insufficient to guarantee stability under support-query shift: across datasets, all perturbations degrade model performance, with zero-imputation consistently the most harmful, indicating that corrupting global feature structure can break generalization even when key taxa are retained. Sparsification disproportionately affects TFMs relative to a classical random forest baseline, suggesting greater sensitivity to zero-inflation-type shifts. The code is publicly available at: https://github.com/UMMISCO/metagenomics-fm/.

Statistical matching combines partially overlapping datasets that share covariates $X$ but observe the target $Y$ and auxiliary variables $Z$ separately. Classical approaches typically invoke the conditional independence assumption (CIA), which makes the problem identifiable but fundamentally implies that the imported auxiliary variable provides no additional predictive power for $Y$ once $X$ is known. To capture this latent $Y$--$Z$ dependence, we propose a novel dependency-aware Schrödinger bridge for predictive statistical matching. Our approach couples the two separated databases by tilting the conservative CIA baseline with a transportation-based compatibility cost, recovering an informative joint distribution. The resulting statistical learning framework yields full probabilistic posterior rules for bidirectional imputation. Theoretically, we establish a sufficient condition under which the learned bridge strictly improves over the CIA baseline, alongside an exact joint recovery guarantee in the Gaussian setting under an appropriate cost. Across synthetic benchmarks and real-world datasets (CelebA and Adult), we demonstrate that our dependency-aware completion consistently improves downstream predictive utility, proving especially beneficial in settings like data recoding where the underlying population exhibits strong $Y$--$Z$ dependence.

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.

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.

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.

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.

Purpose: Spatial transcriptomics (ST) enables gene expression measurements within the tissue context. However, these measurements are often noisy, low-resolution, and sparsely sampled, which limits the recovery of fine spatial structure. Deep neural networks have become powerful tools for expression imputation from histology, but their performance remains constrained by limited sample sizes and a lack of biologically informed augmentation. Most of the existing augmentation strategies for learning are designed for classification tasks rather than regression, which neglect spatial and transcriptomic relationships, leading to biologically implausible interpolations that hinder prediction performance. Approach: To address these limitations, we propose SNR-ST-Mix, a geometry- and expression-aware data augmentation framework designed specifically for ST data. It constrains mixing to a spot's k-nearest spatial neighbors and adaptively weights interpolation coefficients based on expression similarity, generating augmented samples that preserve local biological structure while ensuring spatial smoothness. This dual conditioning yields synthetic examples that expand the effective training manifold, promote generalization, and enhance prediction stability under sample-specific training. Results: Extensive experiments with various tissue types demonstrate that SNR-ST-Mix consistently outperforms conventional augmentation methods without requiring architectural changes or additional computation. Conclusions: SNR-ST-Mix provides an effective and biologically principled augmentation strategy for spatial transcriptomics regression tasks. By explicitly leveraging spatial geometry and transcriptomic similarity, it expands the effective training manifold and improves predictive performance without increasing model complexity.

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.

Foundation models mark a profound paradigm shift in time series modeling, with task-specific models being superseded by general-purpose zero-shot models. Yet, current approaches primarily focus on forecasting, while real-world time series are often irregularly and partially observed, requiring models that can jointly forecast, impute missing values, and handle degraded sampling conditions. To address these challenges, we introduce TS-ICL, a novel probabilistic In-Context Learning encoder--regressor Transformer that unifies forecasting and imputation. TS-ICL formulates time series tasks as timestamp-aligned regression and naturally incorporates covariates by training on synthetic dependency structures generated from a novel causal data prior. Empirically, TS-ICL achieves a new state-of-the-art in imputation, while remaining competitive with leading forecasting foundation models across both univariate and covariate-aware benchmarks. It shows particularly strong performance in forecasting with partially observed look-back windows.

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.

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.

Standard IMVC evaluation retrains separate models for different missing-data configurations. We show that this paradigm obscures a fundamental vulnerability: missing rate alone is insufficient to characterize data incompleteness. Specifically, we show that protocols with identical nominal missing rates can differ by up to $50\times$ in their proportion of fully observed samples, inducing drastically different learning regimes. We formalize this phenomenon as incompleteness divergence, providing measures that capture structural disparities across missing-data protocols. We further prove that for a broad class of reconstruction-based objectives, learning becomes structurally ill-posed when the proportion of complete samples falls below a critical threshold, leading to near-random performance. To bypass this theoretical bound, we propose CRAFT (Complete-data Robust Attention-masked Fusion Transformer). CRAFT shifts the burden of robustness from the loss function to the architecture via two key properties: (i) per-sample independence, which removes reliance on complete-sample co-occurrence, and (ii) mask-aware variable-length fusion, which aggregates only observed views through attention masking. This design allows a single model, trained once on complete data, to generalize to diverse missing patterns at inference time without retraining. Extensive experiments on seven benchmarks show that CRAFT matches or outperforms per-configuration baselines while reducing training overhead by $8.8\times$, demonstrating that robustness to missing data can be achieved as an inherent architectural property. Code (CRAFT) and our imvc-audit toolkit are available at https://anonymous.4open.science/r/CRAFT-BF80/ and https://anonymous.4open.science/r/imvc-audit-8263/.

Diffusion models have demonstrated strong performance in time series modeling due to their ability to progressively capture complex data distributions through iterative denoising. However, existing approaches struggle with frequency-sensitive denoising, high-frequency reconstruction and balancing global trends with local dynamics. To address these limitations, we propose \textbf{HyFAD}, a \textbf{Hy}brid time-frequency \textbf{D}iffusion model with \textbf{F}requency-\textbf{A}ware embedding for time series imputation. Built upon the DDPM paradigm, HyFAD adopts a coupled time-frequency diffusion framework, in which the reverse denoising proceeds sequentially from the time domain to the frequency domain, enabling coarse-to-fine generation. Specifically, the time-domain diffusion process captures low-frequency global trends, while the frequency-domain diffusion process refines high-frequency spectral components. We further introduce a frequency-aware step embedding that exploits the relationship between diffusion steps and spectral components, providing step-dependent spectral guidance and facilitates more accurate band-wise reconstruction. Extensive experiments on multiple benchmark datasets demonstrate that HyFAD achieves state-of-the-art performance. Our source code is available at https://github.com/hongfangao/HyFAD.

Training quantum neural networks (QNNs) on quantum hardware is currently bottlenecked by the cost of gradient estimation: standard parameter-shift methods require a number of circuit evaluations that grows quadratically with the number of trainable parameters, making hardware-based optimisation impractical beyond small system sizes. In this work, we introduce a training framework that reduces this cost to logarithmic in the number of qubits, making gradient-based QNN optimisation feasible on near-term hardware at increasing scales. Our framework combines three co-designed ingredients: (i) a structured, subspace-preserving Butterfly circuit architecture with $O(n \log n)$ parameters and logarithmic depth; (ii) a layer-wise training strategy that confines on-hardware optimisation to one small, well-structured layer at a time; and (iii) a parallelised parameter-shift rule that exploits the commuting structure within each Butterfly layer to extract all gradients in a constant number of circuit executions. Together these reduce the number of distinct circuit evaluations per optimisation step from $O(n^2)$ to $O(\log n)$. We validate the framework on clinical data imputation using the MIMIC-III electronic health record dataset, a demanding benchmark sensitive to optimisation instability and model variance. Hybrid classical-quantum models are trained directly on IonQ Forte Enterprise trapped-ion hardware at 16 qubits without performance degradation relative to ideal or noisy simulation and via tensor-network simulation at 32 qubits, with 32-qubit inference executed on hardware. The resulting models match or exceed strong classical neural baselines in downstream patient survival prediction while exhibiting reduced variance across runs, demonstrating that the proposed framework enables practical, scalable QNN training under realistic hardware constraints.

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.

Approximately 10% of newborns require assistance to initiate breathing at birth, and around 5% need ventilation support. Fetal heart rate (FHR) monitoring plays a crucial role in assessing fetal well-being during prenatal care, enabling the detection of abnormal patterns and supporting timely obstetric interventions to mitigate fetal risks during labor. Applying artificial intelligence (AI) methods to analyze large datasets of continuous FHR monitoring episodes with diverse outcomes may offer novel insights into predicting the risk of needing breathing assistance or interventions. Recent advances in wearable FHR monitors have enabled continuous fetal monitoring without compromising maternal mobility. However, sensor displacement during maternal movement, as well as changes in fetal or maternal position, often lead to signal dropout, resulting in gaps in recorded FHR data. Such missing data limits the extraction of meaningful insights and complicates automated (AI-based) analysis. Traditional approaches to handling missing data, such as simple interpolation techniques, often fail to preserve the spectral characteristics of the signals. In this paper, we propose a masked transformer-based autoencoder approach to reconstruct missing FHR signals by capturing both local temporal and frequency components of the data. The proposed method demonstrates robustness across varying durations of missing data and can be used for signal inpainting and forecasting. The proposed approach can be applied retrospectively to research datasets to support the development of AI-based risk algorithms. In the future, the proposed method could be integrated into wearable FHR monitoring devices to achieve earlier and more robust risk detection.

Fraud detection models in payment networks train on chargeback labels that are systematically biased. Every label must survive three sequential gates: authorization (declined transactions generate no labels), issuer reporting (unreported fraud is invisible), and delay (pending chargebacks are missing at training time). Labels that do arrive may be corrupted by first-party misuse or issuer misclassification. A companion paper [arXiv:2605.27557] proved that these four impairments impose a minimax lower bound on detection performance. This paper asks: can that bound be achieved? We formalize the observation pipeline as a sequential missing-data problem with three propensity stages and a corruption layer, and construct the Sequential Triply Robust (STR) estimator. The STR corrects for all four impairments simultaneously and achieves the semiparametric efficiency bound -- no estimator can have lower asymptotic variance. It is sequentially triply robust: at each gate, consistency requires only that either the propensity model or the outcome regression is correctly specified, not both. We provide corruption correction via noise-rate-adjusted pseudo-labels, empirical Bayes shrinkage to stabilize inverse-propensity weights for small issuers, a plug-in variance estimator yielding valid confidence intervals, and a Bernstein concentration inequality for finite-sample guarantees. On the operational side, we derive the optimal training delay -- the maturity window that minimizes the sum of label-quality loss and model staleness -- and prove that the STR permits training on data that is days old rather than months old, decoupling model freshness from the chargeback maturity cycle. The STR provably dominates naive chargeback-based training in mean squared error for any sample size.

LLM-based agents for industrial asset operations show limited accuracy when reasoning over flat document stores. AssetOpsBench (KDD 2026) establishes that GPT-4 agents achieve 65% on 139 industrial maintenance scenarios, and compares LLM orchestration paradigms (Agent-As-Tool vs. Plan-Execute) on a fixed data layer. We ask the orthogonal question: how much does the data model behind the tools matter? We treat a typed knowledge graph as a grounding substrate and route each question by how it is best answered: (i) LLM-generated Cypher for structured retrieval, which lifts the same GPT-4 model from 65% to 82-83%; (ii) native graph and optimization primitives, with no LLM, reaching 99% on graph-answerable scenarios; and (iii) generation-augmented knowledge (GAK) for answers absent from the data -- the engine's agent materializes the missing facts as provenance-tagged graph nodes, then answers. A recurring theme is inverted LLM usage: we constrain the LLM to query generation or one-shot enrichment from a typed schema and let the graph execute deterministically. On the 88 real AssetOpsBench failure-mode scenarios the benchmark itself flags non-deterministic -- ten equipment types absent from the graph -- GAK lifts answerability from zero to 100% of equipment types and answers 81.8% of scenarios, every materialized fact tagged source:LLM-derived for auditability. We also contribute 40 graph-native scenarios. For structured operational domains the data layer -- not the LLM orchestration -- is the primary lever, and a typed knowledge graph serves as a grounding substrate between raw industrial data and LLM reasoning.

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.

Integrating multimodal datasets in clinical oncology is frequently hindered by high dimensionality and blockwise missingness, where entire data sources are unavailable for specific patient subsets. Standard survival models often struggle with these gaps, leading to biased results or patient exclusion. We introduce Multimodality Stacking with Blockwise missing values (MSB), a late-fusion framework for survival analysis that independently models modality-specific features before aggregating predictions via a cross-validated stacking meta-learner. MSB was validated on the PIONeeR study (n=443 patients, 378 biomarkers across eight heterogeneous sources) to predict progression-free survival in advanced non-small cell lung cancer patients receiving immunotherapy. MSB yielded higher predictive performance (C-index) than baseline algorithms. Improvements varied by baseline strength: linear models showed a 15.9% increase (p<0.001 for the Wilcoxon signed-rank test), random survival forests gained 5.4% (p=0.002), and gradient boosting methods improved by 2.1% (p=0.030). Beyond discrimination, MSB reduced the generalization gap (train-test difference in 5 folds cross-validation repeated 3 times: 0.055 vs 0.380 for linear models). Permutation importance analysis identified routine laboratory markers, clinical features, and PD-L1 expression as primary predictive drivers. Missing block indicators showed negligible importance, suggesting the model learned from biomarker values rather than data availability patterns. MSB provides a statistically validated framework for multimodal survival prediction with blockwise missingness. By enabling systematic biomarker evaluation without requiring complete data, MSB offers a practical tool for predictive modeling in biomedical research, pending external validation. Implementation is available at https://github.com/MohamedBoussena/MSB under Inria license.

Low-density EEG is more suitable for wearable and IoT-based brain sensing, but sparse electrode sampling often lacks sufficient spatial information to characterize cross-regional neural activity. EEG spatial super-resolution aims to recover dense-channel EEG from sparse recordings, yet remains challenging because channel missingness typically occurs at the whole-channel level, spatiotemporal dependencies over the full electrode layout are often underexplored, and the mapping from sparse to dense signals is inherently ambiguous. To address these issues, we propose TGSD, a topology-guided state-space diffusion framework for EEG spatial super-resolution. TGSD first employs a Hierarchical Spatial Prior Encoder to learn topology-aware priors over the complete electrode layout by integrating local geometric relationships with region-level contextual information. Based on these priors and sparse observations, a Conditional State-Space Diffusion Reconstructor progressively generates missing-channel signals through reverse diffusion, while alternating temporal and channel-wise state-space modeling captures long-range temporal dynamics and inter-channel dependencies in a unified framework. Experiments on the SEED and PhysioNet MM/I datasets show that TGSD consistently outperforms representative baselines under different super-resolution factors in both reconstruction fidelity and downstream classification performance. These results demonstrate the effectiveness of combining topology-aware spatial priors with conditional diffusion for enhancing practical low-density EEG sensing in wearable and IoT scenarios. The official implementation code is available at https://github.com/jtggz/TGSD.