Imputation

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.

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.

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.

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.

Kernel regression with tensor trains and Hadamard overparameterization (KReTTaH) is introduced as a training-data-free, interpretable, and nonparametric framework for multi-way data imputation. The imputation problem is reformulated as regression in reproducing kernel Hilbert spaces (RKHS), where the tensor regression coefficients are explicitly constrained to lie on fixed-rank tensor-train (TT) manifolds and structured via Hadamard overparameterization to promote sparsity and high representational efficiency. Rather than relying on costly cross-validation, KReTTaH jointly optimizes the TT coefficient tensors and the kernel covariance matrices within a Riemannian product-manifold framework -- the former on fixed-rank TT manifolds, the latter on the manifold of positive-definite matrices -- thereby enabling automated kernel-hyperparameter selection. Numerical tests on two challenging applications -- imputation of high-dimensional functional magnetic resonance imaging (fMRI) data and recovery of missing edge flows in dynamic graphs -- demonstrate that KReTTaH consistently outperforms state-of-the-art tensor-, Bayesian-, and neural-network-based baselines in terms of modeling accuracy.

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.

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.

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.

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, 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.

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.

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.

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.

Stochastic gradient methods are central to modern large-scale learning, but their use with incomplete covariates remains delicate since imputation schemes generally introduce systematic gradient biases, as shown for linear models. In this work, we prove that all parametric models exhibit similar gradient bias for various imputation procedures and characterize exactly the dependence on the missingness ratio vector $p$, with $O(\|p\|)$ as the leading term. We exploit this analysis to propose a simple debiasing procedure for stochastic gradient descent (SGD) with missing values based on Richardson extrapolation, which leverages the exact expression of the gradient bias. The key idea is to \emph{deliberately add missingness}: from an already incomplete observation, we generate a further-thinned version at a higher, controlled missingness level, and combine the two resulting stochastic gradients to cancel the leading bias term. We prove that one Richardson step reduces the gradient bias from $O(\|p\|)$ to $O(\|p\|^2)$ under several missingness scenarios. Our proposed method is computationally efficient, model-agnostic and applies to any parametric loss whose stochastic gradient can be computed after imputation. Furthermore, when missing indicators are independent, the population gradient bias is a multilinear polynomial in $p$ and depends only on population gradient errors induced by declaring a single coordinate missing. In this case, our method generalizes to a multi-step Richardson procedure which recursively cancels higher-order terms. Empirically, Richardson debiasing improves optimization and estimation across several generalized linear models and combines positively with widely used imputation procedures such as MICE. These results suggest that, somewhat counter-intuitively, adding controlled missingness on top of existing missing data can make stochastic learning from incomplete data more accurate.

Survey research faces mounting structural challenges: declining response rates, sample bias, block-wise missingness among at-risk respondents, and AI-assisted fraudulent completions in online panels. Large language models (LLMs) have been proposed as a remedy, yet rigorous evaluations across the full survey workflow remain scarce, particularly in disaster contexts where data quality matters most. We present and evaluate a five-stage framework for LLM integration covering questionnaire design, sample selection, pilot testing, missing-data imputation, and post-collection analysis, using the 2024 Hurricane Milton preparedness survey of Florida residents (n=946) as a shared empirical testbed. We introduce a Protection Motivation Theory (PMT)-constrained co-occurrence knowledge graph and develop seven LLM configurations spanning zero-shot inference, retrieval-augmented baselines, and novel theory-informed variants. Our proposed Anchored Marginal Theory-Informed LLM (A-TLM) outperforms all three classical imputation baselines (IPW/MI, MICE+PMM, missForest) on RMSE under disaster-relevant block-wise MNAR conditions (S4 RMSE 1.439 vs. 1.496 for the next-best), while achieving near-zero signed bias (-0.121) where the random-forest imputer produces the largest absolute bias (-0.631). Organizing retrieval around PMT causal structure and integrating all evidence in a single model call outperforms unstructured retrieval and staged sequential inference (MAE 0.993 vs. 1.097 for standard RAG). We document that near-zero aggregate bias can mask opposing subgroup errors and propose subgroup-stratified bias auditing as a reporting standard. A retrieval-constrained knowledge-graph chatbot demonstrates that hallucination is architecturally manageable through grounded refusal.

Federated Learning (FL) enables collaborative training across decentralized clients, but most methods assume aligned feature schemas, an assumption that rarely holds in tabular settings where clients observe only partially overlapping feature subsets. In these heterogeneous feature spaces, parameter-averaging methods (e.g., FedAvg) transfer little information across weakly overlapping or disjoint feature groups, limiting their effectiveness for federated imputation. To overcome this, we propose \textbf{FedHF-Impute}, a federated imputation framework that separates structural feature unavailability from conventional missingness and uses a shared global feature graph to propagate information across statistically related features through message passing. This enables indirect cross-client knowledge transfer, even when features are never jointly observed locally, while preserving standard federated communication. Under simulated partial schema overlap on the SECOM and AirQuality datasets, FedHF-Impute improves imputation accuracy (RMSE) over FL baselines by 26.9%, and 8.4% respectively, while achieving comparable performance on PhysioNET, with only a 0.3% difference relative to the best baseline.

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

The efficient operation of modern cellular networks hinges on the accurate analysis of spatio-temporal traffic data. Mastering these patterns is essential for core network functions, chiefly forecasting future load to pre-empt congestion and imputing missing values caused by sensor failures or transmission errors to ensure data continuity. While deeply connected, forecasting and imputation have historically evolved as separate sub-fields. The dominant paradigm, Spatio-Temporal Graph Neural Networks (STGNNs), while effective, are often specialized, computationally intensive, and exhibit limited generalization. Concurrently, adapting large pre-trained language models (LLMs) offers a powerful alternative for sequence modeling, yet existing approaches provide weak structural guidance, leading to unstable convergence and a narrow focus on forecasting. To bridge these gaps, we propose U-STS-LLM, a unified framework built on a spatio-temporally steered LLM. Our core innovation is a Dynamic Spatio-Temporal Attention Bias Generator that synthesizes a persistent functional graph with transient nodal states to explicitly steer the LLM's attention. Coupled with a partially frozen backbone tuned via Low-Rank Adaptation (LoRA) and a Gated Adaptive Fusion mechanism, the model achieves stable, parameter-efficient adaptation. Trained under a unified multi-task objective, U-STS-LLM learns a holistic data representation. Extensive experiments on real-world cellular datasets demonstrate that U-STS-LLM establishes new state-of-the-art performance in both long-horizon forecasting and high-missing-rate imputation, while maintaining remarkable training efficiency and stability, offering a novel blueprint for harnessing foundation models in structured, non-linguistic domains.

Order-Agnostic autoregressive models have demonstrated strong performance in deep generative modeling, yet their use in settings with incomplete data remains largely unexplored. In this work, we reinterpret them through the lens of missing data. First, we show that their standard training procedure on fully observed data implicitly performs imputation under a missing completely at random mechanism, resulting in robust out-of-sample imputation performance in settings with high missingness. Second, we introduce the first principled framework for training them directly on incomplete datasets under general missingness mechanisms. Third, we leverage their amortized conditional density estimation to perform active information acquisition, i.e., sequentially selecting the most informative missing variables for downstream prediction or inference. Across a suite of real-world benchmarks, our Missingness-Aware Order-Agnostic Autoregressive Model (MO-ARM) consistently outperforms established imputation baselines.

Knowledge Tracing (KT) is fundamental to intelligent education systems, yet relies on educational logs that are selectively observed. The non-random nature of exercise recommendations and student choices inevitably induces severe selection bias. Most existing KT methods neglect this issue, training on observed logs using standard empirical risk, which yields biased mastery estimates and accumulates errors in subsequent recommendations. To address this, we introduce a doubly robust (DR) formulation for KT that integrates a propensity model with an error imputation model, theoretically guaranteeing unbiasedness if either model is accurate. Beyond unbiasedness, in the sequential setting of KT, we identify that the estimator's performance is compromised by variance-dependent stochastic deviations that accumulate over time, thereby causing training instability and limiting performance. To mitigate this, we derive a generalization bound that explicitly characterizes the impact of estimator variance and identifies temporal smoothness as a key factor in controlling it. Building on these theoretical insights, we propose the Temporal Smoothness Doubly Robust (TSDR) framework. TSDR jointly optimizes the KT predictor and the imputation model with a smoothness regularizer, effectively reducing variance while preserving the unbiasedness guarantee of DR. Experiments on multiple real-world benchmarks demonstrate that TSDR consistently enhances various state-of-the-art KT backbones, underscoring the vital role of principled bias correction in KT.

Time series imputation benefits from leveraging cross-feature correlations, yet existing attention-based methods re-discover feature relationships at each layer, lacking persistent anchors to maintain consistent representations. To address this, we propose HELIX, which assigns each feature a learnable feature identity, a persistent embedding that captures intrinsic semantic properties throughout the network. Unlike graph-based methods that rely on predefined topology and assume homogeneous spatial relationships, HELIX learns arbitrary feature dependencies end-to-end from temporal co-variation, naturally handling datasets where features mix spatial locations with semantic variables. Integrated with hybrid temporal-feature attention, HELIX achieves the state-of-the-art performance, surpassing all 16 baselines on 5 public datasets across 21 experimental settings in our evaluation. Furthermore, our mechanistic analysis reveals that HELIX aligns learned feature identities and dependencies with latent physical and semantic structure progressively across layers, demonstrating that it more effectively translates cross-feature structure into imputation accuracy.

Evaluating large language models across many benchmarks is expensive, yet many benchmarks are highly correlated. We formalize the selection of a small, informative subset as submodular maximization under a multivariate Gaussian model. Entropy (log-determinant covariance) and mutual information between selected and remaining benchmarks arise as natural objectives. Both are submodular; entropy selection coincides with pivoted Cholesky and has spectral residual bounds, while mutual information is non-monotone in general but empirically monotone for small subsets, so we optimize it greedily. Experiments on three matrices from ten public leaderboards show that mutual information selection outperforms entropy for imputation at small subsets.

Generative models for time-series imputation achieve strong reconstruction accuracy, yet provide no finite-sample reliability guarantees, a critical limitation in power systems where imputed values inform dispatch and planning. We introduce SPLICE (Self-supervised Predictive Latent Inpainting with Conformal Envelopes), a modular framework coupling latent generative imputation with distribution-free, online-adaptive prediction intervals. A JEPA encoder maps daily load segments into a 64-dimensional latent space; a conditional latent bridge with four sampling modes generates candidate gap trajectories; an hourly-conditioned decoder maps back to signal space; and Adaptive Conformal Inference (ACI) wraps the output with coverage-guaranteed prediction bands. The flow-matching variant achieves comparable quality to DDIM in 5--10 ODE steps (5-10x speedup). On thirteen load datasets (nine proprietary, three UCI Electricity, ETTh1), SPLICE achieves the lowest mean Load-only MSE (0.056), winning 9/12 non-degenerate datasets at 91-day gaps and 18/32 across all gap lengths vs. five established baselines, and produces the best CRPS (0.161, -18.3% vs. the strongest competitor). ACI delivers 93--95% empirical coverage, correcting under-coverage failures of up to 7.5 pp observed with static conformal prediction. A pooled JEPA encoder trained on nine feeds transfers to four unseen domains, matching or exceeding per-dataset oracles with only a quick bridge fine-tuning.

Multivariate time series imputation is fundamental in applications such as healthcare, traffic forecasting, and biological modeling, where sensor failures and irregular sampling lead to pervasive missing values. Existing Transformer- and diffusion-based imputers achieve strong performance, but they often rely mainly on time-domain modeling and lack adaptive spectral bias for recovering structured temporal gaps. We propose FADTI, a Fourier- and attention-driven diffusion framework for multivariate time series imputation. FADTI introduces a Fourier Bias Projection (FBP) module that injects learnable frequency-aware bias into intermediate hidden states during denoising. It projects intermediate hidden states onto Fourier bases, avoiding direct spectral estimation from masked or zero-filled inputs. With DFT, STFT, and FSST instantiations, FBP captures global periodicity, localized time--frequency variations, and non-stationary oscillatory patterns. By coupling FBP with self-attention and gated convolution, FADTI integrates frequency-domain guidance, temporal dependency modeling, and probabilistic denoising in a unified framework. Experiments on multiple benchmarks, including a new biological imputation benchmark, show that FADTI improves accuracy, uncertainty estimation, and sampling efficiency, especially under high missing rates and structured missing patterns. Code is available at https://github.com/RazeenLI/FADTI

Handling missing data in time series classification remains a significant challenge in various domains. Traditional methods often rely on imputation, which may introduce bias or fail to capture the underlying temporal dynamics. In this paper, we propose TANDEM (Temporal Attention-guided Neural Differential Equations for Missingness), an attention-guided neural differential equation framework that effectively classifies time series data with missing values. Our approach integrates raw observation, interpolated control path, and continuous latent dynamics through a novel attention mechanism, allowing the model to focus on the most informative aspects of the data. We evaluate TANDEM on 30 benchmark datasets and a real-world medical dataset, demonstrating its superiority over existing state-of-the-art methods. Our framework not only improves classification accuracy but also provides insights into the handling of missing data, making it a valuable tool in practice.

We introduce Temporal Variational Implicit Neural Representations (TV-INRs), a probabilistic framework for modeling irregular multivariate time series that enables efficient and accurate individualized imputation and forecasting. By integrating implicit neural representations with latent variable models, TV-INRs learn distributions over time-continuous generator functions conditioned on signal-specific covariates. Unlike existing INR approaches that require extensive training, fine-tuning or meta-learning, our method achieves accurate individualized predictions through a single forward pass. Our experiments demonstrate that with a single TV-INRs instance, we can accurately solve diverse imputation and forecasting tasks, offering a computationally efficient and scalable solution for real-world applications. TV-INRs performs particularly well in low-data regimes, where on several datasets it achieves substantially lower imputation error, including order-of-magnitude improvements.

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

Psychiatry research seeks to understand the manifestations of psychopathology in behavior, as measured in questionnaire data, by identifying a small number of latent factors that explain them. While factor analysis is the canonical tool for this purpose, the resulting factors may not be interpretable, and may also be subject to confounding variables. Moreover, missing data are common, and explicit imputation is often required. To overcome these limitations, we introduce Interpretability Constrained Questionnaire Factorization (ICQF), a non-negative matrix factorization method with regularization tailored for questionnaire data. Our method aims to promote factor interpretability and solution stability. We provide an optimization procedure with theoretical convergence guarantees, and an automated procedure to determine latent dimensionality accurately. We validate these procedures using realistic synthetic data. We demonstrate the effectiveness of our method in a widely used general-purpose questionnaire, in two independent datasets (the Healthy Brain Network and Adolescent Brain Cognitive Development studies). Specifically, we show that ICQF preserves diagnostic information across a range of disorders, outperforming competing methods for smaller dataset sizes, and improves interpretability, as assessed by our clinical research collaborators and co-authors. This suggests that the regularization in our method matches domain characteristics, in addition to satisfying qualitative desiderata.

Clinical care often relies on key laboratory indicators, yet real-world patient visits are sparse and tests are ordered irregularly, leading to pervasive missingness. While many imputation methods improve average accuracy, they provide limited guidance on which imputed values are reliable enough for high-stakes downstream use. In this work, we study reliable clinical imputation, aiming to produce accurate imputations while selectively releasing the reliable results, with statistical control over clinically unacceptable errors. To achieve this goal, we propose SafeImpute, a reliable imputation framework for irregular and sparse clinical longitudinal records. SafeImpute constructs an event graph that captures both intra-patient temporal trajectories and inter-patient clinical similarity, and learns imputations with a two-relation GNN and adaptive fusion, regularized by an auxiliary masked reconstruction objective. For reliability guarantees, SafeImpute converts a proxy risk score into conformal p-values and applies the Benjamini--Hochberg procedure to control the false discovery rate (FDR) of unacceptable errors among released imputations at a user-specified tolerance. Experiments on our Mayo Clinic data, the public MIMIC-III and MIMIC-IV datasets show that SafeImpute achieves strong imputation accuracy while providing reliable error control, outperforming diverse baselines in both standard imputation evaluation and FDR-controlled selective-release evaluation.