Iterative imputation is a prevalent method for missing data imputation, where each feature is imputed iteratively by treating it as a target variable estimated from all other features. However, iterative imputation method suffers from two principal limitations: it imposes a single parametric model form to impute all features, neglecting the potential for optimal models to vary among features, which risks model misspecification; and it assumes every feature contains missing values, overlooking the potential presence of non-missing features, termed as oracle features, which are informative for imputation. To address these limitations, we propose kernel point imputation (KPI), a bi-level optimization framework for iterative missing data imputation. At the inner level, KPI adaptively learns the optimal model form for each feature within a reproducing kernel Hilbert space, addressing limitation . At the outer level, KPI utilizes oracle features as supervisory signals to iteratively refine the imputations, addressing limitation . Experiments demonstrate that KPI outperforms competitive imputation methods. Code is available at https://github.com/FMLYD/kpi.git.

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

Incomplete spatio-temporal data in the real world has spawned much research.

Motivated by a recent literature on the double-descent phenomenon in machine learning, we consider highly over-parameterized models in causal inference, including synthetic control with many control units.

Real-world tabular databases routinely combine continuous measurements and categorical records, yet missing entries are pervasive and can distort downstream analysis. We propose Statistical-Neural Interaction (SNI), an interpretable mixed-type imputation framework that couples correlation-derived statistical priors with neural feature attention through a Controllable-Prior Feature Attention (CPFA) module. CPFA learns head-wise prior-strength coefficients $\{λ_h\}$ that softly regularize attention toward the prior while allowing data-driven deviations when nonlinear patterns appear to be present in the data. Beyond imputation, SNI aggregates attention maps into a directed feature-dependency matrix that summarizes which variables the imputer relied on, without requiring post-hoc explainers. We evaluate SNI against six baselines (Mean/Mode, MICE, KNN, MissForest, GAIN, MIWAE) on six datasets spanning ICU monitoring, population surveys, socio-economic statistics, and engineering applications. Under MCAR/strict-MAR at 30\% missingness, SNI is generally competitive on continuous metrics but is often outperformed by accuracy-first baselines (MissForest, MIWAE) on categorical variables; in return, it provides intrinsic dependency diagnostics and explicit statistical-neural trade-off parameters. We additionally report MNAR stress tests (with a mask-aware variant) and discuss computational cost, limitations -- particularly for severely imbalanced categorical targets -- and deployment scenarios where interpretability may justify the trade-off.

Missing values in high-dimensional, mixed-type datasets pose significant challenges for data imputation, particularly under Missing Not At Random (MNAR) mechanisms. Existing methods struggle to integrate local and global data characteristics, limiting performance in MNAR and high-dimensional settings. We propose an innovative framework, RefiDiff, combining local machine learning predictions with a novel Mamba-based denoising network efficiently capturing long-range dependencies among features and samples with low computational complexity. RefiDiff bridges the predictive and generative paradigms of imputation, leveraging pre-refinement for initial warm-up imputations and post-refinement to polish results, enhancing stability and accuracy. By encoding mixed-type data into unified tokens, RefiDiff enables robust imputation without architectural or hyperparameter tuning. RefiDiff outperforms state-of-the-art (SOT A) methods across missing-value settings, demonstrating strong performance in MNAR settings and superior out-of-sample generalization. Extensive evaluations on nine real-world datasets demonstrate its robustness, scalability, and effectiveness in handling complex missingness patterns.

Incomplete spatio-temporal data in the real world has spawned much research.

Tabular data are central to many applications, especially longitudinal data in healthcare, where missing values are common, undermining model fidelity and reliability. Prior imputation methods either impose restrictive assumptions or struggle with complex cross-feature structure, while recent generative approaches suffer from instability and costly inference. We propose Impute-MACFM, a mask-aware conditional flow matching framework for tabular imputation that addresses missingness mechanisms, missing completely at random, missing at random, and missing not at random. Its mask-aware objective builds trajectories only on missing entries while constraining predicted velocity to remain near zero on observed entries, using flexible nonlinear schedules. Impute-MACFM combines: (i) stability penalties on observed positions, (ii) consistency regularization enforcing local invariance, and (iii) time-decayed noise injection for numeric features. Inference uses constraint-preserving ordinary differential equation integration with per-step projection to fix observed values, optionally aggregating multiple trajectories for robustness. Across diverse benchmarks, Impute-MACFM achieves state-of-the-art results while delivering more robust, efficient, and higher-quality imputation than competing approaches, establishing flow matching as a promising direction for tabular missing-data problems, including longitudinal data.

Recent advances in wearable technology have enabled the continuous monitoring of vital physiological signals, essential for predictive modeling and early detection of extreme physiological events. Among these physiological signals, heart rate (HR) plays a central role, as it is widely used in monitoring and managing cardiovascular conditions and detecting extreme physiological events such as hypoglycemia. However, data from wearable devices often suffer from missing values. To address this issue, recent studies have employed various imputation techniques. Traditionally, the effectiveness of these methods has been evaluated using predictive accuracy metrics such as RMSE, MAPE, and MAE, which assess numerical proximity to the original data. While informative, these metrics fail to capture the complex statistical structure inherent in physiological signals. This study bridges this gap by presenting a comprehensive evaluation of four statistical imputation methods, linear interpolation, K Nearest Neighbors (KNN), Piecewise Cubic Hermite Interpolating Polynomial (PCHIP), and B splines, for short term HR data gaps. We assess their performance using both predictive accuracy metrics and statistical distance measures, including the Cohen Distance Test (CDT) and Jensen Shannon Distance (JS Distance), applied to HR data from the D1NAMO dataset and the BIG IDEAs Lab Glycemic Variability and Wearable Device dataset. The analysis reveals limitations in existing imputation approaches and the absence of a robust framework for evaluating imputation quality in physiological signals. Finally, this study proposes a foundational framework to develop a composite evaluation metric to assess imputation performance.