Hanzhang Lu, Jeffrey L. Andrews, Ryan P. Brownestat.ME stat.CO stat.ML
Matrix-variate data with missing entries arise frequently in applications where observations are naturally organized as two-dimensional arrays. Although the matrix normal distribution provides a parsimonious model through its Kronecker covariance structure, standard EM estimation can be computationally expensive because arbitrary missingness patterns typically destroy this separability in the E-step. In this paper, we propose an efficient partial EM algorithm for matrix-variate normal data with missing entries. The proposed method updates the conditional mean and covariance of the missing component through coordinate-wise approximations, avoiding repeated inversion of pattern-specific covariance matrices and avoiding construction of the full vectorized covariance matrix. We further develop a specialized update for submatrix missingness, where the missing-block precision retains a Kronecker product structure, and the covariance update can be carried out independently in the row and column directions. Simulation studies show that the proposed methods substantially reduce computation time compared with exact EM while preserving nearly identical observed-data likelihood across a range of dimensions and missing proportions. A real-data application to hyperspectral image patches demonstrates that the proposed imputation strategy can be embedded within a matrix-variate mixture model for simultaneous imputation and clustering.
Yasin Khadem Charvadeh, Grace Y. Yi, Mithat Gönen +1stat.ML cs.LG
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.
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.
Andrea Basteri, Carlo Ciliberto, Alessandro Rudistat.ML cs.LG
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.
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.
Etienne Le Naour, Tahar Nabil, Adrien Petraliacs.LG
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 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.
In-context learning for tabular data sets strong predictive standards in observational settings; it however primarily relies on correlational structure, which becomes unreliable under distribution shift or intervention. While established methods to discover causal structure exist, they are often focused on structure identifiability and decoupled from the predictive architectures that could benefit from them. To bridge these perspectives, we study how to simultaneously infer and enforce causal structure in the form of topological variable orderings into tabular prediction. Unlike standard architectures, our model TabOrder uses causal order-constrained attention, basing predictions only on features that precede a target under a learned causal order. Similar to causal discovery methods, TabOrder learns the optimal variable ordering in an unsupervised manner through a likelihood-based objective. We justify this choice under standard functional model classes and also study how sample missingness, a common challenge in tabular data, interacts with causal direction identification. Empirically, we confirm that TabOrder recovers accurate variable orderings while addressing prediction and imputation tasks, as well as gives insight into real-world biological data under intervention.
Wenjie Du, Yiyuan Yang, Tianxiang Zhan +1cs.LG cs.AI
Partially-observed time series (POTS) is ubiquitous in real-world applications, yet most existing toolchains separate missing-value handling from downstream learning, which limits reproducibility and overall performance. This tutorial introduces PyPOTS, an open-source Python ecosystem for end-to-end data mining and machine learning on POTS. We present practical workflows spanning missingness simulation, data preprocessing, model training, and evaluation across core tasks, including imputation, forecasting, classification, clustering, and anomaly detection. The tutorial consists of two parts: Part I emphasizes hands-on application for practitioners through unified APIs and benchmark-oriented experiments. Part II targets developers and researchers, focusing on extending PyPOTS with custom models, domain-specific constraints, and contribution-ready engineering practices. Participants will gain both conceptual understanding and implementation experience for building robust, transparent, and reusable POTS pipelines in research and production settings. PyPOTS is publicly available at https://github.com/WenjieDu/PyPOTS