Collaborative filtering methods based on implicit feedback (e.g., purchase records and browsing history) are widely used in recommender systems. Compared to explicit feedback (e.g., 1-5 star ratings), implicit feedback is more abundant and accessible in real-world applications. However, the missing data of implicit feedback also brings two challenges.

We propose a constructive algorithm for identifying complete data distributions in graphical models of missing data. The complete data distribution is unrestricted, while the missingness mechanism is assumed to factorize according to a conditional directed acyclic graph. Our approach follows an interventionist perspective in which missingness indicators are treated as variables that can be intervened on. A central challenge in this setting is that sequences of interventions on missingness indicators may induce and propagate selection bias, so that identification can fail even when a propensity score is invariant to available interventions. To address this challenge, we introduce a tree-based identification algorithm that explicitly tracks the creation and propagation of selection bias and determines whether it can be avoided through admissible intervention strategies. The resulting tree provides both a diagnostic and a constructive characterization of identifiability under a given missingness mechanism. Building on these results, we develop recursive inverse probability weighting procedures that mirror the intervention logic of the identification algorithm, yielding valid estimating equations for both the missingness mechanism and functionals of the complete data distribution. Simulation studies and a real-data application illustrate the practical performance of the proposed methods. An accompanying R package, flexMissing, implements all proposed procedures.

Abstract--This paper presents a semi-supervised learning framework for Gaussian mixture modelling under a Missing at Random (MAR) mechanism. T o quantify classification uncertainty, we introduce margin confidence and incorporate the Aranda-Ordaz (AO) link function to flexibly capture the asymmetric relationships between uncertainty and missing probability. Based on this formulation, we develop an efficient Expectation-Conditional Maximization (ECM) algorithm that jointly estimates all parameters appearing in both the Gaussian mixture model (GMM) and the missingness mechanism, and subsequently imputes the missing labels by a Bayesian classifier derived from the fitted mixture model. This method effectively alleviates the bias induced by ignoring the missingness mechanism while enhancing the robustness of semi-supervised learning. The resulting uncertainty-aware framework delivers reliable classification performance in realistic MAR scenarios with substantial proportions of missing labels.

Semi-supervised learning (SSL) constructs classifiers using both labelled and unlabelled data. It leverages information from labelled samples, whose acquisition is often costly or labour-intensive, together with unlabelled data to enhance prediction performance. This defines an incomplete-data problem, which statistically can be formulated within the likelihood framework for finite mixture models that can be fitted using the expectation-maximisation (EM) algorithm. Ideally, one would prefer a completely labelled sample, as one would anticipate that a labelled observation provides more information than an unlabelled one. However, when the mechanism governing label absence depends on the observed features or the class labels or both, the missingness indicators themselves contain useful information. In certain situations, the information gained from modelling the missing-label mechanism can even outweigh the loss due to missing labels, yielding a classifier with a smaller expected error than one based on a completely labelled sample analysed. This improvement arises particularly when class overlap is moderate, labelled data are sparse, and the missingness is informative. Modelling such informative missingness thus offers a coherent statistical framework that unifies likelihood-based inference with the behaviour of empirical SSL methods.

Handling missing data remains a fundamental challenge in real-world tabular datasets, especially when data are heterogeneous with both numerical and categorical features. Existing imputation methods often fail to capture complex structural dependencies and handle heterogeneous data effectively. We present \textbf{IVGAE}, a Variational Graph Autoencoder framework for robust imputation of incomplete heterogeneous data. IVGAE constructs a bipartite graph to represent sample-feature relationships and applies graph representation learning to model structural dependencies. A key innovation is its \textit{dual-decoder architecture}, where one decoder reconstructs feature embeddings and the other models missingness patterns, providing structural priors aware of missing mechanisms. To better encode categorical variables, we introduce a Transformer-based heterogeneous embedding module that avoids high-dimensional one-hot encoding. Extensive experiments on 16 real-world datasets show that IVGAE achieves consistent improvements in RMSE and downstream F1 across MCAR, MAR, and MNAR missing scenarios under 30\% missing rates. Code and data are available at: https://github.com/echoid/IVGAE.

Handling missing data is a central challenge in data-driven analysis. Modern imputation methods not only aim for accurate reconstruction but also differ in how they represent and quantify uncertainty. Yet, the reliability and calibration of these uncertainty estimates remain poorly understood. This paper presents a systematic empirical study of uncertainty in imputation, comparing representative methods from three major families: statistical (MICE, SoftImpute), distribution alignment (OT-Impute), and deep generative (GAIN, MIWAE, TabCSDI). Experiments span multiple datasets, missingness mechanisms (MCAR, MAR, MNAR), and missingness rates. Uncertainty is estimated through three complementary routes: multi-run variability, conditional sampling, and predictive-distribution modeling, and evaluated using calibration curves and the Expected Calibration Error (ECE). Results show that accuracy and calibration are often misaligned: models with high reconstruction accuracy do not necessarily yield reliable uncertainty. We analyze method-specific trade-offs among accuracy, calibration, and runtime, identify stable configurations, and offer guidelines for selecting uncertainty-aware imputers in data cleaning and downstream machine learning pipelines.

Implicit feedback is widely used in collaborative filtering methods for recommendation.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This is an interesting paper - the application of graphical methods to analyze missing data patterns may prove to be very useful. The paper contains the word causal graph in the title and in the introduction. However, none of the results seem to depend on the graph being causal. The results are entirely about conditional independence and factorizations.

Missing data imputation in tabular datasets remains a pivotal challenge in data science and machine learning, particularly within socioeconomic research. However, real-world socioeconomic datasets are typically subject to strict data protection protocols, which often prohibit public sharing, even for synthetic derivatives. This severely limits the reproducibility and accessibility of benchmark studies in such settings. Further, there are very few publicly available synthetic datasets. Thus, there is limited availability of benchmarks for systematic evaluation of imputation methods on socioeconomic datasets, whether real or synthetic. In this study, we utilize the World Bank's publicly available synthetic dataset, Synthetic Data for an Imaginary Country, which closely mimics a real World Bank household survey while being fully public, enabling broad access for methodological research. With this as a starting point, we derived the IMAGIC-500 dataset: we select a subset of 500k individuals across approximately 100k households with 19 socioeconomic features, designed to reflect the hierarchical structure of real-world household surveys. This paper introduces a comprehensive missing data imputation benchmark on IMAGIC-500 under various missing mechanisms (MCAR, MAR, MNAR) and missingness ratios (10\%, 20\%, 30\%, 40\%, 50\%). Our evaluation considers the imputation accuracy for continuous and categorical variables, computational efficiency, and impact on downstream predictive tasks, such as estimating educational attainment at the individual level. The results highlight the strengths and weaknesses of statistical, traditional machine learning, and deep learning imputation techniques, including recent diffusion-based methods. The IMAGIC-500 dataset and benchmark aim to facilitate the development of robust imputation algorithms and foster reproducible social science research.

We address the problem of deciding whether a causal or probabilistic query is estimable from data corrupted by missing entries, given a model of missingness process. We extend the results of Mohan et al. [2013] by presenting more general conditions for recovering probabilistic queries of the form P(y|x) and P(y,x) as well as causal queries of the form P(y|do(x)). We show that causal queries may be recoverable even when the factors in their identifying estimands are not recoverable. Specifically, we derive graphical conditions for recovering causal effects of the form P(y|do(x)) when Y and its missingness mechanism are not d-separable. Finally, we apply our results to problems of attrition and characterize the recovery of causal effects from data corrupted by attrition.