Christophe Muller | Searcharxiv

arXiv2025

Do we Need Dozens of Methods for Real World Missing Value Imputation?

Missing values pose a persistent challenge in modern data science. Consequently, there is an ever-growing number of publications introducing new imputation methods in various fields. While many studies compare imputation approaches, they often focus on a limited subset of algorithms and evaluate performance primarily through pointwise metrics such as RMSE, which are not suitable to measure the preservation of the true data distribution. In this work, we provide a systematic benchmarking method based on the idea of treating imputation as a distributional prediction task. We consider a large number of algorithms and, for the first time, evaluate them not only on synthetic missing mechanisms, but also on real-world missingness scenarios, using the concept of Imputation Scores. Finally, while the focus of previous benchmark has often been on numerical data, we also consider mixed data sets in our study. The analysis overwhelmingly confirms the superiority of iterative imputation algorithms, especially the methods implemented in the mice R package.

stat.CO↗

arXiv2025

When Pattern-by-Pattern Works: Theoretical and Empirical Insights for Logistic Models with Missing Values

Predicting with missing inputs challenges even parametric models, as parameter estimation alone is insufficient for prediction on incomplete data. While several works study prediction in linear models, we focus on logistic models, where optimal predictors lack closed-form expressions. We prove that a Pattern-by-Pattern strategy (PbP), which learns one logistic model per missingness pattern, accurately approximates Bayes probabilities under a Gaussian Pattern Mixture Model (GPMM). Crucially, this result holds across standard missing data scenarios (MCAR and MAR) and, notably, in Missing Not at Random (MNAR) settings where standard methods often fail. Empirically, we compare PbP against imputation and EM methods across classification, probability estimation, calibration, and inference. Our analysis provides a comprehensive view of logistic regression with missing values. It reveals that mean imputation can be used as baseline for low sample sizes and PbP for large sample sizes, as both methods are fast to train and may have good performances in some settings. The best performances are achieved by non-linear multiple iterative imputation techniques that include the response label (Random Forest MICE with response), which are more computationally expensive.

stat.ML↗