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Distribution Shift in Missing Data Imputation: A Risk-Based Perspective and Importance-Weighted Correction under MAR

NeurIPS 2026 · Learning theory and algorithms › Kernels and regression theory · approach: Statistical perspectives on generalization · 0 citations (OpenAlex)

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Shows that risk-based imputation under MAR must correct for observed-data distribution shift, and proposes an importance-weighted round-robin iterative imputer that reweights observed rows by estimated missingness density ratios.

Problem

Learning imputation models from observed data under MAR missingness that depends on the data, where the training distribution (observed rows) differs from the full-data distribution used for evaluation, so standard MSE-trained imputers are biased for the missing entries.

Approach

Rewrites the coordinate-wise imputation MSE risk on missing entries as an importance-weighted expectation over observed data (weights = density ratio of missing vs observed covariates) and plugs estimated weights into a round-robin iterative imputer (logistic-regression density ratio estimation plus tempered weighted least squares).

Key results

• Weighted method improves RMSE in 20 of 24 simulation settings and Wasserstein distance in 23 of 24 settings relative to unweighted round-robin baselines.
• Average reductions of 3% in RMSE and 7% in Wasserstein distance across simulations (per abstract).
• Weighted linear imputation runs in about 47% of the unweighted runtime; RF and MLP variants are about 12.5% and 11.3% slower overall.

Surprising findings

• RMSE gains are smaller or statistically indistinguishable from 1 for more expressive RF and MLP imputers, and MLP can degrade under weighting due to variance.
• Weighted linear models are faster than unweighted ones in runtime.

Limitations

• Performance can degrade for high-variance conditional models such as MLPs.
• Gains are limited under weak MAR, and MAR violations or poor weight estimation can hurt performance relative to unweighted methods.

Experimental setup

Datasets: Blood Airfoil California Letter Gas Metro Motor Acceleration MNIST

Benchmarks: Blood Airfoil California Letter Gas Metro Motor Acceleration MNIST

Metrics: RMSE Wasserstein distance runtime downstream regression RMSE downstream classification accuracy correlation matrix recovery

Baselines: HyperImpute (linear) scikit-learn IterativeImputer GAIN Sinkhorn SoftImpute MissForest

Builds on: MICE HyperImpute MissForest covariate shift importance weighting

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