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Interpretable Generalized Additive Models for Datasets with Missing Values
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Proposes M-GAM, a sparse generalized additive model that handles missing values by adding missingness indicators and missingness-by-threshold interaction terms, with l0 regularization for sparsity, avoiding imputation.
Problem
Maintaining interpretability of models on datasets with missing feature values; imputation complicates feature-to-label mappings, while naive missingness indicators and interactions blow up the number of terms and cause overfitting.
Approach
Extend sparse GAMs with missingness indicators and missingness-interaction terms that adjust other features' shape functions when a feature is missing, and use l0 regularization (FastSparse) to keep the model sparse, rather than imputing values.
Key results
- Under added informative MAR missingness, M-GAM with interactions achieves much higher accuracy than imputation-based GAMs, with the gap growing as missingness rate increases.
- On FICO, M-GAM with only 20 nonzero coefficients achieves accuracy superior to dense multiple-imputation alternatives.
- M-GAM is at least an order of magnitude faster than impute-then-predict methods using multiple imputation, and performs on par with imputation baselines on real datasets.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add missingness interaction terms to M-GAM | M-GAM · FICO and Breast Cancer with synthetic MAR missingness | accuracy (FICO); AUC (Breast Cancer) | Helped |
| Add missingness interaction terms rather than use indicators only (ablation) | M-GAM · FICO and Breast Cancer with synthetic MAR missingness | accuracy (FICO); AUC (Breast Cancer) | Helped |
| Use M-GAM instead of impute-then-predict | M-GAM · FICO, Breast Cancer, MIMIC, and Pharyngitis with naturally occurring missingness | accuracy (FICO, MIMIC, Pharyngitis); AUC (Breast Cancer) | No clear effect |
| Use M-GAM with missingness interactions instead of impute-then-predict | M-GAM · FICO, Breast Cancer, MIMIC, and Pharyngitis | runtime | Helped |
| Use 32 evenly spaced quantiles instead of fewer quantiles (ablation) | M-GAM · FICO | accuracy | Helped |
| Vary the number of evenly spaced quantiles among 4, 8, 16, and 32 (ablation) | M-GAM · FICO | accuracy | No clear effect |
| Increase MICE imputations from 1 to 5 (ablation) | MICE impute-then-predict classifiers · FICO | accuracy | Helped |
| Increase MICE imputations beyond 5 (ablation) | MICE impute-then-predict classifiers · FICO | accuracy | No clear effect |
Surprising findings
- Perfect imputation can reduce the best achievable Bayes-optimal accuracy compared with using missingness as a value (Proposition 3.1 and Corollary 3.2).
Limitations
- l0 penalty is applied uniformly, so new missingness terms are not regularized differently from existing features.
- Missingness indicators are vulnerable to distribution shift, especially in medical settings.
- Synthetic MAR experiments rely on an added missingness mechanism that is constructed by the authors rather than observed in real data.
Experimental setup
Datasets: FICO (Explainable ML Challenge) Breast Cancer (Razavi et al., 2018) MIMIC-III Pharyngitis (Miyagi, 2023) CKD (UCI) Heart Disease (UCI)
Benchmarks: FICO Breast Cancer MIMIC Pharyngitis CKD Heart Disease
Metrics: test accuracy test AUC number of nonzero coefficients runtime in seconds
Baselines: MICE MIWAE MissForest GAM w/ mean-value imputation SMIM XGBoost random forest decision tree
Builds on: FastSparse (Liu et al., 2022) Van Ness et al. (2023) missingness indicators (SMIM) multiple imputation (MICE) Le Morvan et al. (2021)
Closest papers by meaning
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- Learning What Not to Impute: An Uncertainty-Aware Diffusion Framework for Meaningful Missingness (NeurIPS 2026 · similarity 0.86)
- Random features models: a way to study the success of naive imputation (ICML 2024 · similarity 0.85)
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- Missing data and cluster graphs: cluster-level missingness vs variable-level missingness (NeurIPS 2026 · similarity 0.84)
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