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Generative Modeling under Non-Monotone MAR Missingness via Approximate Wasserstein Gradient Flows
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Proposes FLOWGEM, a nonparametric generative method for MAR data (including non-monotone missingness) that runs an approximate Wasserstein gradient flow minimizing the pattern-averaged KL divergence on observed coordinates, using local linear density-ratio velocity estimates.
Problem
Generating a complete sample from data with non-monotone MAR missing values, where existing imputation methods lack theoretical identification guarantees for the underlying distribution.
Approach
Minimize the expected KL divergence between observed-coordinate distributions and the generated sample's marginals averaged over missingness patterns (the ignoring-MLE target), and simulate its Wasserstein gradient flow with a closed-form local linear velocity estimator solved as a linear system, avoiding neural networks.
Key results
- On the uniform simulation (n=2000, B=20), FLOWGEM is among the best in energy distance and quantile estimation, with MICE the only close competitor.
- On real data, FLOWGEM has the lowest or second-lowest standardized energy distance on all ten datasets (e.g., concrete 5.84 vs 12.79 for next best, scm20d 17.65 best).
- Velocity approximation error is bounded by O(sqrt(|M|/(n sigma^d)) + sigma^2), vanishing as n grows and sigma goes to zero with n sigma^d diverging.
Surprising findings
- MICE is competitive with or beats FLOWGEM on several real datasets (e.g., scm1d, pumadyn32nm, stock), and in the Gaussian simulation it narrowly beats FLOWGEM.
- Several competing methods (GAIN, MIRI, NewImp) produce energy distances above 10^3 on many datasets, indicating instability under the shared setting.
Limitations
- Assumes continuous features; categorical or mixed-type data is not handled and filtering to continuous columns was required.
- Algorithm reported as slower for higher dimensions (fast for d<100), and runtime grows with d.
- Consistency in terms of a distributional distance is not yet established; velocity error bound constants may depend on x and t.
Experimental setup
Datasets: scm1d scm20d pumadyn32nm parkinsons allergens concrete stock forest housing windspeed
Benchmarks: simulated MAR example (uniform and Gaussian, d=3) ten real UCI/other datasets with simulated MAR missingness
Metrics: standardized energy distance quantile estimation error (0.1 quantile of X1) computation time
Baselines: MICE GAIN Hyperimpute MIRI Bayes MissDiff NewImp
Builds on: approximate Wasserstein gradient flow (Fathi/Stephanovits-style density ratio es ignoring maximum likelihood estimator under MAR MICE
Closest papers by meaning
- Towards Non-Asymptotic Convergence for Diffusion-Based Generative Models (ICLR 2024 · similarity 0.87)
- Rethinking the Diffusion Models for Missing Data Imputation: A Gradient Flow Perspective (NeurIPS 2024 · similarity 0.86)
- Bernoulli Flow Models: Self-Consistent Generative Modeling for Binary Data (NeurIPS 2026 · similarity 0.86)
- Inverse Flow and Consistency Models (ICML 2025 · similarity 0.86)
- DiffPuter: Empowering Diffusion Models for Missing Data Imputation (ICLR 2025 · similarity 0.86)
- Parameter Estimation in DAGs from Incomplete Data via Optimal Transport (ICML 2024 · similarity 0.85)
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