Reproduce “(De)-regularized Maximum Mean Discrepancy Gradient Flow” on OpenResearch
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About this paper
Zonghao Chen, Aratrika Mustafi, Pierre Glaser, Anna Korba, Arthur Gretton, Bharath K. Sriperumbudur
DrMMD combines sample-based MMD updates with a regularized discrepancy that approaches χ²-divergence at low regularization and squared MMD at high regularization. Its algorithm computes a witness function from source and target samples and adapts regularization. Under assumptions, it gives exponential KL decay with a discretization barrier; experiments report MMD² and Wasserstein-2 curves in two settings, not universal convergence.
Key insights
- DrMMD provides a principled framework that bridges the gap between the sample-based implementability of MMD and the strong theoretical convergence guarantees of χ²-divergence.
- The derivation of an optimal adaptive schedule for the `λ` parameter offers theoretical justification for the benefits of adaptive kernel methods in MMD-based generative models.
- The continuous-time DrMMD flow achieves near-global exponential convergence to the target distribution, overcoming the local optima issues common in traditional MMD flows.
Summary by alphaXiv.
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