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About this paper
Pierre Glaser, Michael Arbel, Arthur Gretton
KALE Flow transports source particles toward a target known only through samples, including when source and target have disjoint support. It learns a smooth force by optimizing a regularized KL variational objective in an RKHS, then updates particles along its gradient. In a three-ring experiment, KALE stayed near the rings while MMD remained scattered; this is empirical, not universal.
Key insights
- KALE functions as a weakly continuous probability divergence that metrizes weak convergence, making it a theoretically sound metric for implicit generative models and other sample-based learning tasks.
- The regularization parameter (λ) within KALE provides a continuous interpolation between MMD (as λ approaches infinity) and KL divergence (as λ approaches zero under certain conditions), offering tunable sensitivity to support differences.
- The velocity field of the KALE gradient flow is driven by the gradient of an optimal witness function within an RKHS, allowing for practical and theoretically grounded gradient estimation from samples.
Summary by alphaXiv.
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