Arbitrary Distributions Mapping via SyMOT-Flow: A Flow-based Approach Integrating Maximum Mean Discrepancy and Optimal Transport
CoRR(2023)
摘要
Finding a transformation between two unknown probability distributions from
finite samples is crucial for modeling complex data distributions and
performing tasks such as sample generation, domain adaptation and statistical
inference. One powerful framework for such transformations is normalizing flow,
which transforms an unknown distribution into a standard normal distribution
using an invertible network. In this paper, we introduce a novel model called
SyMOT-Flow that trains an invertible transformation by minimizing the symmetric
maximum mean discrepancy between samples from two unknown distributions, and an
optimal transport cost is incorporated as regularization to obtain a
short-distance and interpretable transformation. The resulted transformation
leads to more stable and accurate sample generation. Several theoretical
results are established for the proposed model and its effectiveness is
validated with low-dimensional illustrative examples as well as
high-dimensional bi-modality medical image generation through the forward and
reverse flows.
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