Kernel MMDs, Optimal Transport
Thanks to its support of the Sum and LogSumExp reductions, KeOps is perfectly suited to the large-scale computation of Kernel norms and Sinkhorn divergences. Going further, the block-sparse routines allow us to implement genuine coarse-to-fine strategies that scale (almost) linearly with the number of samples, as advocated in (Schmitzer, 2016).
Relying on the KeOps routines
the GeomLoss library
provides Geometric Loss functions as simple PyTorch layers,
with a fully-fledged gallery of examples.
Implemented on the GPU for the very first time, these routines
outperform the standard Sinkhorn algorithm by a factor 50-100
and redefine the state-of-the-art
for discrete Optimal Transport: on modern hardware,
Wasserstein distances between clouds of 100,000 points can now be
computed in less than a second.