Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gaussian-Smooth Optimal Transport: Metric Structure and Statistical
  Efficiency   Optimal transport (OT), and in particular the Wasserstein distance, has seen
a surge of interest and applications in machine learning. However, empirical
approximation under Wasserstein distances suffers from a severe curse of
dimensionality, rendering them impractical in high dimensions. As a result,
entropically regularized OT has become a popular workaround. However, while it
enjoys fast algorithms and better statistical properties, it looses the metric
structure that Wasserstein distances enjoy. This work proposes a novel
Gaussian-smoothed OT (GOT) framework, that achieves the best of both worlds:
preserving the 1-Wasserstein metric structure while alleviating the empirical
approximation curse of dimensionality. Furthermore, as the Gaussian-smoothing
parameter shrinks to zero, GOT $\Gamma$-converges towards classic OT (with
convergence of optimizers), thus serving as a natural extension. An empirical
study that supports the theoretical results is provided, promoting
Gaussian-smoothed OT as a powerful alternative to entropic OT.

17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph