# Sinkhorn Distance

This article is super helpful to get the intuition https://dfdazac.github.io/sinkhorn.html of why it exists.

I was originally considering the Wasserstein Metric / EMD to solve for the Poker AI, but I found this.

See original paper.

This is a very fast approximation for the Optimal Transport problem.

It seems that EMD solves the solution exactly, but Sinkhorn is an approximation, to make the problem Convex and thus solvable much faster.

To make the problem Convex, we apply entropic Regularization.

The entropy of a matrix is given by $H(P)=ββ_{ij}P_{ij}gP_{ij}$ Low entropy = sparse matrix, i.e. most of non-zero values c are concentrated in a few points. The lower the entropy, the closer we are approximating to the original solution for the EMD.

Well Sinkhorn provides this regularization, I donβt understand why you would use sinkhorn.