Feb 8 2021 · 8 min read

Estimating Monge Maps Kantorovich relaxes Monge If you look in a modern treatment of optimal transportation, you will likely find the problem defined as something like $$ W_c(\mu,\nu) = \inf_{\pi \in \Pi(\mu,\nu)} \int_{X \times Y} c(x,y) d\pi $$ This is the modern definition of the problem, where we model the objective as finding the minimum cost coupling between $\mu$ and $\nu$. But this is not the original formulation of the problem.

Jan 22 2021 · 6 min read

Prelude In this series I’m going to detail some interesting ideas I tried in my research that didn’t pan out. By doing so I hope to help other people avoid wasting time on the same things I did. Perhaps they will even realize that something here is not a waste of time and do something cool with it.
Definitions One of my areas of interest is Optimal Transportation. The curious reader can no doubt find a better expose of these ideas on Wikipedia or in one of many books, but the gist is …