High-dimensional statistics and probability theory

  1. Statistical bounds for entropic optimal transport: sample complexity and the central limit theorem [PDF] (2019)
  2. Statistical optimal transport via factored couplings [PDF] (2018)
  3. Entropic optimal transport is maximum likelihood deconvolution [PDF] (2018)
  4. Minimax rates of estimation for smooth optimal transport maps [PDF] (2019)
  5. Overview of transportation inequalities (e.g. Chapter 4 of these lectures notes)

Wasserstein Gradient Flows and applications

  1. Overview of WGFs (e.g. Santambrogio)
  2. Implicit Bias of Gradient Descent for Wide Two-layer Neural Networks Trained with the Logistic Loss [PDF] (2020)
  3. The Variational Formulation of the Fokker-Planck Equation [PDF] (1998)
  4. Gradient Flows in Wasserstein Spaces and Applications to Crowd Movement [PDF] (2009)
  5. On the Global Convergence of Gradient Descent for Over-parametrized Models using OT [PDF] (2019)

Applications in machine learning/deep learing/reinforcement learning

  1. How well do WGANs estimate the Wasserstein metric? [PDF] (2019)
  2. Policy Optimization as Wasserstein Gradient Flows [PDF] (2018)

Computational OT

  1. Overview of dynamical formulation of OT (Benamou-Brenier) [PDF] (2000)
  2. Gradient descent perspective of Sinkhorn [PDF] (2020)
  3. Gradient descent algorithms for Bures-Wasserstein barycenters [PDF] (2020)
  4. A fast approach to optimal transport: The back-and-forth method [PDF] (2019)