Computational optimal transport

Discrete optimal transport

• Optimal transport between gaussians in R
• Optimal transport between gaussians in R2
• Linear program
• Minimum cost bipartite matching
• Relaxing the Monge formulation
• Sinkhorn algorithm and Birkhoff-Von Neuman decomposition
• Euclidian space
• Grayscale histogram equalization
• Image colour transfer

Semi-discrete optimal transport

• Projective gradient ascent
• Nesterov smoothing

Continuous optimal transport

• Continuous optimal transport between gaussians

Wasserstein

• Wasserstein distance (Bipartite graph formulation and Hungarian algorithm)
• Wasserstein geodesic and barycenter

Regularization

• Entropic regularization

Unbalanced optimal transport

Partial optimal transport

Statistical learning and ML

• Optimal transport as a statistical learning problem
• [] Background density estimation
• [] Density estimation with continuous normalizing flows
• [] Classification
• [] Wasserstein Generative Adverserial Network

PDEs

• [] Gradient flows
• [] Linear diffusion equation
• [] Non-linear diffusion equation
• [] Mean field limits
• [] Functional inequalities
• [] Geometric inequalities
• [] Ricci curvature