Optimal transport map estimation in general function spaces
一般函数空间中的最优传输映射估计
We study the problem of estimating a function T, given independent samples from a distribution P and from the pushforward distribution T♯P. This setting is motivated by applications in the sciences, where T represents the evolution of a physical system over time, and in machine learning, where, for example, T may represent a transformation learned by a deep neural network trained for a generative modeling task. To ensure identifiability, we assume that T=∇φ0 is the gradient…