TransportMaps¶
We use (transport) maps from \(\mathbb{R}^d\) to \(\mathbb{R}^d\) to represent transformations between probability distributions. These transformations lead to efficient algorithms for the solution of practical inference problems, or for the estimation of densities from samples.
For example, if \(Y \sim \nu_\pi\) is a complex distribution and \(X \sim \nu_\rho\) is an amenable distribution (e.g. standard normal) we look for a computable and invertible map \(T\) such that \(Y = T(X)\). This allows us to apply the following change of variables
obtaining a tractable integral from an otherwise intractable one.
The actual version of TransportMaps implements a
taxonomy of maps, distributions
and likelihoods which allow for modeling many complex problems.