# 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

$\int f(y) \pi(y) dy = \int f(T(x)) \rho(x) dx ;,$

obtaining a tractable integral from an otherwise intractable one.