Score Operator Newton transport
This provides a new approach for Bayesian inference and sampling tasks, though it appears incremental as it builds on existing transport map and Newton method concepts.
The authors tackled the problem of sampling and Bayesian computation by proposing a score-operator Newton transport method that constructs a transport map using the target distribution's score, proving convergence conditions and demonstrating fast convergence while avoiding mode collapse in elementary settings.
We propose a new approach for sampling and Bayesian computation that uses the score of the target distribution to construct a transport from a given reference distribution to the target. Our approach is an infinite-dimensional Newton method, involving a linear PDE, for finding a zero of a ``score-residual'' operator. We prove sufficient conditions for convergence to a valid transport map. Our Newton iterates can be computed by exploiting fast solvers for elliptic PDEs, resulting in new algorithms for Bayesian inference and other sampling tasks. We identify elementary settings where score-operator Newton transport achieves fast convergence while avoiding mode collapse.