We establish links between the conditional independence structure of the target measure and the existence of certain low-dimensional couplings, induced by transport maps that are sparse or decomposable. Our analysis not only facilitates the construction of couplings in high-dimensional settings, but also suggests new inference methodologies. For instance, in the context of nonlinear and non-Gaussian state space models, we will describe new variational algorithms for nonlinear smoothing and sequential parameter estimation. We will also outline a new class of nonlinear filters induced by local couplings, for inference in high-dimensional spatiotemporal processes with chaotic dynamics.
This is joint work with Alessio Spantini and Daniele Bigoni.
Discovery Building, Orchard View Room
Youssef M Marzouk