A1222
Title: Diff-Fusion: Bayesian fusion via denoising diffusions
Authors: Adrien Corenflos - University of Warwick (United Kingdom) [presenting]
Adam Johansen - University of Warwick (United Kingdom)
Gareth Roberts - University of Warwick (United Kingdom)
Abstract: The Fusion problem is concerned with the distributed aggregation of independent subposteriors ${(f^c(x_c))}_{c=1}^C$ into a common target distribution $\pi(x) \propto \prod_{c=1}^C f^c(x)$. Several methods have been proposed to treat this problem, which can be broadly classified into two categories: Approximate solutions, which exhibit an irreducible bias, and exact solutions, which are usually computationally expensive. The aim is to propose a novel sampling algorithm for the Fusion, based on a denoising diffusion model, where the Fusion distribution is noised towards independence by a set of Langevin dynamics, and then denoised back to the target distribution via sequential Monte Carlo methods. The method is embarrassingly parallel and provides an asymptotically consistent approximation of the Fusion distribution at a fraction of the cost of prior alternatives. A theoretical analysis of the method is provided, showing that, when a thin discretization is used, the algorithm is close to the exact solution of the Fusion problem, and its performance is illustrated on a set of numerical experiment benchmarks.
