Latent-IMH: Efficient Bayesian Inference for Inverse Problems with Approximate Operators

arXiv:2601.20888v3 Announce Type: replace-cross Abstract: We study sampling from posterior distributions in Bayesian linear inverse problems where A, the parameters to observables operator, is computationally expensive. In many applications, A can be factored in a manner that facilitates the construction of a cost-effective approximation ilde{A}. In this framework, we introduce Latent-IMH, a sampling method based on the Metropolis-Hastings independence (IMH) sampler. Latent-IMH first generates intermediate latent variables using the approximate ilde{A}, and then refines them using the exact A. Its primary benefit is that it shifts the computational cost to an offline phase. We theoretically analyze the performance of Latent-IMH using KL divergence and mixing time bounds. Using numerical experiments on several model problems, we show that, under reasonable assumptions, it outperforms state-of-the-art methods such as the No-U-Turn sampler (NUTS) in computational efficiency. In some cases, Latent-IMH can be orders of magnitude faster than existing schemes.

Source: arXiv cs.LG | 2026-05-19