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

• URL: http://arxiv.org/abs/2601.20888v1
• Date: Wed, 28 Jan 2026 03:44:01 GMT
• Title: Latent-IMH: Efficient Bayesian Inference for Inverse Problems with Approximate Operators
• Authors: Youguang Chen, George Biros,
• Abstract summary: We introduce Latent-IMH, a sampling method based on the Metropolis-Hastings independence (IMH) sampler.<n>Latent-IMH first generates intermediate latent variables using the approximate $tildeA$, and then refines them using the exact $A$.<n>We theoretically analyze the performance of Latent-IMH using KL divergence and mixing time bounds.
• Score: 4.887201041798969
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $\tilde{A}$. 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 $\tilde{A}$, 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.

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