Latent-IMH: Efficient Bayesian Inference for Inverse Problems with Approximate Operators. Chen, Y. & Biros, G. May, 2026. arXiv:2601.20888 [stat.ML]![Latent-IMH: Efficient Bayesian Inference for Inverse Problems with Approximate Operators [link]](https://bibbase.org/img/filetypes/link.svg "link")
Paper doi abstract bibtex 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 costeffective approximation ˜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 ˜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.
@misc{chen_latent-imh_2026,
title = {Latent-{IMH}: {Efficient} {Bayesian} {Inference} for {Inverse} {Problems} with {Approximate} {Operators}},
shorttitle = {Latent-{IMH}},
url = {http://arxiv.org/abs/2601.20888},
doi = {10.48550/arXiv.2601.20888},
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 costeffective approximation ˜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 ˜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.},
language = {en},
urldate = {2026-08-06},
publisher = {arXiv},
author = {Chen, Youguang and Biros, George},
month = may,
year = {2026},
note = {arXiv:2601.20888 [stat.ML]},
keywords = {Computer Science - Machine Learning, Mathematics - Statistics Theory, Statistics - Computation, Statistics - Machine Learning, WG: Accelerated},
}
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