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

Youguang Chen, George Biros
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:4456-4464, 2026.

Abstract

We study sampling from posterior distributions in Bayesian linear inverse problems where $\mathbf{A}$, the parameters to observables operator, is computationally expensive. In many applications $\mathbf{A}$ can be factored in a manner that facilitates the construction of a cost-effective approximation $\widetilde{\mathbf{A}}$. 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 $\widetilde{\mathbf{A}}$, and then refines them using the exact $\mathbf{A}$. 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-chen26g, title = { Latent-IMH: Efficient Bayesian Inference for Inverse Problems with Approximate Operators }, author = {Chen, Youguang and Biros, George}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {4456--4464}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/chen26g/chen26g.pdf}, url = {https://proceedings.mlr.press/v300/chen26g.html}, abstract = { We study sampling from posterior distributions in Bayesian linear inverse problems where $\mathbf{A}$, the parameters to observables operator, is computationally expensive. In many applications $\mathbf{A}$ can be factored in a manner that facilitates the construction of a cost-effective approximation $\widetilde{\mathbf{A}}$. 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 $\widetilde{\mathbf{A}}$, and then refines them using the exact $\mathbf{A}$. 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. } }
Endnote
%0 Conference Paper %T Latent-IMH: Efficient Bayesian Inference for Inverse Problems with Approximate Operators %A Youguang Chen %A George Biros %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-chen26g %I PMLR %P 4456--4464 %U https://proceedings.mlr.press/v300/chen26g.html %V 300 %X We study sampling from posterior distributions in Bayesian linear inverse problems where $\mathbf{A}$, the parameters to observables operator, is computationally expensive. In many applications $\mathbf{A}$ can be factored in a manner that facilitates the construction of a cost-effective approximation $\widetilde{\mathbf{A}}$. 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 $\widetilde{\mathbf{A}}$, and then refines them using the exact $\mathbf{A}$. 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.
APA
Chen, Y. & Biros, G.. (2026). Latent-IMH: Efficient Bayesian Inference for Inverse Problems with Approximate Operators . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:4456-4464 Available from https://proceedings.mlr.press/v300/chen26g.html.

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