Latent-IMH: Efficient Bayesian Inference for Inverse Problems with Approximate Operators
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911691428593664 |
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| author | Chen, Youguang Biros, George |
| author_facet | Chen, Youguang Biros, George |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20888 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Latent-IMH: Efficient Bayesian Inference for Inverse Problems with Approximate Operators Chen, Youguang Biros, George Machine Learning Statistics Theory Computation 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. |
| title | Latent-IMH: Efficient Bayesian Inference for Inverse Problems with Approximate Operators |
| topic | Machine Learning Statistics Theory Computation |
| url | https://arxiv.org/abs/2601.20888 |