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

arXiv: https://arxiv.org/abs/2601.20888 · HTML: https://mlsanity.com/paper/2601.20888/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 47 references that are in the map.
- First posted on arXiv 28 Jan 2026.

## Builds on (most cited first, 11 of 11)

- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Survey of multifidelity methods in uncertainty propagation, inference, and optimization](https://mlsanity.com/paper/1806.10761/) (2018)
- [Log-concave sampling: Metropolis-Hastings algorithms are fast](https://mlsanity.com/paper/1801.02309/) (2018)
- [Connecting the Dots: Identifying Network Structure via Graph Signal Processing](https://mlsanity.com/paper/1810.13066/) (2018)
- [NeuTra-lizing Bad Geometry in Hamiltonian Monte Carlo Using Neural Transport](https://mlsanity.com/paper/1903.03704/) (2019)
- [Graph signal processing for machine learning: A review and new perspectives](https://mlsanity.com/paper/2007.16061/) (2020)
- [Optimal low-rank approximations of Bayesian linear inverse problems](https://mlsanity.com/paper/1407.3463/) (2014)
- [On Sampling with Approximate Transport Maps](https://mlsanity.com/paper/2302.04763/) (2023)
- [A Cubic Algorithm for Computing Gaussian Volume](https://mlsanity.com/paper/1306.5829/) (2013)

## Built on by (most cited first, 1 of 1)

- [Proximal-IMH: Proximal Posterior Proposals for Independent Metropolis-Hastings with Approximate Operators](https://mlsanity.com/paper/2602.21426/) (2026)

## Abstract (arXiv)

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 tildeA. 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 tildeA, 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.