# Data-Free Likelihood-Informed Dimension Reduction of Bayesian Inverse Problems

arXiv: https://arxiv.org/abs/2102.13245 · HTML: https://mlsanity.com/paper/2102.13245/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Feb 2021.

## Built on by (most cited first, 8 of 8)

- [A low-rank ensemble Kalman filter for elliptic observations](https://mlsanity.com/paper/2203.05120/) (2022)
- [Expected information gain estimation via density approximations: Sample allocation and dimension reduction](https://mlsanity.com/paper/2411.08390/) (2024)
- [Sharp detection of low-dimensional structure in probability measures via dimensional logarithmic Sobolev inequalities](https://mlsanity.com/paper/2406.13036/) (2024)
- [Self-reinforced polynomial approximation methods for concentrated probability densities](https://mlsanity.com/paper/2303.02554/) (2023)
- [Nonlinear Bayesian optimal experimental design using logarithmic Sobolev inequalities](https://mlsanity.com/paper/2402.15053/) (2024)
- [Coupled Input-Output Dimension Reduction: Application to Goal-oriented Bayesian Experimental Design and Global Sensitivity Analysis](https://mlsanity.com/paper/2406.13425/) (2024)
- [Dimension reduction via score ratio matching](https://mlsanity.com/paper/2410.19990/) (2024)
- [A reduced-order derivative-informed neural operator for subsurface fluid-flow](https://mlsanity.com/paper/2509.13620/) (2025)

## Abstract (arXiv)

Identifying a low-dimensional informed parameter subspace offers a viable path to alleviating the dimensionality challenge in the sampled-based solution to large-scale Bayesian inverse problems. This paper introduces a novel gradient-based dimension reduction method in which the informed subspace does not depend on the data. This permits an online-offline computational strategy where the expensive low-dimensional structure of the problem is detected in an offline phase, meaning before observing the data. This strategy is particularly relevant for multiple inversion problems as the same informed subspace can be reused. The proposed approach allows controlling the approximation error (in expectation over the data) of the posterior distribution. We also present sampling strategies that exploit the informed subspace to draw efficiently samples from the exact posterior distribution. The method is successfully illustrated on two numerical examples: a PDE-based inverse problem with a Gaussian process prior and a tomography problem with Poisson data and a Besov-B211 prior.