# Sparse Variational Bayesian Approximations for Nonlinear Inverse Problems: applications in nonlinear elastography

arXiv: https://arxiv.org/abs/1412.0473 · HTML: https://mlsanity.com/paper/1412.0473/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Dec 2014.

## Built on by (most cited first, 3 of 3)

- [Learning to solve Bayesian inverse problems: An amortized variational inference approach using Gaussian and Flow guides](https://mlsanity.com/paper/2305.20004/) (2023)
- [Weak neural variational inference for solving Bayesian inverse problems without forward models: applications in elastography](https://mlsanity.com/paper/2407.20697/) (2024)
- [Variational Inference at Glacier Scale](https://mlsanity.com/paper/2108.07263/) (2021)

## Abstract (arXiv)

This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on a Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an optimization problem over an appropriately selected family of distributions. The goal is two-fold. Firstly, to find lower-dimensional representations of the unknown parameter vector that capture as much as possible of the associated posterior density, and secondly to enable the computation of the approximate posterior density with as few forward calls as possible. We discuss how these objectives can be achieved by using a fully Bayesian argumentation and employing the marginal likelihood or evidence as the ultimate model validation metric for any proposed dimensionality reduction. We demonstrate the performance of the proposed methodology for problems in nonlinear elastography where the identification of the mechanical properties of biological materials can inform non-invasive, medical diagnosis. An Importance Sampling scheme is finally employed in order to validate the results and assess the efficacy of the approximations provided.