Amortized Energy-Based Bayesian Inference for Inverse Problems
A recent preprint on arXiv (2605.15407) introduces a Bayesian inference technique designed for nonlinear inverse issues, relying solely on joint samples of parameters and observations. This method develops an observation-dependent transport map that transforms a reference measure to estimate the posterior distribution, achieved by minimizing an averaged energy-distance criterion. This likelihood-free approach circumvents the need for density evaluations, invertibility conditions, and calculations of the Jacobian determinant. In the context of function-space inverse challenges with Gaussian priors, the transport map is defined as the identity function augmented by a perturbation.
Key facts
- arXiv preprint 2605.15407
- Amortized Bayesian inference for nonlinear inverse problems
- Only joint samples of parameters and observations are required
- Transport-based approach learns observation-dependent map
- Minimizes averaged energy-distance objective
- Likelihood-free, avoids density evaluation and Jacobian computations
- Parameterizes transport map as identity plus perturbation for Gaussian priors
Entities
Institutions
- arXiv