Amortized Energy-Based Bayesian Inference
The article discusses a new approach to amortized Bayesian inference for nonlinear inverse problems. It introduces a transport-based method that approximates the posterior distribution using joint samples, avoiding traditional computational burdens. The proposed method is illustrated through various inverse problems, demonstrating its effectiveness in capturing posterior structures and enabling fast sampling.
- ▪The proposed method learns an observation-dependent map to approximate the posterior distribution.
- ▪It is a likelihood-free approach that requires only joint samples, avoiding density evaluation and Jacobian computations.
- ▪The method is illustrated on finite-dimensional nonlinear inverse problems and PDE-constrained inverse problems.
Opening excerpt (first ~120 words) tap to expand
Mathematics > Numerical Analysis arXiv:2605.15407 (math) [Submitted on 14 May 2026] Title:Amortized Energy-Based Bayesian Inference Authors:Hojjat Kaveh, Ricardo Baptista, Andrew M. Stuart View a PDF of the paper titled Amortized Energy-Based Bayesian Inference, by Hojjat Kaveh and 2 other authors View PDF HTML (experimental) Abstract:We consider amortized Bayesian inference for nonlinear inverse problems in settings where only samples from the joint distribution of parameters and observations are available. Classical methods such as Markov chain Monte Carlo require solving a new inference problem for each observation, which can be computationally prohibitive when inference must be repeated many times.
…
Excerpt limited to ~120 words for fair-use compliance. The full article is at arXiv cs.AI.
Discussion
0 commentsMore from arXiv cs.AI
