Energy-based Transport for Amortized Bayesian Inference
We consider amortized Bayesian inference for nonlinear inverse problems using only samples from the joint distribution of parameters and observations, including problems with unknown functions in a Banach space. Classical methods such as Markov chain Monte Carlo solve a new inference problem for each observation, making repeated posterior inference computationally prohibitive, particularly in infinite dimensions. Amortized Bayesian inversion instead learns a reusable map that rapidly generates posterior samples for new observations. We learn an observation-dependent transport map that pushes a reference measure to an approximate posterior. Training minimizes the average energy distance be...
| Authors | Ricardo Baptista, Hojjat Kaveh, Andrew M. Stuart |
|---|---|
| Primary category | math.NA |
| Published | 14 May 2026 |
| Last updated at source | 17 July 2026 |
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