Jana: Jointly amortized neural approximation of complex Bayesian models
Stefan T. Radev, Marvin Schmitt, Valentin Pratz, Umberto Picchini, Ullrich Köthe, Paul-Christian Bürkner
Abstract
This work proposes “jointly amortized neural approximation” (JANA) of intractable likelihood functions and posterior densities arising in Bayesian surrogate modeling and simulation-based inference. We train three complementary networks in an end-to-end fashion: 1) a summary network to compress individual data points, sets, or time series into informative embedding vectors; 2) a posterior network to learn an amortized approximate posterior; and 3) a likelihood network to learn an amortized approximate likelihood. Their interaction opens a new route to amortized marginal likelihood and posterior predictive estimation – two important ingredients of Bayesian workflows that are often too expensive for standard methods. We benchmark the fidelity of JANA on a variety of simulation models against state of-the-art Bayesian methods and propose a powerful and interpretable diagnostic for joint calibration. In addition, we investigate the ability of recurrent likelihood networks to emulate complex time series models without resorting to hand-crafted summary statistics.
BibTeX
@InProceedings{pmlr-v216-radev23a,
title = {Jana: Jointly amortized neural approximation of complex {B}ayesian models},
author = {Radev, Stefan T. and Schmitt, Marvin and Pratz, Valentin and Picchini, Umberto and K\"othe, Ullrich and B\"urkner, Paul-Christian},
booktitle = {Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence},
pages = {1695--1706},
year = {2023},
editor = {Evans, Robin J. and Shpitser, Ilya},
volume = {216},
series = {Proceedings of Machine Learning Research},
month = {31 Jul--04 Aug},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v216/radev23a/radev23a.pdf},
url = {https://proceedings.mlr.press/v216/radev23a.html},
abstract = {This work proposes “jointly amortized neural approximation” (JANA) of intractable likelihood functions and posterior densities arising in Bayesian surrogate modeling and simulation-based inference. We train three complementary networks in an end-to-end fashion: 1) a summary network to compress individual data points, sets, or time series into informative embedding vectors; 2) a posterior network to learn an amortized approximate posterior; and 3) a likelihood network to learn an amortized approximate likelihood. Their interaction opens a new route to amortized marginal likelihood and posterior predictive estimation – two important ingredients of Bayesian workflows that are often too expensive for standard methods. We benchmark the fidelity of JANA on a variety of simulation models against state of-the-art Bayesian methods and propose a powerful and interpretable diagnostic for joint calibration. In addition, we investigate the ability of recurrent likelihood networks to emulate complex time series models without resorting to hand-crafted summary statistics.}
}