JANA: Jointly Amortized Neural Approximation of Complex Bayesian Models
This addresses the computational expense of Bayesian workflows for researchers in statistics and machine learning, though it appears incremental as it builds on existing amortized inference techniques.
The paper tackles the problem of approximating intractable likelihoods and posteriors in Bayesian modeling by proposing JANA, a method that trains three neural networks jointly, achieving competitive performance against state-of-the-art Bayesian methods on various simulation models.
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.