JANA: Jointly Amortized Neural Approximation of Complex Bayesian Models (2302.09125v3)

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.

• The paper introduces JANA, a framework that jointly amortizes neural networks for efficient approximation of complex Bayesian posteriors and likelihoods.
• It employs interconnected Summary, Posterior, and Likelihood networks to accurately emulate challenging benchmarks like Gaussian mixtures and infectious disease models.
• JANA achieves robust calibration and comparable performance to sequential methods while reducing retraining overhead, enhancing scalable Bayesian inference.

Jointly Amortized Neural Approximation of Complex Bayesian Models: An Expert Overview

The paper proposes a novel approach titled "Jointly Amortized Neural Approximation" (JANA) for the efficient approximation of intractable likelihoods and posterior densities frequently encountered in Bayesian surrogate modeling and simulation-based inference. The methodology leverages neural networks for amortized inference, a strategy that pre-trains models for application across multiple data sets, enhancing both theoretical development and practical utility in computational science.

Methodology

JANA consists of three interconnected neural networks:

1. Summary Network: This network compresses data points, sets, or time series into informative embeddings. The goal is to extract maximum informative value from complex data structures efficiently.
2. Posterior Network: Utilizing a conditional invertible neural network (cINN), this network learns an amortized approximation of the posterior distribution, thereby facilitating efficient Bayesian inference.
3. Likelihood Network: Also implemented as a cINN, this network estimates an amortized approximation of the likelihood.

These networks interact to enable the estimation of marginal likelihoods and posterior predictive distributions, which are typically computationally expensive within traditional Bayesian workflows.

Experimental Results

The research validates JANA across a spectrum of simulation models, demonstrating its fidelity compared to state-of-the-art Bayesian methodologies. In challenging benchmarks, including Gaussian mixture models and infectious disease models, the proposed joint framework shows robust calibration and accurate likelihood emulation.

In a detailed comparison using the Two Moons benchmark, JANA demonstrates comparable performance to sequential neural methods such as SNPE-C and SNL, with the added advantage of amortization, reducing computational demands. Furthermore, JANA's hybrid approach simultaneously tackles both likelihood and posterior approximations with no loss in accuracy.

The paper also showcases applications of JANA in real-world scenarios such as Bayesian model comparison and validation, evidenced by successful evaluations in the Drift Diffusion Model and infectious disease simulations. The framework's ability to produce strong numerical results without the necessity for sequential retraining attests to its practical relevance.

Implications and Future Directions

By addressing the computational inefficiencies often associated with marginal likelihood estimation and posterior predictive performance metrics, JANA provides a scalable and efficient Bayesian inference framework. This approach holds potential for wide application in domains requiring robust probabilistic modeling, from financial analytics to biomedical research.

Future research could focus on exploring weight-sharing strategies within the neural architectures to enhance computational efficiency and extend the applications of JANA to more diverse model structures. Additionally, creating a standard benchmark database for joint estimation in non-trivial models would provide the community with more comprehensive evaluation tools.

In conclusion, the JANA framework advances the computational efficiency of Bayesian workflows, enabling fully amortized and practical solutions to complex inference problems, making it a significant contribution to the field of Bayesian neural inference.