Evidence Networks: simple losses for fast, amortized, neural Bayesian model comparison

TL;DR

Evidence Networks provide a fast, neural-based approach for Bayesian model comparison that works even with intractable likelihoods, offering scalable and accurate evidence estimation across various complex models.

Contribution

The paper introduces Evidence Networks, a novel class of loss functions and neural estimators for efficient Bayesian model comparison, especially in challenging intractable likelihood scenarios.

Findings

Evidence Networks outperform traditional density estimation in accuracy and scalability.

They are independent of parameter space dimensionality and scale mildly with posterior complexity.

Successful application to gravitational lensing data demonstrates practical utility.

Abstract

Evidence Networks can enable Bayesian model comparison when state-of-the-art methods (e.g. nested sampling) fail and even when likelihoods or priors are intractable or unknown. Bayesian model comparison, i.e. the computation of Bayes factors or evidence ratios, can be cast as an optimization problem. Though the Bayesian interpretation of optimal classification is well-known, here we change perspective and present classes of loss functions that result in fast, amortized neural estimators that directly estimate convenient functions of the Bayes factor. This mitigates numerical inaccuracies associated with estimating individual model probabilities. We introduce the leaky parity-odd power (l-POP) transform, leading to the novel ``l-POP-Exponential'' loss function. We explore neural density estimation for data probability in different models, showing it to be less accurate and scalable than Evidence Networks. Multiple real-world and synthetic examples illustrate that Evidence Networks are explicitly independent of dimensionality of the parameter space and scale mildly with the complexity of the posterior probability density function. This simple yet powerful approach has broad implications for model inference tasks. As an application of Evidence Networks to real-world data we compute the Bayes factor for two models with gravitational lensing data of the Dark Energy Survey. We briefly discuss applications of our methods to other, related problems of model comparison and evaluation in implicit inference settings.