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Evidence Networks can enable Bayesian model comparison when state-of-the-artmethods (e.g. nested sampling) fail and even when likelihoods or priors areintractable or unknown. Bayesian model comparison, i.e. the computation ofBayes 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 infast, amortized neural estimators that directly estimate convenient functionsof the Bayes factor. This mitigates numerical inaccuracies associated withestimating individual model probabilities. We introduce the leaky parity-oddpower (l-POP) transform, leading to the novel ``l-POP-Exponential'' lossfunction. We explore neural density estimation for data probability indifferent models, showing it to be less accurate and scalable than EvidenceNetworks. Multiple real-world and synthetic examples illustrate that EvidenceNetworks are explicitly independent of dimensionality of the parameter spaceand scale mildly with the complexity of the posterior probability densityfunction. This simple yet powerful approach has broad implications for modelinference tasks. As an application of Evidence Networks to real-world data wecompute the Bayes factor for two models with gravitational lensing data of theDark Energy Survey. We briefly discuss applications of our methods to other,related problems of model comparison and evaluation in implicit inferencesettings.

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