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.

翻译：证据网络能够在现有最优方法（如嵌套采样）失效，甚至似然函数或先验分布不可计算或未知的情况下，实现贝叶斯模型比较。贝叶斯模型比较（即贝叶斯因子或证据比的计算）可转化为优化问题。尽管最优分类的贝叶斯解释已广为人知，本文切换视角，提出一系列损失函数类，这些函数能产生快速、摊销化的神经估计器，直接估算贝叶斯因子的便捷函数形式。这避免了因单独估算模型概率而引入的数值不准确性。我们引入泄露奇次幂（l-POP）变换，进而提出新型"l-POP指数"损失函数。我们探索了不同模型中数据概率的神经密度估计方法，结果表明其准确性与可扩展性均不如证据网络。多个真实与合成案例表明，证据网络显式独立于参数空间维度，仅以温和方式随后验概率密度函数的复杂度增长。这种简单而强大的方法对模型推断任务具有广泛意义。作为证据网络在真实数据中的应用，我们利用暗能量巡天的引力透镜数据计算了两个模型的贝叶斯因子。我们简要讨论了该方法在隐式推断场景中其他模型比较与评估相关问题的应用。