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：证据网络能够在最先进方法（如嵌套采样）失效的情况下实现贝叶斯模型比较，甚至在似然函数或先验分布难以处理或未知时仍可适用。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广为人知，但本文转换视角，提出一类损失函数，可构建快速、摊销化的神经估计器，直接估计贝叶斯因子的便捷函数形式。这避免了估计单个模型概率时产生的数值不稳定性。我们引入漏奇宇称幂（leaky parity-odd power, l-POP）变换，并由此提出新型"l-POP-指数"损失函数。通过对比不同模型中数据概率的神经密度估计方法，我们发现其准确性和可扩展性均不及证据网络。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，且对后验概率密度函数的复杂度仅具轻微依赖性。这种简洁而强大的方法对模型推断任务具有广泛影响。作为证据网络在真实数据上的应用，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。最后简要讨论了本方法在隐式推断场景中其他模型比较与评估相关问题中的应用。