In a world blessed with a great diversity of loss functions, we argue that that choice between them is not a matter of taste or pragmatics, but of model. Probabilistic depencency graphs (PDGs) are probabilistic models that come equipped with a measure of "inconsistency". We prove that many standard loss functions arise as the inconsistency of a natural PDG describing the appropriate scenario, and use the same approach to justify a well-known connection between regularizers and priors. We also show that the PDG inconsistency captures a large class of statistical divergences, and detail benefits of thinking of them in this way, including an intuitive visual language for deriving inequalities between them. In variational inference, we find that the ELBO, a somewhat opaque objective for latent variable models, and variants of it arise for free out of uncontroversial modeling assumptions -- as do simple graphical proofs of their corresponding bounds. Finally, we observe that inconsistency becomes the log partition function (free energy) in the setting where PDGs are factor graphs.

通过概率依赖图描述合适的情境，我们证明许多常见的损失函数可以视为自然PDG的不一致性，并使用相同的方法来证明正则化和先验之间的已知联系，并发现不一致性捕获了大量统计差别，包括用于推导它们之间的不等式的直观图形语言。同时，我们发现不一致性在PDGs是因子图时变成了对数分区函数（自由能）。

概率依赖图的不一致性作为损失：选择您的模型，而不是损失函数