Data augmentation is a highly effective approach for improving performance in deep neural networks. The standard view is that it creates an enlarged dataset by adding synthetic data, which raises a problem when combining it with Bayesian inference: how much data are we really conditioning on? This question is particularly relevant to recent observations linking data augmentation to the cold posterior effect. We investigate various principled ways of finding a log-likelihood for augmented datasets. Our approach prescribes augmenting the same underlying image multiple times, both at test and train-time, and averaging either the logits or the predictive probabilities. Empirically, we observe the best performance with averaging probabilities. While there are interactions with the cold posterior effect, neither averaging logits or averaging probabilities eliminates it.

本文提出了几种方法来开发基于贝叶斯神经网络的数据增强，实现隐式使用随机扰动的对数似然，引入“有限轨道”设置，允许精确计算似然函数，并在更常见的“全轨道”设置中提供紧密的多样本边界。通过这些模型，我们发现冷后验效应即使在使用正确的似然函数的原则模型中使用数据增强仍然存在，因此，冷后验效应不能被视为使用不正确的似然函数的数据增强的人造因素。

贝叶斯神经网络中的数据增强和冷后验效应