Dropout, a stochastic regularisation technique for training of neural networks, has recently been reinterpreted as a specific type of approximate inference algorithm for Bayesian neural networks. The main contribution of the reinterpretation is in providing a theoretical framework useful for analysing and extending the algorithm. We show that the proposed framework suffers from several issues; from undefined or pathological behaviour of the true posterior related to use of improper priors, to an ill-defined variational objective due to singularity of the approximating distribution relative to the true posterior. Our analysis of the improper log uniform prior used in variational Gaussian dropout suggests the pathologies are generally irredeemable, and that the algorithm still works only because the variational formulation annuls some of the pathologies. To address the singularity issue, we proffer Quasi-KL (QKL) divergence, a new approximate inference objective for approximation of high-dimensional distributions. We show that motivations for variational Bernoulli dropout based on discretisation and noise have QKL as a limit. Properties of QKL are studied both theoretically and on a simple practical example which shows that the QKL-optimal approximation of a full rank Gaussian with a degenerate one naturally leads to the Principal Component Analysis solution.

将Dropout重新解释为贝叶斯神经网络的近似推理算法，提出了一个有用的理论框架，但对于使用不当的先验概率，存在未定义或病态行为的真后验分布问题；对于近似分布相对于真后验分布的奇异性而言，近似难以定义。为了解决这些问题，提出了Quasi-KL（QKL）差异作为新的近似推理目标。

变分贝叶斯的dropout: 陷阱与修正