Variational inference transforms posterior inference into parametric optimization thereby enabling the use of latent variable models where otherwise impractical. However, variational inference can be finicky when different variational parameters control variables that are strongly correlated under the model. Traditional natural gradients based on the variational approximation fail to correct for correlations when the approximation is not the true posterior. To address this, we construct a new natural gradient called the variational predictive natural gradient. It is constructed as an average of the Fisher information of the reparameterized predictive model distribution. Unlike traditional natural gradients for variational inference, this natural gradient accounts for the relationship between model parameters and variational parameters. We also show the variational predictive natural gradient relates to the negative Hessian of the expected log-likelihood. A simple example shows the insight. We demonstrate the empirical value of our method on a classification task, a deep generative model of images, and probabilistic matrix factorization for recommendation.

本文提出一种新的自然梯度VPNG，用于解决传统自然梯度在变分参数强烈相关的情况下不能修正相关性的问题，并在分类任务、图像生成模型和概率矩阵分解等方面进行了实证验证。

变分预测自然梯度