Variational Rejection Sampling

Learning latent variable models with stochastic variational inference is challenging when the approximate posterior is far from the true posterior, due to high variance in the gradient estimates. We propose a novel rejection sampling step that discards samples from the variational posterior which are assigned low likelihoods by the model. Our approach provides an arbitrarily accurate approximation of the true posterior at the expense of extra computation. Using a new gradient estimator for the resulting unnormalized proposal distribution, we achieve average improvements of 3.71 nats and 0.21 nats over state-of-the-art single-sample and multi-sample alternatives respectively for estimating marginal log-likelihoods using sigmoid belief networks on the MNIST dataset.

当近似后验分布与真实后验分布相差甚远时，由于梯度估计的高方差，使用随机变分推断来学习隐变量模型具有挑战性。我们提出了一种新颖的拒绝采样步骤，该步骤舍弃变分后验分布中被模型赋予低似然性的样本。我们的方法以额外计算为代价，提供了对真实后验分布的任意精确近似。对于所得的非归一化提议分布使用一种新的梯度估计器，在MNIST数据集上使用S型信念网络估计边际对数似然时，我们分别比最先进的单样本和多样本替代方法平均提高了3.71纳特和0.21纳特。