Havasi Marton, Snoek Jasper, Tran Dustin, Gordon Jonathan, Hernández-Lobato José Miguel
Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UK.
Brain Team, Google Research, Mountain View, CA 94043, USA.
Entropy (Basel). 2021 Nov 8;23(11):1475. doi: 10.3390/e23111475.
Variational inference is an optimization-based method for approximating the posterior distribution of the parameters in Bayesian probabilistic models. A key challenge of variational inference is to approximate the posterior with a distribution that is computationally tractable yet sufficiently expressive. We propose a novel method for generating samples from a highly flexible variational approximation. The method starts with a coarse initial approximation and generates samples by refining it in selected, local regions. This allows the samples to capture dependencies and multi-modality in the posterior, even when these are absent from the initial approximation. We demonstrate theoretically that our method always improves the quality of the approximation (as measured by the evidence lower bound). In experiments, our method consistently outperforms recent variational inference methods in terms of log-likelihood and ELBO across three example tasks: the Eight-Schools example (an inference task in a hierarchical model), training a ResNet-20 (Bayesian inference in a large neural network), and the Mushroom task (posterior sampling in a contextual bandit problem).
变分推断是一种基于优化的方法，用于逼近贝叶斯概率模型中参数的后验分布。变分推断的一个关键挑战是用一种计算上易于处理但又具有足够表达能力的分布来逼近后验分布。我们提出了一种从高度灵活的变分近似中生成样本的新方法。该方法从一个粗糙的初始近似开始，并通过在选定的局部区域对其进行细化来生成样本。这使得样本能够捕捉后验分布中的依赖性和多模态性，即使初始近似中不存在这些特性。我们从理论上证明了我们的方法总是能提高近似的质量（以证据下界衡量）。在实验中，在三个示例任务中，我们的方法在对数似然和证据下界方面始终优于最近的变分推断方法：八所学校示例（层次模型中的一个推断任务）、训练ResNet - 20（大型神经网络中的贝叶斯推断）以及蘑菇任务（上下文博弈问题中的后验采样）。
