面向高维变分推断的归一化流稳定训练
Stable Training of Normalizing Flows for High-dimensional Variational Inference
AI总结：
本文针对深度 Real NVPs 在高维变分推断中因随机梯度高方差而训练不稳定的问题，提出尺度软阈值处理与样本双射软对数变换的组合方法，并在数千维后验上验证了稳定训练和更准确的边际似然估计。
摘要：
基于归一化流（NFs）的变分推断正日益成为 MCMC 方法的一种流行替代方案。特别是基于耦合层构建的归一化流（Real NVPs），因其良好的经验性能而被频繁使用。理论上，增加归一化流的深度应当能够带来更准确的后验近似。然而在实践中，由于随机梯度的高方差，训练用于逼近高维后验分布的深度归一化流通常不可行。本文表明，以往用于稳定随机梯度下降方差的方法可能不足以实现 Real NVPs 的稳定训练。我们指出问题的根源在于：训练过程中样本常常表现出异常高的数值。作为解决方案，我们提出两种方法的组合：（1）对 Real NVPs 中的尺度进行软阈值处理，以及（2）对样本进行双射软对数变换。我们在多个具有挑战性的目标分布上评估了这些修改以及其他先前提出的修改，包括一个高维 horseshoe 逻辑回归模型。实验表明，通过我们的修改，可以在数千维的后验上稳定训练 Real NVPs，从而能够通过重要性采样进行更准确的边际似然估计。此外，我们还评估了几种常见的训练技术和架构选择，并为高维变分推断中的归一化流训练提供了实用建议。
英文摘要：
Variational inference with normalizing flows (NFs) is an increasingly popular alternative to MCMC methods. In particular, NFs based on coupling layers (Real NVPs) are frequently used due to their good empirical performance. In theory, increasing the depth of normalizing flows should lead to more accurate posterior approximations. However, in practice, training deep normalizing flows for approximating high-dimensional posterior distributions is often infeasible due to the high variance of the stochastic gradients. In this work, we show that previous methods for stabilizing the variance of stochastic gradient descent can be insufficient to achieve stable training of Real NVPs. As the source of the problem, we identify that, during training, samples often exhibit unusual high values. As a remedy, we propose a combination of two methods: (1) soft-thresholding of the scale in Real NVPs, and (2) a bijective soft log transformation of the samples. We evaluate these and other previously proposed modification on several challenging target distributions, including a high-dimensional horseshoe logistic regression model. Our experiments show that with our modifications, stable training of Real NVPs for posteriors with several thousand dimensions is possible, allowing for more accurate marginal likelihood estimation via importance sampling. Moreover, we evaluate several common training techniques and architecture choices and provide practical advise for training NFs for high-dimensional variational inference.
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