论文标题

内核Stein生成建模

Kernel Stein Generative Modeling

论文作者

Chang, Wei-Cheng, Li, Chun-Liang, Mroueh, Youssef, Yang, Yiming

论文摘要

我们对基于梯度的显式生成建模感兴趣,其中可以根据数据分布的得分函数的估计来从迭代梯度更新中得出样本。随机梯度Langevin动力学(SGLD)的最新进展为高维和复杂数据分布的基于能量的模型表现出了令人印象深刻的结果。 Stein变异梯度下降(SVGD)是一种确定性抽样算法,它基于功能梯度下降,可迭代地运输一组颗粒以近似给定的分布,从而降低了KL差异。 SVGD在几种贝叶斯推理应用方面具有有希望的结果。但是,在高维问题上应用SVGD仍然不足。这项工作的目的是研究使用SVGD的高维推断。我们首先确定了实用内核SVGD推断高维度中的关键挑战。我们提出了与最近引入的噪声条件分数网络估计器一致的噪声条件内核SVGD(NCK-SVGD)。 NCK对于在高维度上成功推断SVGD至关重要,因为它使内核适应了得分估计值的噪声水平。当我们退火噪声时,NCK-SVGD靶向真实的数据分布。然后,我们使用熵正则化扩展了退火的SVGD。我们表明,这在样本质量和多样性之间提供了灵活的控制,并通过精确和召回评估进行经验验证。 NCK-SVGD产生的样品与甘体和在包括MNIST和CIFAR-10在内的计算机视觉基准上的SGLD相当。

We are interested in gradient-based Explicit Generative Modeling where samples can be derived from iterative gradient updates based on an estimate of the score function of the data distribution. Recent advances in Stochastic Gradient Langevin Dynamics (SGLD) demonstrates impressive results with energy-based models on high-dimensional and complex data distributions. Stein Variational Gradient Descent (SVGD) is a deterministic sampling algorithm that iteratively transports a set of particles to approximate a given distribution, based on functional gradient descent that decreases the KL divergence. SVGD has promising results on several Bayesian inference applications. However, applying SVGD on high dimensional problems is still under-explored. The goal of this work is to study high dimensional inference with SVGD. We first identify key challenges in practical kernel SVGD inference in high-dimension. We propose noise conditional kernel SVGD (NCK-SVGD), that works in tandem with the recently introduced Noise Conditional Score Network estimator. NCK is crucial for successful inference with SVGD in high dimension, as it adapts the kernel to the noise level of the score estimate. As we anneal the noise, NCK-SVGD targets the real data distribution. We then extend the annealed SVGD with an entropic regularization. We show that this offers a flexible control between sample quality and diversity, and verify it empirically by precision and recall evaluations. The NCK-SVGD produces samples comparable to GANs and annealed SGLD on computer vision benchmarks, including MNIST and CIFAR-10.

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