SVGD as a kernelized Wasserstein gradient flow of the chi-squared divergence
SVGD as a kernelized Wasserstein gradient flow of the chi-squared divergence
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发表时间：
2020-06
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通讯作者：
Sinho Chewi;Thibaut Le Gouic;Chen Lu;Tyler Maunu;P. Rigollet
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作者：
Sinho Chewi;Thibaut Le Gouic;Chen Lu;Tyler Maunu;P. Rigollet
Stein变分梯度下降（SVGD）是一种流行的采样算法，通常被描述为最佳传输几何形状中Kullback-Leibler Divergence的内核梯度流。我们对SVGD介绍了一种新的视角，相反，我们将SVGD视为卡方差异的（内核化）梯度流，我们表明，在像浓度不平等的情况下一样弱的条件下，它表现出强烈的指数式呈现的强烈形式。这种观点使我们提出了SVGD的替代方案，称为Laplacian调整后的Wasserstein梯度下降（Lawgd），可以从与目标密度相关的Laplacian操作员的光谱分解中实现。我们表明，Lawgd表现出强大的融合保证和良好的实践表现。
Stein Variational Gradient Descent (SVGD), a popular sampling algorithm, is often described as the kernelized gradient flow for the Kullback-Leibler divergence in the geometry of optimal transport. We introduce a new perspective on SVGD that instead views SVGD as the (kernelized) gradient flow of the chi-squared divergence which, we show, exhibits a strong form of uniform exponential ergodicity under conditions as weak as a Poincare inequality. This perspective leads us to propose an alternative to SVGD, called Laplacian Adjusted Wasserstein Gradient Descent (LAWGD), that can be implemented from the spectral decomposition of the Laplacian operator associated with the target density. We show that LAWGD exhibits strong convergence guarantees and good practical performance.