论文标题
用各向异性尾巴自适应流动脂肪量变化推断
Fat-Tailed Variational Inference with Anisotropic Tail Adaptive Flows
论文作者
论文摘要
尽管脂肪尾密度通常是在健壮的模型和尺度混合物中作为后部和边际分布而出现的，但当基于高斯的变异推理无法准确捕获尾巴衰减时，它们会带来挑战。我们首先通过量化尾巴如何影响尾巴衰变的速率并将理论扩展到非lipschitz多项式流量来改善Lipschitz流量的先前理论。然后，我们为多元尾部参数开发了一种对尾部 - 触觉敏感的替代理论。在这样做的过程中，我们揭示了一个基本问题，它困扰着许多基于流动的方法：它们只能建模尾部异分分布（即，在各个方向上具有相同的尾巴参数）。为了减轻这种情况并能够对尾部 - 异型靶标进行建模，我们提出了各向异性的尾部自适应流（ATAF）。合成目标和现实世界目标的实验结果证实，ATAF在先前的工作中具有竞争力，同时还表现出适当的尾部触觉。
While fat-tailed densities commonly arise as posterior and marginal distributions in robust models and scale mixtures, they present challenges when Gaussian-based variational inference fails to capture tail decay accurately. We first improve previous theory on tails of Lipschitz flows by quantifying how the tails affect the rate of tail decay and by expanding the theory to non-Lipschitz polynomial flows. Then, we develop an alternative theory for multivariate tail parameters which is sensitive to tail-anisotropy. In doing so, we unveil a fundamental problem which plagues many existing flow-based methods: they can only model tail-isotropic distributions (i.e., distributions having the same tail parameter in every direction). To mitigate this and enable modeling of tail-anisotropic targets, we propose anisotropic tail-adaptive flows (ATAF). Experimental results on both synthetic and real-world targets confirm that ATAF is competitive with prior work while also exhibiting appropriate tail-anisotropy.
