Von Mises-Fisher椭圆分布
Von Mises-Fisher Elliptical Distribution
摘要：
一大类现代概率学习系统假设对称分布，然而，现实世界的数据往往服从偏态分布，因此并不总是通过对称分布充分建模。为了解决这个问题，椭圆分布越来越多地用于推广对称分布，并且对偏斜椭圆分布的进一步改进最近引起了很多关注。然而，现有的方法要么难以估计，要么具有复杂和抽象的表示。为此，我们建议采用冯-米塞斯-费舍尔（vMF）分布，以获得一个明确的和简单的概率表示的偏椭圆分布。这不仅使我们能够处理非对称学习系统，而且还提供了一个物理上有意义的方法来概括偏态分布。严格来说，我们的扩展被证明是共享重要的和理想的属性与对称的。我们还表明，建议的vMF分布是容易产生和稳定的估计，无论是理论上和通过例子。
英文摘要：
A large class of modern probabilistic learning systems assumes symmetric distributions, however, real-world data tend to obey skewed distributions and are thus not always adequately modelled through symmetric distributions. To address this issue, elliptical distributions are increasingly used to generalise symmetric distributions, and further improvements to skewed elliptical distributions have recently attracted much attention. However, existing approaches are either hard to estimate or have complicated and abstract representations. To this end, we propose to employ the von-Mises-Fisher (vMF) distribution to obtain an explicit and simple probability representation of the skewed elliptical distribution. This is shown not only to allow us to deal with non-symmetric learning systems, but also to provide a physically meaningful way of generalising skewed distributions. For rigour, our extension is proved to share important and desirable properties with its symmetric counterpart. We also demonstrate that the proposed vMF distribution is both easy to generate and stable to estimate, both theoretically and through examples.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
