论文标题
对称空间上的指数包装分布
Exponential-wrapped distributions on symmetric spaces
论文作者
论文摘要
在许多应用中，支持数据的空间的曲率使统计建模具有挑战性。在本文中，我们讨论了使用指数图周围包裹的概率分布的构建和使用。这些分布已经在特定的歧管上使用。我们在仿射局部对称空间的统一框架中描述了它们的构造。仿射局部对称空间是一系列广泛的歧管，其中包含数据科学中遇到的许多歧管。我们表明，在这些空间上，指数包裹的分布享有有趣的属性。我们提供了在这些分布中出现的雅各布式的通用表达，并在两个特定的例子上计算出来：格拉斯曼尼亚人和伪hyperboloids。我们在模拟数据的分类实验中说明了这种分布的兴趣。
In many applications, the curvature of the space supporting the data makes the statistical modelling challenging. In this paper we discuss the construction and use of probability distributions wrapped around manifolds using exponential maps. These distributions have already been used on specific manifolds. We describe their construction in the unifying framework of affine locally symmetric spaces. Affine locally symmetric spaces are a broad class of manifolds containing many manifolds encountered in data sciences. We show that on these spaces, exponential-wrapped distributions enjoy interesting properties for practical use. We provide the generic expression of the Jacobian appearing in these distributions and compute it on two particular examples: Grassmannians and pseudo-hyperboloids. We illustrate the interest of such distributions in a classification experiment on simulated data.
