A Gaussian Process Regression Model for Distribution Inputs
A Gaussian Process Regression Model for Distribution Inputs
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DOI：
10.1109/tit.2017.2762322
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发表时间：
2018-10-01
影响因子：
2.5
通讯作者：
Venet, Nil
中科院分区：
文献类型：
--
作者：
Bachoc, Francois;Gamboa, Fabrice;Venet, Nil
Monge-Kantorovich距离，也被称为Wasserstein距离，作为概率分布的强大差异度量，在统计学和机器学习中受到越来越多的关注。在本文中，我们专注于预测的高斯过程的概率分布。为此，我们提供了一个家庭的正定内核使用交通为基础的距离。我们提供了一个概率的理解，这些内核和相应的随机过程的特征。我们证明，高斯过程的分布对应于这些内核索引可以有效地预测，打开高斯过程建模的新视角。
Monge-Kantorovich distances, otherwise known as Wasserstein distances, have received a growing attention in statistics and machine learning as a powerful discrepancy measure for probability distributions. In this paper, we focus on forecasting a Gaussian process indexed by probability distributions. For this, we provide a family of positive definite kernels built using transportation based distances. We provide a probabilistic understanding of these kernels and characterize the corresponding stochastic processes. We prove that the Gaussian processes indexed by distributions corresponding to these kernels can be efficiently forecast, opening new perspectives in Gaussian process modeling.