论文标题
WASSERSTEIN多元自动回归模型，用于建模分布时间序列
Wasserstein multivariate auto-regressive models for modeling distributional time series
论文作者
论文摘要
本文的重点是对数据组成的数据的统计分析，这些数据包括一系列概率度量的集合，这些概率度量由不同的时间瞬间索引，并在实际线路的有界间隔内支持。通过将这些与时间相关的概率度量建模为Wasserstein空间中的随机对象，我们为多元分布时间序列的统计分析提出了一种新的自动回归模型。使用迭代的随机功能系统的理论，提供了这种模型解决方案的存在，独特性和平稳性的结果。我们还提出了该模型自动回归系数的一致估计器。由于我们对模型系数强加了单纯限制，因此在这些约束下学习的提出的估计器自然具有稀疏的结构。稀疏性允许将所提出的模型应用于从多变量分布时间序列中学习时间依赖性图。我们使用模拟数据探讨了估计过程的数值性能。为了阐明我们对实际数据分析方法的好处，我们还将这种方法应用于两个数据集，分别是由不同国家 /地区的年龄分布和巴黎自行车共享网络的观察结果制成的。
This paper is focused on the statistical analysis of data consisting of a collection of multiple series of probability measures that are indexed by distinct time instants and supported over a bounded interval of the real line. By modeling these time-dependent probability measures as random objects in the Wasserstein space, we propose a new auto-regressive model for the statistical analysis of multivariate distributional time series. Using the theory of iterated random function systems, results on the existence, uniqueness and stationarity of the solution of such a model are provided. We also propose a consistent estimator for the auto-regressive coefficients of this model. Due to the simplex constraints that we impose on the model coefficients, the proposed estimator that is learned under these constraints, naturally has a sparse structure. The sparsity allows the application of the proposed model in learning a graph of temporal dependency from multivariate distributional time series. We explore the numerical performances of our estimation procedure using simulated data. To shed some light on the benefits of our approach for real data analysis, we also apply this methodology to two data sets, respectively made of observations from age distribution in different countries and those from the bike sharing network in Paris.
