Autoregressive optimal transport models.
Autoregressive optimal transport models.
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DOI：
10.1093/jrsssb/qkad051
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发表时间：
2023-07
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--
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由等间隔时间点索引的一元分布序列在应用中是普遍存在的，并且它们的分析构成了新兴的分布数据分析领域的挑战之一。为了量化这样的分布时间序列，我们提出了一类内在的自回归模型，在最优运输地图的空间中运行。我们在这里介绍的自回归传输模型是基于回归最优传输映射，其中预测因子可以是从整体重心到当前分布的传输映射，也可以是分布时间序列的过去连续分布之间的传输映射。自回归传输模型及其相关的分布回归模型通过在Wasserstein空间中沿测地线沿着移动来指定预测和响应传输图之间的联系。这些模型作为经典自回归模型在欧氏空间中的自然扩展而出现。在Wu & Shao [（2004）Limit Theorems for iterated random functions. Journal of Applied Probability 41，425-436）]，使用迭代随机函数的性质。我们还讨论了一阶自回归迁移模型的变系数模型的扩展。除了模拟，所提出的模型与美国各县的房价分布时间序列和每年夏季温度分布。
Series of univariate distributions indexed by equally spaced time points are ubiquitous in applications and their analysis constitutes one of the challenges of the emerging field of distributional data analysis. To quantify such distributional time series, we propose a class of intrinsic autoregressive models that operate in the space of optimal transport maps. The autoregressive transport models that we introduce here are based on regressing optimal transport maps on each other, where predictors can be transport maps from an overall barycenter to a current distribution or transport maps between past consecutive distributions of the distributional time series. Autoregressive transport models and their associated distributional regression models specify the link between predictor and response transport maps by moving along geodesics in Wasserstein space. These models emerge as natural extensions of the classical autoregressive models in Euclidean space. Unique stationary solutions of autoregressive transport models are shown to exist under a geometric moment contraction condition of Wu & Shao [(2004) Limit theorems for iterated random functions. Journal of Applied Probability 41, 425–436)], using properties of iterated random functions. We also discuss an extension to a varying coefficient model for first-order autoregressive transport models. In addition to simulations, the proposed models are illustrated with distributional time series of house prices across U.S. counties and annual summer temperature distributions.
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DOI：
10.1214/15-aihp706
发表时间：
2017-02-01
影响因子：
1.5
作者：
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通讯作者：
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影响因子：
2.2
作者：
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DOI：
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发表时间：
1997-04-15
影响因子：
0.9
作者：
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Parzen, E
影响因子：
1.1
作者：
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通讯作者：
Dai, Xiongtao
DOI：
10.1111/rssa.12053
发表时间：
2015-01-01
影响因子：
2
作者：
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通讯作者：
Scarpa, Bruno