Machine learning and optimal transport: some statistical and algorithmic tools

Elsa Cazelles
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Abstract

In this paper, we focus on the analysis of data that can be described by probability measures supported on a Euclidean space, by way of optimal transport. Our main objective is to present a first and second order statistical analyses in the space of distributions in a concise manner, as a first approach to understand the general modes of variation of a set of observations. In the context of optimal transport, these studies correspond to the barycenter and the decomposition into geodesic principal components in theWasserstein space. In particular, we aim attention at a regularised estimator of the barycenter, in order to handle the noise coming from the observations. Additionally, we leverage these tools for time series analysis, whose spectral informations are compared using optimal transport.
机器学习和优化运输:一些统计和算法工具
在本文中,我们通过最优传输的方式,重点分析可以用欧几里得空间上支持的概率度量来描述的数据。我们的主要目标是以简洁的方式介绍分布空间中的一阶和二阶统计分析,作为了解一组观测数据的一般变化模式的第一种方法。在最优传输的背景下,这些研究与瓦瑟斯坦空间中的原点和大地主成分分解相对应。特别是,我们将注意力放在了对原心的正则化估计上,以处理来自观测数据的噪声。此外,我们还利用这些工具进行时间序列分析,并使用最优传输对其频谱信息进行比较。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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