论文标题
使用线性化最佳传输监督剪切分布的学习
Supervised learning of sheared distributions using linearized optimal transport
论文作者
论文摘要
在本文中，我们研究了有关概率措施空间的监督学习任务。我们通过使用最佳传输框架将概率度量的空间嵌入到$ l^2 $空间中来解决此问题。在嵌入空间中，常规机器学习技术用于实现线性可分离性。这个想法已证明在应用程序中成功了，何时要分开的类是通过固定度量的班次和尺度产生的。本文将适合该框架的基本变换延伸到剪切家族，描述了可以线性分离的两类剪切分布的条件。此外，我们在转换方面给出了必要的界限，以达到预先指定的分离水平，并展示如何使用多个嵌入来允许更大的转换族。我们在图像分类任务上演示了结果。
In this paper we study supervised learning tasks on the space of probability measures. We approach this problem by embedding the space of probability measures into $L^2$ spaces using the optimal transport framework. In the embedding spaces, regular machine learning techniques are used to achieve linear separability. This idea has proved successful in applications and when the classes to be separated are generated by shifts and scalings of a fixed measure. This paper extends the class of elementary transformations suitable for the framework to families of shearings, describing conditions under which two classes of sheared distributions can be linearly separated. We furthermore give necessary bounds on the transformations to achieve a pre-specified separation level, and show how multiple embeddings can be used to allow for larger families of transformations. We demonstrate our results on image classification tasks.
