Supervised learning of sheared distributions using linearized optimal transport
Supervised learning of sheared distributions using linearized optimal transport
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DOI：
10.1007/s43670-022-00038-2
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发表时间：
2022-01
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通讯作者：
Varun Khurana;Harish Kannan;A. Cloninger;Caroline Moosmüller
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作者：
Varun Khurana;Harish Kannan;A. Cloninger;Caroline Moosmüller
本文研究概率度量空间上的监督学习任务。我们通过使用最优传输框架将概率度量空间嵌入到空间中来解决这个问题。在嵌入空间中，使用规则机器学习技术来实现线性可分性。这个想法已经在应用中被证明是成功的，当要分离的类是通过固定度量的移位和缩放来生成的时候。本文将适用于该框架的初等变换类推广到剪切族，刻画了两类剪切分布线性分离的条件。此外，我们还给出了实现预先指定的分离级别的变换的必要界限，并展示了如何使用多重嵌入来允许更大的变换族。我们在图像分类任务中展示了我们的结果。
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 intospaces 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.