Supervised learning of sheared distributions using linearized optimal transport. (arXiv:2201.10590v1 [math.ST])

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 …

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