Title: Local and Unbalanced Optimal Transport for Feature Learning with Probabilistic Guarantees
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
Keywords: optimal transport, feature learning, generalization bound

Abstract: This paper explores the local and unbalanced optimal transport for feature learning in an embedding space. Instead of using joint distributions of data, we introduce conditional distributions in terms of the
Kullback-Leibler (KL) divergence where some reference conditional distributions are utilized. Using conditional distributions provides the flexibility in controlling the transferring range of  given data points. When the  block coordinate descent method  is employed to solve our model,  it is interesting to find that conditional and marginal distributions have  closed-form solutions. Moreover, the use of conditional distributions facilitates the derivation of the generalization  bound of our model via the Rademacher complexity, which characterizes its convergence speed in terms of the number of samples. By optimizing  the anchors (centroids)  defined in the model, we also employ the unbalanced  optimal transport and  autoencoders to explore an embedding space of samples in the clustering problem. In the experimental part, we demonstrate that the proposed model achieves promising performance on some learning tasks. Moreover, we construct a local and unbalanced optimal transport classifier to classify set-valued objects.