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Mutual Regression Distance by Qiao, Dong; Fan, Jicong is a scholarly article available to read on EtoBox.

What is Mutual Regression Distance about?

The maximum mean discrepancy and Wasserstein distance are popular distance measures between distributions and play important roles in many machine learning problems such as metric learning, generative modeling, domain adaption, and clustering. However, since they are functions of pair-wise distances between data points in two distributions, they do not exploit the potential manifold properties of data such as smoothness and hence are not effective in measuring the dissimilarity between the two distributions in the form of manifolds. In this paper, different from existing measures, we propose a novel distance called Mutual Regression Distance (MRD) induced by a constrained mutual regression problem, which can exploit the manifold property of data. We prove that MRD is a pseudometric that satisfies almost all the axioms of a metric. Since the optimization of the original MRD is costly, we provide a tight MRD and a simplified MRD, based on which a heuristic algorithm is established. We also provide kernel variants of MRDs that are more effective in handling nonlinear data. Our MRDs especially the simplified MRDs have much lower computational complexity than the Wasserstein distance. W

Author

Qiao, Dong; Fan, Jicong

Published

2025

Language

EN