Lipschitz Continuity of Mahalanobis Distances and Bilinear Forms

2016/04/04 by Zantedeschi, Valentina, Emonet, Rémi, Sebban, Marc · 1 citation
#FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1604.01376

Abstract

Many theoretical results in the machine learning domain stand only for functions that are Lipschitz continuous. Lipschitz continuity is a strong form of continuity that linearly bounds the variations of a function. In this paper, we derive tight Lipschitz constants for two families of metrics: Mahalanobis distances and bounded-space bilinear forms. To our knowledge, this is the first time the Mahalanobis distance is formally proved to be Lipschitz continuous and that such tight Lipschitz constants are derived.

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