Geometry and Stability of Supervised Learning Problems

arXiv:2403.01660v1 Announce Type: new
Abstract: We introduce a notion of distance between supervised learning problems, which we call the Risk distance. This optimal-transport-inspired distance facilitates stability results; one can quantify how seriously issues like sampling bias, noise, limited data, and approximations might change a given problem by bounding how much these modifications can move the problem under the Risk distance. With the distance established, we explore the geometry of the resulting space of supervised learning problems, providing explicit geodesics and …

abstract arxiv bias call change cs.lg data geometry math.mg noise notion results risk sampling stability supervised learning transport type