Fast and Robust Shortest Paths on Manifolds Learned from Data

Autor:	Arvanitidis, Georgios, Hauberg, Søren, Hennig, Philipp, Schober, Michael
Rok vydání:	2019
Předmět:	Statistics - Machine Learning Computer Science - Machine Learning
Druh dokumentu:	Working Paper
Popis:	We propose a fast, simple and robust algorithm for computing shortest paths and distances on Riemannian manifolds learned from data. This amounts to solving a system of ordinary differential equations (ODEs) subject to boundary conditions. Here standard solvers perform poorly because they require well-behaved Jacobians of the ODE, and usually, manifolds learned from data imply unstable and ill-conditioned Jacobians. Instead, we propose a fixed-point iteration scheme for solving the ODE that avoids Jacobians. This enhances the stability of the solver, while reduces the computational cost. In experiments involving both Riemannian metric learning and deep generative models we demonstrate significant improvements in speed and stability over both general-purpose state-of-the-art solvers as well as over specialized solvers. Comment: Accepted at Artificial Intelligence and Statistics (AISTATS) 2019
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1901.07229 Zobrazit plný text záznamu View this record from Arxiv