The Galerkin method beats Graph-Based Approaches for Spectral Algorithms

arXiv:2306.00742v3 Announce Type: replace
Abstract: Historically, the machine learning community has derived spectral decompositions from graph-based approaches. We break with this approach and prove the statistical and computational superiority of the Galerkin method, which consists in restricting the study to a small set of test functions. In particular, we introduce implementation tricks to deal with differential operators in large dimensions with structured kernels. Finally, we extend on the core principles beyond our approach to apply them to non-linear spaces of …

abstract algorithms arxiv community computational cs.ai cs.lg functions graph graph-based implementation machine machine learning prove set small statistical stat.ml study test type