Relating Leverage Scores and Density using Regularized Christoffel Functions - Archive ouverte HAL
Communication Dans Un Congrès Année : 2018

Relating Leverage Scores and Density using Regularized Christoffel Functions

Résumé

Statistical leverage scores emerged as a fundamental tool for matrix sketching and column sampling with applications to low rank approximation, regression, random feature learning and quadrature. Yet, the very nature of this quantity is barely understood. Borrowing ideas from the orthogonal polynomial literature, we introduce the regularized Christoffel function associated to a positive definite kernel. This uncovers a variational formulation for leverage scores for kernel methods and allows to elucidate their relationships with the chosen kernel as well as population density. Our main result quantitatively describes a decreasing relation between leverage score and population density for a broad class of kernels on Euclidean spaces. Numerical simulations support our findings.
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Dates et versions

hal-01796591 , version 1 (21-05-2018)
hal-01796591 , version 2 (21-11-2018)

Identifiants

  • HAL Id : hal-01796591 , version 2

Citer

Edouard Pauwels, Francis Bach, Jean-Philippe Vert. Relating Leverage Scores and Density using Regularized Christoffel Functions. 32nd Conference on Neural Information Processing Systems (NIPS 2018), Dec 2018, Montréal, Canada. pp.1-21. ⟨hal-01796591v2⟩
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