Nyström landmark sampling and regularized Christoffel functions

Selecting diverse and important items, called landmarks, from a large set is a problem of interest in machine learning. As a specific example, in order to deal with large training sets, kernel methods often rely on low rank matrix Nyström approximations based on the selection or sampling of landmark...

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Bibliographic Details
Published inMachine learning Vol. 111; no. 6; pp. 2213 - 2254
Main Authors Fanuel, Michaël, Schreurs, Joachim, Suykens, Johan A. K.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.06.2022
Springer Nature B.V
Subjects
Accuracy
Adaptive algorithms
Algorithms
Approximation
Artificial Intelligence
Computer Science
Control
Datasets
Kernel functions
Machine Learning
Mechatronics
Natural Language Processing (NLP)
Robotics
Sampling
Simulation and Modeling
Sparsity
Training
Determinantal point process
Kernel
Nyström
Diversity
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Summary:Selecting diverse and important items, called landmarks, from a large set is a problem of interest in machine learning. As a specific example, in order to deal with large training sets, kernel methods often rely on low rank matrix Nyström approximations based on the selection or sampling of landmarks. In this context, we propose a deterministic and a randomized adaptive algorithm for selecting landmark points within a training data set. These landmarks are related to the minima of a sequence of kernelized Christoffel functions. Beyond the known connection between Christoffel functions and leverage scores , a connection of our method with finite determinantal point processes (DPPs) is also explained. Namely, our construction promotes diversity among important landmark points in a way similar to DPPs. Also, we explain how our randomized adaptive algorithm can influence the accuracy of Kernel Ridge Regression.
ISSN:0885-6125
1573-0565
DOI:10.1007/s10994-022-06165-0