Diversity sampling in kernel method

Abstract: A well-known technique for large scale kernel methods is the Nyström approximation. Based on a subset of landmarks, it gives a low rank approximation of the kernel matrix, and is known to provide a form of implicit regularization. We will discuss the impact of sampling diverse landmarks for constructing the Nyström approximation in supervised and unsupervised problems. In particular, three methods will be considered: uniform sampling, leverage score sampling and Determinantal Point Processes (DPP). The implicit regularization due the diversity of the landmarks will be made explicit by numerical simulations and analysed further in the case of DPP sampling by some theoretical results.

analysis of PDEsfunctional analysisgeneral mathematicsnumerical analysisoptimization and controlprobabilitystatistics theory

Audience: researchers in the topic

One World seminar: Mathematical Methods for Arbitrary Data Sources (MADS)

Series comments: Description: Research seminar on mathematics for data

The lecture series will collect talks on mathematical disciplines related to all kind of data, ranging from statistics and machine learning to model-based approaches and inverse problems. Each pair of talks will address a specific direction, e.g., a NoMADS session related to nonlocal approaches or a DeepMADS session related to deep learning.

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