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Activity Number:
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386
- Nonparametric Modeling II
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Type:
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Contributed
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Date/Time:
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Thursday, August 12, 2021 : 12:00 PM to 1:50 PM
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Sponsor:
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Section on Nonparametric Statistics
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Abstract #318907
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Title:
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A Spectral Analysis of Dot-Product Kernels
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Author(s):
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Meyer Scetbon* and Zaid Harchaoui
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Companies:
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CREST, ENSAE and University of Washington
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Keywords:
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Kernel methods;
Nonparametric statistics;
Statistical learning ;
data science
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Abstract:
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We present eigenvalue decay estimates of integral operators associated with compositional dot-product kernels. The estimates improve on previous ones established for power series kernels on spheres. This allows us to obtain the volumes of balls in the corresponding reproducing kernel Hilbert spaces. We discuss the consequences on statistical estimation with compositional dot product kernels and highlight interesting trade-offs between the approximation error and the statistical error depending on the number of compositions and the smoothness of the kernels. We illustrate our results on three examples related to the theoretical analysis of deep neural networks.
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Authors who are presenting talks have a * after their name.
