For multi-index polynomials, the top r eigenspace of the AGOP matrix from KRR recovers the central subspace at sample complexity n ~ d^{p+δ} where p is the degree of the informative component.
Orthogonal Polynomials: <i>Orthogonal Polynomials</i> . By Gabor Szegö. ix +401 pp. Colloquium Publications
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Average Gradient Outer Product in kernel regression provably recovers the central subspace for multi-index models
For multi-index polynomials, the top r eigenspace of the AGOP matrix from KRR recovers the central subspace at sample complexity n ~ d^{p+δ} where p is the degree of the informative component.