Geometry on Probability Spaces

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Boosting multi-kernel locality-sensitive hashing for scalable image retrieval (2012, unknown): “According to the concentration inequality of linear operator [32], we have, with a probability 1− δ, that ∣∣∣A− t p I ∣∣∣ F ≤ √”
Improved Bounds for the Nyström Method With Application to Kernel Classification (2011, unknown): “Their analysis shows that a low rank kernel matrix with incoherent eigvenvectors (i.e., with low coherence) can be accurately approximated by the Nystr¨om method using an uniform sampling.”
Towards Understanding the Spectral Bias of Deep Learning (2019, methodology): “The following lemma is a direct application of Proposition 1 in Smale and Zhou (2009) or Propo-sition 10 in Rosasco et al. (2010).”
On Learning with Integral Operators (2010, result): “Another result similar to ours is independently given in Smale and Zhou (2009), where the authors considered a single eigenfunction with multiplicity 1.”
Nyström Method vs Random Fourier Features: A Theoretical and Empirical Comparison (2012, background): “According to [18], the eigenvalues of LN and Lm are λi/N, i ∈ [N ] and λ̂i/m, i ∈ [m], respectively, and their corresponding normalized eigenfunctions φj , j ∈ [N ] and φ̂j , j ∈ [m] are given by φj(·) = 1 √ λj N ∑”