Sums and Gaussian Vectors

By V. Yurinsky. 1995

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Citations in the corpus

Minimax Estimation of Kernel Mean Embeddings (2016, background): “Using Bernstein’s inequality in separable Hilbert spaces (Yurinsky, 1995, Theorem 3.3.4), it follows that for bounded continuous kernels, ‖µPn − µP ‖Hk = OP (n−1/2) for any P , i.e., the empirical estimator is a √ n-consistent estimator of µP in Hk-norm.”
Optimal Rates for Random Fourier Features (2015, background): “ntegration, we have Z∞ loga √ te−tdt= [ √ te−t]loga ∞ + Z∞ loga 1 2 √ t e−tdt≤ √ loga a + 1 2 √ loga Z∞ loga e−tdt= √ loga a + 1 2a √ loga , thereby yields the result. Lemma C.3 (Bernstein inequality [12]). Let ξ ∈ Rbe a random variable, Eξ∼P[ξ] = 0, and assume that ∃L>0,S >0 satisfying Xm j=1”
Optimal Rates for the Regularized Least-Squares Algorithm (2007, neutral): “4 of [35].”
Large ball probabilities, Gaussian comparison and anti-concentration (2017, background): “ small balls probabilities IP kξ−ak ≤ ε , or large deviation bounds IP kξk ≥ 1/ε for small ε can be found e.g. in Bogachev (1998), Ledoux and Talagrand (2002), Li and Shao (2001), Lifshits (2012) and Yurinsky (1995). The paper is organizedas follows: a list of examples motivating our results and pos”
Moderate Deviations via Cumulants (2010, unknown): “1 by Yurinsky [36].”
Less is More: Nyström Computational Regularization (2015, background): “Extensive experimental analysis shows that the considered approach achieves state of the art performances on benchmark large scale datasets.”
Less is More: Nystr\"om Computational Regularization (2015, background): “ions. From a theoretical perspective, the effect of Nystrom¨ approaches has been primarily characterized considering the discrepancy between a given empirical kernel matrix and its subsampled version [13, 14, 15, 16, 17, 18, 19]. While interesting in their own right, these latter results do not dire”
Generalization Properties of Learning with Random Features (2016, background): “In particular, let X a probability space and ρ be a probability distribution on X×R satisfying Assumption 1.”
Elastic-net regularization in learning theory (2008, background): “4 of [38] as well as [39] for concentration inequalities for Hilbert-space-valued random variables.”