Statistical Consistency of Kernel Canonical Correlation Analysis

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Kernel Bayes' Rule (2010, methodology): “1+β }, 11 we have bC Y X Cb XX +εnI −1 mbΠ −mQY HY = Op(n −min{2 3α, 2β+1 2β+2α}), (n→ ∞). Theorem 5 shows that the best rate is O(n−2α/3) for β≥ 1/2. The idea of the proof is essentially the same as [7, 10], which uses the standard techniques in regularization theory [8]. The condition π/pX ∈ R(AXC”
Consistency of the group Lasso and multiple kernel learning (2007, unknown): “This implies notably, as shown in Section 3.1, that we can deﬁne covariance, cross-covariance and correlation operators that are all Hilbert-Schmidt (Baker, 1973; Fukumizu et al., 2007) and can all be estimated at rate O p ( n (cid:0) 1 = 2 ) in operator norm.”
Strongly consistent nonparametric tests of conditional independence (2012, background): “As further literature we mention Bakirov et al. (2006), Beran et al. (2007), Dauxois and Nkiet (1998), Fukumizu et al. (2007), Gieser and Randles (1997), Gretton et al. (2005), Kankainen (1995), Genest et al. (2007), Dette and Neumeyer (2000) with references.”