Supplementary Material for Kernel Alignment Risk Estimator: Risk Prediction from Training Data

We organize the Supplementary Material (Supp. We replace the categorical labels's' and'b' with regression There are two special cases where a weaker Gaussianity property applies, i.e. that the These two special cases are: 1. 's are close to the Stieltjes transform's around m, we have the following result: Lemma 2. F or any N,s N and any z H The second inequality will be proven while proving the first one. The second bound is a direct consequence of the first one, Lemma 2 and convexity. Proposition 5. F or any λ > 0, we have λ < ϑ(λ,N) λ + 1 N Tr[T Let λ > 0. 1. Recall that ϑ (λ) is the unique positive real number such that ϑ ( λ) = λ + ϑ (λ) N Tr null T This yields the lower bound on N ( t) . This allows us to conclude.