We derive an upper bound on the local Rademacher complexity of lp-norm multiple kernel learning, which yields a tighter excess risk bound than global approaches. Previous local approaches analyzed the case p= 1 only while our analysis covers all cases 1≤ p≤ ∞, assuming the different feature mappings corresponding to the different kernels to be uncorrelated. We also show a lower bound that shows...

We give a formula for the tail of the distribution of the noncommutative Rademacher series, which generalizes the result that is already available in the commutative case. As a result, we are able to calculate the norm of these series in many rearrangement invariant spaces, generalizing work of Pisier and Rodin and Semyonov.

A basic result of B. Maurey and G. Pisier states that Gaussian and Rademacher averages in a Banach space X are equivalent if and only if X has finite cotype. We complement this for linear bounded operators between Banach spaces. For T ∈ L(X, Y ), let %(T |Gn,Rn) be the least c such that ( E‖ n ∑ k=1 Txkgk‖ )1/2 ≤ c ( E‖ n ∑

In this paper, we study Dedekind sums and we connect them to the mean values of Dirichlet L-functions. For this, we introduce and investigate higher order dimensional Dedekind-Rademacher sums given by the expression Sd( −→ a0 , −→ m0) = 1 a0 0 a0−1 ∑

1 Review of VC theory Our primary interest so far is deriving the generalization bound for the binary classifiers. We have studied the Rademacher complexity techniques, and shown that the VC bound is an upper bound of the Rademacher complexity bound. For a binary classification with 0-1 loss l, we have R m (l • H) ≤ 2 log g H (m) m (1) where H = {h : X → {+1, −1}} is a hypothesis space. The gro...