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 aimed at 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 boun...

We study the supremum of random Dirichlet polynomials DN (t) = ∑ N n=1 εnd(n)n , where (εn) is a sequence of independent Rademacher random variables, and d is a sub-multiplicative function. The approach is gaussian and entirely based on comparison properties of Gaussian processes, with no use of the metric entropy method.

The paper [5] presented a bound on the generalisation error of classifiers learned through multiple kernel learning. The bound has (an improved) additive dependence on the number of kernels (with the same logarithmic dependence on this number). However, parts of the proof were incorrectly presented in that paper. This note remedies this weakness by restating the problem and giving a detailed pr...

This paper studies the problem of learning weighted automata from a finite labeled training sample. We consider several general families of weighted automata defined in terms of three different measures: the norm of an automaton’s weights, the norm of the function computed by an automaton, or the norm of the corresponding Hankel matrix. We present new data-dependent generalization guarantees fo...

We introduce a formalism of localization for online learning problems, which, similarly to statistical learning theory, can be used to obtain fast rates. In particular, we introduce local sequential Rademacher complexities and other local measures. Based on the idea of relaxations for deriving algorithms, we provide a template method that takes advantage of localization. Furthermore, we build a...

The rate of convergence for an almost surely convergent series of Banach space valued random elements is studied in this paper. As special cases of the main result, known results are obtained for a sequence of independent random elements in a Rademacher type p Banach space, and new results are obtained for a martingale difference sequence of random elements in a martingale type p Banach space a...

where F = {yh(x) : ∀ h ∈ H} and φ(h(x), y) is the loss function of interest. The labeled training sample S = {(xi, yi) | i ∈ {1, ..., n}, xi ∈ R, yi ∈ {±1}} is assumed to be generated from an independent, identically distributed (IID) random process. Given each Rademacher random variable σi ∈ {±1} with uniform odds, a realization of the Rademacher random variables σ amounts to a partition of th...

Let S = a1r1+a2r2+ · · ·+anrn be a weighted Rademacher sum. Friedgut, Kalai, and Naor have shown that if Var(|S|) is much smaller than Var(S), then the sum is largely determined by one of the summands. We provide a simple and elementary proof of this result, strengthen it, and extend it in various ways to a more general setting. ACM Classification: G.3 AMS Classification: 60E15, 42C10