Earlier approaches to random compact testing use a random pattern generator which depends on the combinational function under test and a circuit signature which remains the same independent of the circuit. In this correspondence we analyze the performance of a new scheme in which the pattern generator is simple and independent of the function being tested but the circuit signature is chosen to ...

This paper presents a novel learning scenario which combines dimensionality reduction, supervised learning as well as kernel selection. We carefully define the hypothesis class that addresses this setting and provide an analysis of its Rademacher complexity and thereby provide generalization guarantees. The proposed algorithm uses KPCA to reduce the dimensionality of the feature space, i.e. by ...

N. Kolmogorov introduced a law of the iterated logarithm, abbreviated LIL, in case independent random variables. Over years, an analog his result has been various contexts analysis. Here, we introduce similar LIL context sums Rademacher functions.

Let F be a class of measurable functions f :S 7→ [0,1] defined on a probability space (S,A, P ). Given a sample (X1, . . . ,Xn) of i.i.d. random variables taking values in S with common distribution P , let Pn denote the empirical measure based on (X1, . . . ,Xn). We study an empirical risk minimization problem Pnf →min, f ∈ F . Given a solution f̂n of this problem, the goal is to obtain very ge...

1 The joys of symmetry (a) We prove the following proposition. The claim that Z is symmetric then follows by induction. Proposition 1. If Y is a symmetric random variable and X is a Rademacher random variable independent of Y , then for any real constant r, the random variable Y + rX is symmetric.

We develop a general framework for margin-based multicategory classification in metric spaces. The basic work-horse is a margin-regularized version of the nearest-neighbor classifier. We prove generalization bounds that match the state of the art in sample size n and significantly improve the dependence on the number of classes k. Our point of departure is a nearly Bayes-optimal finite-sample r...