This chapter gives generalization bounds for structured output learning. We show

In this paper we develop a novel probabilistic generalization bound for learning the kernel problem. First, we show that the generalization analysis of the regularized kernel learning system reduces to investigation of the suprema of the Rademacher chaos process of order two over candidate kernels

This paper presents several novel generalization bounds for the problem of learning kernels based on a combinatorial analysis of the Rademacher complexity of the corresponding hypothesis sets. Our bound for learning kernels with a convex combination of p base kernels using L1 regularization admits

In this paper we propose a new combinatorial technique for obtaining data dependent generalization bounds. We introduce a splitting and connectivity graph (SC-graph) over the set of classifiers. In some cases the knowledge of this graph leads to an exact generalization bound. Typically

In this paper, we provide a new framework to study the generalization bound of the learning process for domain adaptation. We consider two kinds of representative domain adaptation settings: one is domain adaptation with multiple sources and the other is domain adaptation combining source

The problem of ranking is to predict or to guess the ordering between objects on the basis of their observed features. In this paper we consider ranking estimators that minimize the empirical convex risk. We prove generalization bounds for the excess risk of such estimators with rates

.g., fitting a linear curve to clearly quadratic data. The fundamental question is how many parameters, or what concept size, should one allow for a given amount of training data. A standard theoretical approach is to prove a bound on generalization error as a function of the training error and the concept

reliable. Finally, we show that the probability that the algorithm abstains is comparable to the generalization error of the best hypothesis in the class.

and the feature dimensionality, making them applicable even to large data sets in high-dimensional feature spaces. To the best of our knowledge, these are the first algorithms to perform exact multinomial logistic regression with a sparsity-promoting prior. Third, we show how nontrivial generalization bounds can

It is known that the covering numbers of a function class on a double sample (length 2m, where m is the number of points in the sample) can be used to bound the generalization performance of a classifier by using a margin based analysis. Traditionally this has been done using a "