Related papers: The Local Rademacher Complexity of Lp-Norm Multipl…
In this paper, we correct an upper bound, presented in~\cite{hs-11}, on the generalisation error of classifiers learned through multiple kernel learning. The bound in~\cite{hs-11} uses Rademacher complexity and has an\emph{additive}…
This paper presents several novel generalization bounds for the problem of learning kernels based on the analysis of the Rademacher complexity of the corresponding hypothesis sets. Our bound for learning kernels with a convex combination of…
We present a novel notion of complexity that interpolates between and generalizes some classic existing complexity notions in learning theory: for estimators like empirical risk minimization (ERM) with arbitrary bounded losses, it is upper…
We show a Talagrand-type concentration inequality for Multi-Task Learning (MTL), using which we establish sharp excess risk bounds for MTL in terms of distribution- and data-dependent versions of the Local Rademacher Complexity (LRC). We…
This paper provides a general result on controlling local Rademacher complexities, which captures in an elegant form to relate the complexities with constraint on the expected norm to the corresponding ones with constraint on the empirical…
Linear predictors form a rich class of hypotheses used in a variety of learning algorithms. We present a tight analysis of the empirical Rademacher complexity of the family of linear hypothesis classes with weight vectors bounded in…
This paper introduces a new and effective algorithm for learning kernels in a Multi-Task Learning (MTL) setting. Although, we consider a MTL scenario here, our approach can be easily applied to standard single task learning, as well. As…
We propose new bounds on the error of learning algorithms in terms of a data-dependent notion of complexity. The estimates we establish give optimal rates and are based on a local and empirical version of Rademacher averages, in the sense…
We analyze the local Rademacher complexity of empirical risk minimization (ERM)-based multi-label learning algorithms, and in doing so propose a new algorithm for multi-label learning. Rather than using the trace norm to regularize the…
In this paper, we give a new sharp generalization bound of lp-MKL which is a generalized framework of multiple kernel learning (MKL) and imposes lp-mixed-norm regularization instead of l1-mixed-norm regularization. We utilize localization…
This paper examines the problem of learning with a finite and possibly large set of p base kernels. It presents a theoretical and empirical analysis of an approach addressing this problem based on ensembles of kernel predictors. This…
Similarity learning has received a large amount of interest and is an important tool for many scientific and industrial applications. In this framework, we wish to infer the distance (similarity) between points with respect to an arbitrary…
We propose Rademacher complexity bounds for multiclass classifiers trained with a two-step semi-supervised model. In the first step, the algorithm partitions the partially labeled data and then identifies dense clusters containing $\kappa$…
This paper proposes a simple approach to derive efficient error bounds for learning multiple components with sparsity-inducing regularization. We show that for such regularization schemes, known decompositions of the Rademacher complexity…
Many machine learning models are vulnerable to adversarial attacks; for example, adding adversarial perturbations that are imperceptible to humans can often make machine learning models produce wrong predictions with high confidence.…
Recent research on multiple kernel learning has lead to a number of approaches for combining kernels in regularized risk minimization. The proposed approaches include different formulations of objectives and varying regularization…
We consider a problem of risk estimation for large-margin multi-class classifiers. We propose a novel risk bound for the multi-class classification problem. The bound involves the marginal distribution of the classifier and the Rademacher…
We propose a novel combination of optimization tools with learning theory bounds in order to analyze the sample complexity of optimal kernel sum classifiers. This contrasts the typical learning theoretic results which hold for all…
Existing Rademacher complexity bounds for neural networks rely only on norm control of the weight matrices and depend exponentially on depth via a product of the matrix norms. Lower bounds show that this exponential dependence on depth is…
Despite their many appealing properties, kernel methods are heavily affected by the curse of dimensionality. For instance, in the case of inner product kernels in $\mathbb{R}^d$, the Reproducing Kernel Hilbert Space (RKHS) norm is often…