New Generalization Bounds for Learning Kernels

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 p base kernels has only a log(p) dependency on the number of kernels, p, which is considerably more favorable than the previous best bound given for the same problem. We also give a novel bound for learning with a linear combination of p base kernels with an L_2 regularization whose dependency on p is only in p^{1/4}

Multiple Kernel Learning from Noisy Labels by Stochastic Programming

We study the problem of multiple kernel learning from noisy labels. This is in contrast to most of the previous studies on multiple kernel learning that mainly focus on developing efficient algorithms and assume perfectly labeled training examples. Directly applying the existing multiple kernel learning algorithms to noisily labeled examples often leads to suboptimal performance due to the incorrect class assignments. We address this challenge by casting multiple kernel learning from noisy labels into a stochastic programming problem, and presenting a minimax formulation. We develop an efficient algorithm for solving the related convex-concave optimization problem with a fast convergence rate of $O(1/T)$ where $T$ is the number of iterations. Empirical studies on UCI data sets verify both the effectiveness of the proposed framework and the efficiency of the proposed optimization algorithm.Comment: ICML201

Structured Sparsity and Generalization

We present a data dependent generalization bound for a large class of regularized algorithms which implement structured sparsity constraints. The bound can be applied to standard squared-norm regularization, the Lasso, the group Lasso, some versions of the group Lasso with overlapping groups, multiple kernel learning and other regularization schemes. In all these cases competitive results are obtained. A novel feature of our bound is that it can be applied in an infinite dimensional setting such as the Lasso in a separable Hilbert space or multiple kernel learning with a countable number of kernels

Voted Kernel Regularization

This paper presents an algorithm, Voted Kernel Regularization , that provides the flexibility of using potentially very complex kernel functions such as predictors based on much higher-degree polynomial kernels, while benefitting from strong learning guarantees. The success of our algorithm arises from derived bounds that suggest a new regularization penalty in terms of the Rademacher complexities of the corresponding families of kernel maps. In a series of experiments we demonstrate the improved performance of our algorithm as compared to baselines. Furthermore, the algorithm enjoys several favorable properties. The optimization problem is convex, it allows for learning with non-PDS kernels, and the solutions are highly sparse, resulting in improved classification speed and memory requirements.Comment: 16 page

Guaranteed Classification via Regularized Similarity Learning

Learning an appropriate (dis)similarity function from the available data is a central problem in machine learning, since the success of many machine learning algorithms critically depends on the choice of a similarity function to compare examples. Despite many approaches for similarity metric learning have been proposed, there is little theoretical study on the links between similarity met- ric learning and the classification performance of the result classifier. In this paper, we propose a regularized similarity learning formulation associated with general matrix-norms, and establish their generalization bounds. We show that the generalization error of the resulting linear separator can be bounded by the derived generalization bound of similarity learning. This shows that a good gen- eralization of the learnt similarity function guarantees a good classification of the resulting linear classifier. Our results extend and improve those obtained by Bellet at al. [3]. Due to the techniques dependent on the notion of uniform stability [6], the bound obtained there holds true only for the Frobenius matrix- norm regularization. Our techniques using the Rademacher complexity [5] and its related Khinchin-type inequality enable us to establish bounds for regularized similarity learning formulations associated with general matrix-norms including sparse L 1 -norm and mixed (2,1)-norm

Ensembles of Kernel Predictors

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 includes novel theoretical guarantees based on the Rademacher complexity of the corresponding hypothesis sets, the introduction and analysis of a learning algorithm based on these hypothesis sets, and a series of experiments using ensembles of kernel predictors with several data sets. Both convex combinations of kernel-based hypotheses and more general Lq-regularized nonnegative combinations are analyzed. These theoretical, algorithmic, and empirical results are compared with those achieved by using learning kernel techniques, which can be viewed as another approach for solving the same problem