Learning the kernel with hyperkernels

This paper addresses the problem of choosing a kernel suitable for estimation with a support vector machine, hence further automating machine learning. This goal is achieved by defining a reproducing kernel Hilbert space on the space of kernels itself. Such a formulation leads to a statistical estimation problem similar to the problem of minimizing a regularized risk functional. We state the equivalent representer theorem for the choice of kernels and present a semidefinite programming formulation of the resulting optimization problem. Several recipes for constructing hyperkernels are provided, as well as the details of common machine learning problems. Experimental results for classification, regression and novelty detection on UCI data show the feasibility of our approach

Hierarchic Bayesian models for kernel learning

The integration of diverse forms of informative data by learning an optimal combination of base kernels in classification or regression problems can provide enhanced performance when compared to that obtained from any single data source. We present a Bayesian hierarchical model which enables kernel learning and present effective variational Bayes estimators for regression and classification. Illustrative experiments demonstrate the utility of the proposed method

Combining dissimilarities in a hyper reproducing kernel hilbert space for complex human cancer prediction

9 páginas, 3 tablas.-- This is an open access article distributed under the Creative Commons Attribution License.DNA microarrays provide rich profiles that are used in cancer prediction considering the gene expression levels across a collection of related samples. Support Vector Machines (SVM) have been applied to the classification of cancer samples with encouraging results. However, they rely on Euclidean distances that fail to reflect accurately the proximities among sample profiles. Then, non-Euclidean dissimilarities provide additional information that should be considered to reduce the misclassification errors. In this paper, we incorporate in the -SVM algorithm a linear combination of non-Euclidean dissimilarities. The weights of the combination are learnt in a (Hyper Reproducing Kernel Hilbert Space) HRKHS using a Semidefinite Programming algorithm. This approach allows us to incorporate a smoothing term that penalizes the complexity of the family of distances and avoids overfitting. The experimental results suggest that the method proposed helps to reduce the misclassification errors in several human cancer problems. © 2009 Manuel Mart́n-Merino et al.Financial support from Grant S02EIA-07L01.Peer Reviewe

Combining Dissimilarities in a Hyper Reproducing Kernel Hilbert Space for Complex Human Cancer Prediction

DNA microarrays provide rich profiles that are used in cancer prediction considering the gene expression levels across a collection of related samples. Support Vector Machines (SVM) have been applied to the classification of cancer samples with encouraging results. However, they rely on Euclidean distances that fail to reflect accurately the proximities among sample profiles. Then, non-Euclidean dissimilarities provide additional information that should be considered to reduce the misclassification errors. In this paper, we incorporate in the ν-SVM algorithm a linear combination of non-Euclidean dissimilarities. The weights of the combination are learnt in a (Hyper Reproducing Kernel Hilbert Space) HRKHS using a Semidefinite Programming algorithm. This approach allows us to incorporate a smoothing term that penalizes the complexity of the family of distances and avoids overfitting. The experimental results suggest that the method proposed helps to reduce the misclassification errors in several human cancer problems

Model selection of polynomial kernel regression

Polynomial kernel regression is one of the standard and state-of-the-art learning strategies. However, as is well known, the choices of the degree of polynomial kernel and the regularization parameter are still open in the realm of model selection. The first aim of this paper is to develop a strategy to select these parameters. On one hand, based on the worst-case learning rate analysis, we show that the regularization term in polynomial kernel regression is not necessary. In other words, the regularization parameter can decrease arbitrarily fast when the degree of the polynomial kernel is suitable tuned. On the other hand,taking account of the implementation of the algorithm, the regularization term is required. Summarily, the effect of the regularization term in polynomial kernel regression is only to circumvent the " ill-condition" of the kernel matrix. Based on this, the second purpose of this paper is to propose a new model selection strategy, and then design an efficient learning algorithm. Both theoretical and experimental analysis show that the new strategy outperforms the previous one. Theoretically, we prove that the new learning strategy is almost optimal if the regression function is smooth. Experimentally, it is shown that the new strategy can significantly reduce the computational burden without loss of generalization capability.Comment: 29 pages, 4 figure