Comment on "Support Vector Machines with Applications"

Comment on "Support Vector Machines with Applications" [math.ST/0612817]Comment: Published at http://dx.doi.org/10.1214/088342306000000475 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Random Feature Maps for Dot Product Kernels

Approximating non-linear kernels using feature maps has gained a lot of interest in recent years due to applications in reducing training and testing times of SVM classifiers and other kernel based learning algorithms. We extend this line of work and present low distortion embeddings for dot product kernels into linear Euclidean spaces. We base our results on a classical result in harmonic analysis characterizing all dot product kernels and use it to define randomized feature maps into explicit low dimensional Euclidean spaces in which the native dot product provides an approximation to the dot product kernel with high confidence.Comment: To appear in the proceedings of the 15th International Conference on Artificial Intelligence and Statistics (AISTATS 2012). This version corrects a minor error with Lemma 10. Acknowledgements : Devanshu Bhimwa

Tabu search model selection for SVM

International audienceA model selection method based on tabu search is proposed to build support vector machines (binary decision functions) of reduced complexity and efficient generalization. The aim is to build a fast and efficient support vector machines classifier. A criterion is defined to evaluate the decision function quality which blends recognition rate and the complexity of a binary decision functions together. The selection of the simplification level by vector quantization, of a feature subset and of support vector machines hyperparameters are performed by tabu search method to optimize the defined decision function quality criterion in order to find a good sub-optimal model on tractable times

Screening Data Points in Empirical Risk Minimization via Ellipsoidal Regions and Safe Loss Functions

We design simple screening tests to automatically discard data samples in empirical risk minimization without losing optimization guarantees. We derive loss functions that produce dual objectives with a sparse solution. We also show how to regularize convex losses to ensure such a dual sparsity-inducing property, and propose a general method to design screening tests for classification or regression based on ellipsoidal approximations of the optimal set. In addition to producing computational gains, our approach also allows us to compress a dataset into a subset of representative points

Hierarchical linear support vector machine

This is the author’s version of a work that was accepted for publication in Pattern Recognition. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Pattern Recognition, Vol. 45, Iss. 12, (2012) DOI: 10.1016/j.patcog.2012.06.002The increasing size and dimensionality of real-world datasets make it necessary to design efficient algorithms not only in the training process but also in the prediction phase. In applications such as credit card fraud detection, the classifier needs to predict an event in 10 ms at most. In these environments the speed of the prediction constraints heavily outweighs the training costs. We propose a new classification method, called a Hierarchical Linear Support Vector Machine (H-LSVM), based on the construction of an oblique decision tree in which the node split is obtained as a Linear Support Vector Machine. Although other methods have been proposed to break the data space down in subregions to speed up Support Vector Machines, the H-LSVM algorithm represents a very simple and efficient model in training but mainly in prediction for large-scale datasets. Only a few hyperplanes need to be evaluated in the prediction step, no kernel computation is required and the tree structure makes parallelization possible. In experiments with medium and large datasets, the H-LSVM reduces the prediction cost considerably while achieving classification results closer to the non-linear SVM than that of the linear case.The authors would like to thank the anonymous reviewers for their comments that help improve the manuscript. I.R.-L. is supported by an FPU Grant from Universidad Autónoma de Madrid, and partially supported by the Universidad Autónoma de Madrid-IIC Chair and TIN2010-21575-C02-01. R.H. acknowledges partial support by ONRN00014-07-1-0741, USARIEM-W81XWH-10-C-0040 (ELINTRIX) and JPL-2012-1455933