Support Vector Machines in High Energy Physics

This lecture will introduce the Support Vector algorithms for classification and regression. They are an application of the so called kernel trick, which allows the extension of a certain class of linear algorithms to the non linear case. The kernel trick will be introduced and in the context of structural risk minimization, large margin algorithms for classification and regression will be presented. Current applications in high energy physics will be discussed.Comment: 11 pages, 12 figures. Part of the proceedings of the Track 'Computational Intelligence for HEP Data Analysis' at iCSC 200

Automatic Differentiation of Algorithms for Machine Learning

Automatic differentiation---the mechanical transformation of numeric computer programs to calculate derivatives efficiently and accurately---dates to the origin of the computer age. Reverse mode automatic differentiation both antedates and generalizes the method of backwards propagation of errors used in machine learning. Despite this, practitioners in a variety of fields, including machine learning, have been little influenced by automatic differentiation, and make scant use of available tools. Here we review the technique of automatic differentiation, describe its two main modes, and explain how it can benefit machine learning practitioners. To reach the widest possible audience our treatment assumes only elementary differential calculus, and does not assume any knowledge of linear algebra.Comment: 7 pages, 1 figur

Customizing kernel functions for SVM-based hyperspectral image classification

Previous research applying kernel methods such as support vector machines (SVMs) to hyperspectral image classification has achieved performance competitive with the best available algorithms. However, few efforts have been made to extend SVMs to cover the specific requirements of hyperspectral image classification, for example, by building tailor-made kernels. Observation of real-life spectral imagery from the AVIRIS hyperspectral sensor shows that the useful information for classification is not equally distributed across bands, which provides potential to enhance the SVM's performance through exploring different kernel functions. Spectrally weighted kernels are, therefore, proposed, and a set of particular weights is chosen by either optimizing an estimate of generalization error or evaluating each band's utility level. To assess the effectiveness of the proposed method, experiments are carried out on the publicly available 92AV3C dataset collected from the 220-dimensional AVIRIS hyperspectral sensor. Results indicate that the method is generally effective in improving performance: spectral weighting based on learning weights by gradient descent is found to be slightly better than an alternative method based on estimating ";relevance"; between band information and ground trut

Basics of Feature Selection and Statistical Learning for High Energy Physics

This document introduces basics in data preparation, feature selection and learning basics for high energy physics tasks. The emphasis is on feature selection by principal component analysis, information gain and significance measures for features. As examples for basic statistical learning algorithms, the maximum a posteriori and maximum likelihood classifiers are shown. Furthermore, a simple rule based classification as a means for automated cut finding is introduced. Finally two toolboxes for the application of statistical learning techniques are introduced.Comment: 12 pages, 8 figures. Part of the proceedings of the Track 'Computational Intelligence for HEP Data Analysis' at iCSC 200