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Abstract
This work proposes a novel Support Vector Machine (SVM) methodology for finding accurate probabilities of class memberships in supervised classification problems. Classical SVMs do not complement their class predictions with reliable confidence measures of class assignments. For two-class problems this limitation can be overcome by combining a sequence of weighted SVMs predictions into consistent class probability estimates. In this work we show how a smart use of mathematical programming models can be used to extend this approach to the general multi-class classification problem. Previous attempts to tackle this problem either do not scale well with the number of different classes or rely on sub-optimal partition strategies. Numerical experiments reveal the good scaling properties of the proposal, and the relative advantages of its class probability estimates over alternative approaches.
Short Bio
Pedro Duarte Silva is an Associate Professor at the Católica Porto Business School of the Universidade Católica Portuguesa. He holds a doctorate degree in Business Administration from the Terry College of Business of the University of Georgia with a specialization in Management Sciences. His research focuses on the intersection between Data Science and Computational Statistics, with a particular focus on the development of efficient numerical algorithms for Big Data Analytics, and novel methodologies for the analysis of new forms of complex data known as Symbolic Data. He is the author of numerous communications at reputed scientific conferences, and his research has been published in prestigious scientific journals such as European Journal of Operational Research, Computational Statistics and Data Analysis, Computational Statistics, Journal of Multivariate Analysis, Journal of Classification, Computers and Operations Research, and Decision Sciences. Furthermore, he is an author/co-author of several popular Comprehensive R Archive Network (CRAN) R packages namely, subselect: Selecting variable subsets; corpcor: Efficient Estimation of Covariance and (Partial) Correlation; MAINT.Data: Model and Analize Interval Data, and HiDimDA: High Dimensional Discriminant Analysis.
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