A Note on Probability and Conditional Probability SVM models

Abstract

Support Vector Machines (SVMs) are powerful tools in machine learning, widely used for classification and regression tasks. Over time, various extensions, such as Probability Estimation SVM (PSVM) and Conditional Probability SVM (CPSVM), have been proposed to enhance SVM performance across different conditions and datasets. This article offers a comprehensive review and analysis of SVMs, with a particular focus on the PSVM and CPSVM models. We delve into the intricacies of these models, addressing computational nuances and presenting corrected formulations where necessary. Our empirical evaluation, conducted on diverse benchmark datasets, implements both linear and nonlinear versions of these SVMs. Performance is benchmarked using the Balanced Accuracy metric. The results highlight the comparative strengths of these models in handling varied datasets and their potential advantages over traditional SVM formulations. To rigorously assess and compare the performance of these SVM variants, we employ statistical tests, including the Friedman test and post hoc analysis.