Maximum Margin Classifiers with Specified False Positive and False Negative Error Rates

Abstract

This paper addresses the problem of maximum margin classification given the moments of class conditional densities and the false positive and false negative error rates. Using Chebyshev inequalities, the problem can be posed as a second order cone programming problem. The dual of the formulation leads to a geometric optimization problem, that of computing the distance between two ellipsoids, which is solved by an iterative algorithm. The formulation is extended to non-linear classifiers using kernel methods. The resultant classifiers are applied to the case of classification of unbalanced datasets with asymmetric costs for misclassification. Experimental results on benchmark datasets show the efficacy of the proposed method.

Learning Algorithms for Link Prediction Based on Chance Constraints

“…2) Biased classification: we can vary the preferential bias for each class η 1 and η 2 instead of varying the misclassification costs and try to find a maximummargin hyperplane in the biased classification framework (B-SOCP) [17].…”

“…They are used in a variety of settings such as feature selection [3], dealing with missing features [23], classification and ordinal regression algorithms that scale to large datasets [18], and formulations to deal with unbalanced data [17,10]. In this work, we give a scalable cost-sensitive formulation based on chance-constraints which satisfies all the requirements needed for learning a good link predictor mentioned above and show how it can be used for link prediction to significantly improve performance.…”

Parallelization with Multiplicative Algorithms for Big Data Mining

“…Thus the deployment of the parallelization is extreme simple and require few memory copy operations among computational nodes. Support vector machines [5] and the related max margin based models [23], [19] are robust and accurate classification algorithm, and widely used in many areas. Massive successful efforts have been put on solving SVM problems [13], [21], [14].…”

Asymmetrical and lower bounded support vector regression for power estimation

“…The authors in [4] study Bayesian risk analysis and replace the quadratic loss-function with an asymmetric loss-function to derive a general class of functions which approach infinity near the origin to limit underestimates. In [5], the authors presents a maximum margin classifier which bounds misclassification for each class differently thus allowing for different tolerances levels. In [6], the authors use a smoothing strategy to modify the typical SVR approach into a non-constrained problem thereby only solving a system of linear equations rather than a convex quadratic program.…”