Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Choosing Multiple Parameters for Support Vector Machines
Machine Learning
Estimating the Generalization Performance of an SVM Efficiently
ICML '00 Proceedings of the Seventeenth International Conference on Machine Learning
Radius margin bounds for support vector machines with the RBF kernel
Neural Computation
Kernel Methods for Pattern Analysis
Kernel Methods for Pattern Analysis
Bounds on Error Expectation for Support Vector Machines
Neural Computation
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In the design of support vector machines an important step is to select the optimal hyperparameters. One of the most used estimators of the performance is the Radius-Margin bound. Some modifications of this bound have been made to adapt it to soft margin problems, giving a convex optimization problem for the L2 soft margin formulation. However, it is still interesting to consider the L1 case due to the reduction in the support vector number. There have been some proposals to adapt the Radius-Margin bound to the L1 case, but the use of gradient descent to test them is not possible in some of them because these bounds are not differentiable. In this work we propose to use simulated annealing as a method to find the optimal hyperparameters when the bounds are not differentiable, have multiple local minima or the kernel is not differentiable with respect to its hyperparameters.