Leave-one-out cross-validation-based model selection for multi-input multi-output support vector machine

As an effective approach for multi-input multi-output regression estimation problems, a multi-dimensional support vector regression (SVR), named M-SVR, is generally capable of obtaining better predictions than applying a conventional support vector machine (SVM) independently for each output dimension. However, although there are many generalization error bounds for conventional SVMs, all of them cannot be directly applied to M-SVR. In this paper, a new leave-one-out (LOO) error estimate for M-SVR is derived firstly through a virtual LOO cross-validation procedure. This LOO error estimate can be straightway calculated once a training process ended with less computational complexity than traditional LOO method. Based on this LOO estimate, a new model selection methods for M-SVR based on multi-objective optimization strategy is further proposed in this paper. Experiments on toy noisy function regression and practical engineering data set, that is, dynamic load identification on cylinder vibration system, are both conducted, demonstrating comparable results of the proposed method in terms of generalization performance and computational cost.