Support vector regression for estimating earthquake response spectra

This study uses support vector regression (SVR), a supervised machine learning algorithm, to model the average horizontal response spectrum as a nonparametric function of a set of predictor ground motion variables. Traditional ground motion prediction equations (GMPEs) are derived using parametric regression, where a fixed functional form is selected, and the model coefficients are determined by minimizing the errors on the training set. The SVR model is nonparametric; there is no need to assume a fixed functional form. Using nonlinear basis functions, the data points are mapped into a high dimensional feature space, where nonlinear input-output relationships can be expressed as a linear combination of nonlinear functions, using a subset of the data points. The combination weights are determined by minimizing the generalization error, using a formal mechanism to characterize the trade-off between the model complexity and the quality of fit to the data. Minimization of the generalization error instead of the fitting error leads to better generation to unseen data, and thus reduces the risk of over-fitting for a given number of data points. The SVR model is not based on a specific probability distribution, and is readily applicable to non-Gaussian data. An example application is presented for vertical strike-slip earthquakes, and the predictions from the SVR model are compared to the recently developed GMPEs. The results demonstrate the validity of the proposed model, and suggest that it can be used as an alternative to the conventional ground motion prediction models.