Support vector regression from simulation data and few experimental samples

Abstract

a b s t r a c tThis paper considers nonlinear modeling based on a limited amount of experimental data and a simulator built from prior knowledge. The problem of how to best incorporate the data provided by the simulator, possibly biased, into the learning of the model is addressed. This problem, although particular, is very representative of numerous situations met in engine control, and more generally in engineering, where complex models, more or less accurate, exist and where the experimental data which can be used for calibration are difficult or expensive to obtain. The first proposed method constrains the function to fit to the values given by the simulator with a certain accuracy, allowing to take the bias of the simulator into account. The second method constrains the derivatives of the model to fit to the derivatives of a prior model previously estimated on the simulation data. The combination of these two forms of prior knowledge is also possible and considered. These approaches are implemented in the linear programming support vector regression (LP-SVR) framework by the addition, to the optimization problem, of constraints, which are linear with respect to the parameters. Tests are then performed on an engine control application, namely, the estimation of the in-cylinder residual gas fraction in Spark Ignition (SI) engine with Variable Camshaft Timing (VCT). Promising results are obtained on this application. The experiments have also shown the importance of adding potential support vectors in the model when using Gaussian RBF kernels with very few training samples.

Gaussian case-based reasoning for business failure prediction with empirical data in China

“…Following this, Yip [60] compared the predictive performance of CBR with that of MDA, finding CBR clearly outperformed MDA. Support vector machine (SVM) has been gaining popularity recently because of its high generalization performance and global optimal solution [3,7,15,16,22,27,31,54,61]. Studies of SVM-based BFP [4,9,12,14,35,36,45,58] indicate that SVM outperforms BPNN, MDA, and Logit.…”

Parameter Optimization for Nadaraya-Watson Kernel Regression Method with Small Samples

“…In Table 1, we present experimental comparisons for regression estimation using three representative loss functions: squared loss, Huber's loss (ε=0), and Vapnik's ε-insensitive loss with ε given according to Eq. (8). The noise level (ζ) column indicates the standard deviation of the Gaussian noise with zero mean.…”

“…Therefore, designing a regression approach that performs well with small samples is a significant problem. Support vector www.ijarai.thesai.org regression (SVR) is motivated by the growing popularity of support vector machines (SVM) for regression with small samples (Smola & Scholkopf, 2004;Chu & Keerthi, 2007;Bloch, 2008;Huang, Zheng, et al, 2009). However, the quality of SVR models depends on proper settings of the SVR hyperparameters, and the main issue for practitioners trying to apply SVR is determining these parameter values for a given data set.…”

Probability Distribution and Deviation Information Fusion Driven Support Vector Regression Model and Its Application

“…The SVR model also has been improved by prior knowledge [11,12]. There are numerous types of prior knowledge, including the average value and monotonicity of the sample data.…”