Adaptation of closed form regularization parameters with prior information to the radial basis function neural network for high frequency financial time series
The research presented in this dissertation offers an extension to the classic Broomhead and Lowe Radial Basis Function artificial neural network (RBF ANN) algorithm . The algorithm is extended by incorporating the concepts of Tikhonov's Regularization theory  in the form of ridge regression with prior information matrix. Although, the concepts of Ridge Regression introduced by Hoerl & Kennard  and the concepts of prior-information matrix introduced by Swindel  are not new, their joint implementation in a RBF ANN has not been investigated prior to this research. The objective of this extension is to produce a more accurate system specification when the modified RBF is applied to high frequency time-series data. ^ When implemented in ANNs, ridge regression helps to restore the balance between bias and variance by pruning unwanted nodes thus lowering the overall MSE. In essence, the ridge regression parameter is analogous to introducing a weight decay parameter (λ) or regularization parameter in the ANN. ^ Traditionally, iterative techniques were used to compute the weight decay parameter. The RBF ANN developed in this dissertation implements two parametric closed-form solutions for the derivation of the weight decay parameter. The first method was proposed by Hemmerle . The second method was proposed by Crouse et. al. . In addition, a prior information matrix as defined by Crouse was added to the closed-form version of the ANN. ^ The results of solving the augmented RBF ANN with and without the prior information matrix show a mixed performance by the net based on the computed MSE for the actual and predicted sets. Specifically, the net that incorporated the closed-form solution for the regularization parameter generates lower MSEs for both the actual and predicted sets than the net that uses an iterative method. The enhanced RBF net also generates lower MSEs than that produced by a Multilayer Perceptron ANN net using backpropagation methods. When prior information matrix was introduced in the enhanced RBF ANN the MSE for the actual set was reduced. However, the addition of the prior information matrix did not contribute to lowering the MSEs for the predicted set. ^
"Adaptation of closed form regularization parameters with prior information to the radial basis function neural network for high frequency financial time series"
Dissertations and Master's Theses (Campus Access).