NONLINEAR REGRESSION MODELING VIA REGULARIZED GAUSSIAN BASIS FUNCTIONS

Functional regression modeling via regularized Gaussian basis expansions

We consider the problem of constructing functional regression models for scalar responses and functional predictors, using Gaussian basis functions along with the technique of regularization. An advantage of our regularizedGaussian basis expansions to functional data analysis is that it creates a much more flexible instrument for transforming each individual’s observations into functional form....

Nonlinear regression modeling and spike detection via Gaussian basis expansions

We consider the problem of constructing nonlinear regression models in the case that the structure of data has abrupt change points at unknown points. We propose two stage procedure where the spikes are detected by fused lasso signal approximator at the first stage, and the smooth curve are effectively estimated along with the technique of regularization method at the second. In order to select...

Nonlinear Logistic Discrimination Via Regularized Gaussian Basis Expansions

Semi-supervised logistic discrimination via regularized Gaussian basis expansions

The problem of constructing classification methods based on both classified and unclassified data sets is considered for analyzing data with complex structures. We introduce a semi-supervised logistic discriminant model with Gaussian basis expansions. Unknown parameters included in the logistic model are estimated by regularization method along with the technique of EM algorithm. For selection ...

Gaussian Regularized Sliced Inverse Regression

Sliced Inverse Regression (SIR) is an effective method for dimension reduction in high-dimensional regression problems. The original method, however, requires the inversion of the predictors covariance matrix. In case of collinearity between these predictors or small sample sizes compared to the dimension, the inversion is not possible and a regularization technique has to be used. Our approach...