Discriminant Analysis via Smoothly Varying Regularization

The discriminant method, which uses a basis expansion in the logistic regression model and estimates it by a simply regularized likelihood, is considerably efficient especially when the discrimination boundary is complex. However, when the complexities of the boundary are different by region, the method tends to cause under-fitting or/and over-fitting at some regions. To overcome this difficulty, a smoothly varying regularization is proposed in the framework of the logistic regression. Through simulation studies based on synthetic data, the superiority of the proposed method to some existing methods is checked.