Tree-Structured Nonlinear Regression

Tree Structured Interpretable Regression

Nonlinear Regression with Structured Inputs

For many applications of nonlinear regression, theory does not guide the model building process by suggesting a relevant functional form. This research develops a new technique for use in this situation. Called STAT-ANN, the new method provides modelling flexibility similar to a neural network but provides a statistical basis for model selection, interpretation, and validation by following a tw...

Nonparametric Regression Model with Tree-structured Response

Highly developed science and technology from the last two decades motivated the study of complex data objects. In this paper, we consider the topological properties of a population of tree-structured objects. Our interest centers on modeling the relationship between a tree-structured response and other covariates. For tree objects, this poses serious challenges since most regression methods rel...

Tree-structured smooth transition regression models

This paper introduces a tree-based model that combines aspects of CART (Classification and Regression Trees) and STR (Smooth Transition Regression). The model is called the Smooth Transition Regression Tree (STR-Tree). The main idea relies on specifying a parametric nonlinear model through a tree-growing procedure. The resulting model can be analyzed as a smooth transition regression with multi...

Sketching Structured Matrices for Faster Nonlinear Regression

Motivated by the desire to extend fast randomized techniques to nonlinear lp regression, we consider a class of structured regression problems. These problems involve Vandermonde matrices which arise naturally in various statistical modeling settings, including classical polynomial fitting problems, additive models and approximations to recently developed randomized techniques for scalable kern...