In the classical regression theory we try to build one functional model to fit a set of data. In noisy and complex domains this methodology can be highly unreliable and/or demand too complex functional models. Piecewise regression models provide means to overcome these difficulties. Some existing approaches to piecewise regression are based on regression trees. However, rules are known to be mo...

A simple construction of adaptive confidence sets is proposed in isotonic, convex and unimodal regression. In univariate isotonic regression, the set enjoys uniform coverage over all non-decreasing regression functions. Furthermore, diameter automatically adapts to unknown number pieces true parameter, sense that bounded from above by minimax risk class $k$-piecewise constant The a increasing f...

A new connectionist model for the solution of piecewise linear regression problems is introduced; it is able to reconstruct both continuous and non continuous real valued mappings starting from a finite set of possibly noisy samples. The approximating function can assume a different linear behavior in each region of an unknown polyhedral partition of the input domain. The proposed learning tech...

This study aims to accurately predict glaucomatous visual-field loss from patient disease data. In general, medical data show two kinds of heterogeneity: 1) internal heterogeneity, in which the phase of disease progression changes in an individual patient’s time series dataset; and 2) external heterogeneity, in which the trends of disease progression differ among patients. Although some previou...

Recently, pathfollowing algorithms for parametric optimization problems with piecewise linear solution paths have been developed within the field of regularized regression. This paper presents a generalization of these algorithms to a wider class of problems, namely a class of parametric piecewise quadratic programs and related problems. By using pathfollowing algorithms that exploit the piecew...

The occurrence of significant second-order interactions for group characteristics was examined using real data in a randomized controlled trial (RCT). The interactions exist in all RCTs; they could be easily overlooked when using the simple randomization or stratification methods, but could become more obvious when minimization methods are used. Using real data from an RCT, the minimization met...

This paper introduces a novel mixture model-based approach for simultaneous clustering and optimal segmentation of functional data which are curves presenting regime changes. The proposed model consists in a finite mixture of piecewise polynomial regression models. Each piecewise polynomial regression model is associated with a cluster, and within each cluster, each piecewise polynomial compone...