Terence D. Sanger Richard S. Sutton Christopher J. Matheus Massachusetts Institute GTE Laboratories GTE Laboratories of Technology Incorporated Incorporated Room E25-534 40 Sylvan Road 40 Sylvan Road Cambridge, MA 02139 Waltham, MA 02254 Waltham, MA 02254 tds@ai.mit.edu Abstract We present an iterative algorithm for nonlinear regression based on construction of sparse polynomials. Polynomials are built sequentially from lower to higher order. Selection of new terms is accomplished using a novel look-ahead approach that predicts whether a variable contributes to the remaining error. The algorithm is based on the tree-growing heuristic in LMS Trees which we have extended to approximation of arbitrary polynomials of the input features.

Two projection based feedforward network learning methods for modelfree regression problems are studied and compared in this paper: one is the popular back-propagation learning (BPL); the other is the projection pursuit learning (PPL).

G/SPLINES is an algorithm for building functional models of data. It uses genetic search to discover combinations of basis functions which are then used to build a least-squares regression model. Because it produces a population of models which evolve over time rather than a single model, it allows analysis not possible with other regression-based approaches. 1 INTRODUCTION G/SPLINES is a hybrid of Friedman's Multivariable Adaptive Regression Splines (MARS) algorithm (Friedman, 1990) with Holland's Genetic Algorithm (Holland, 1975). G/SPLINES has advantages over MARS in that it requires fewer least-squares computations, is easily extendable to non-spline basis functions, may discover models inaccessible to local-variable selection algorithms, and allows significantly larger problems to be considered. These issues are discussed in (Rogers, 1991). This paper begins with a discussion of linear regression models, followed by a description of the G/SPLINES algorithm, and finishes with a series of experiments illustrating its performance, robustness, and analysis capabilities.

Terence D. Sanger Richard S. Sutton Christopher J. Matheus Massachusetts Institute GTE Laboratories GTE Laboratories of Technology Incorporated Incorporated Room E25-534 40 Sylvan Road 40 Sylvan Road Cambridge, MA 02139 Waltham, MA 02254 Waltham, MA 02254 tds@ai.mit.edu Abstract We present an iterative algorithm for nonlinear regression based on construction of sparse polynomials. Polynomials are built sequentially from lower to higher order. Selection of new terms is accomplished using a novel look-ahead approach that predicts whether a variable contributes to the remaining error. The algorithm is based on the tree-growing heuristic in LMS Trees which we have extended to approximation of arbitrary polynomials of the input features.

Terence D. Sanger Massachusetts Institute of Technology Room E25-534 Cambridge, MA 02139 tds@ai.mit.edu Abstract We present an iterative algorithm for nonlinear regression based on construction ofsparse polynomials. Polynomials are built sequentially from lower to higher order. Selection of new terms is accomplished using a novel look-ahead approach that predicts whether a variable contributes to the remaining error. The algorithm is based on the tree-growing heuristic in LMS Trees which we have extended to approximation of arbitrary polynomials ofthe input features.

Two projection based feedforward network learning methods for modelfree regressionproblems are studied and compared in this paper: one is the popular back-propagation learning (BPL); the other is the projection pursuit learning (PPL).

G/SPLINES is an algorithm for building functional models of data. It uses genetic search to discover combinations of basis functions which are then used to build a least-squares regression model. Because it produces a population of models which evolve over time rather than a single model, it allows analysis not possible with other regression-based approaches. 1 INTRODUCTION G/SPLINES is a hybrid of Friedman's Multivariable Adaptive Regression Splines (MARS) algorithm (Friedman, 1990) with Holland's Genetic Algorithm (Holland, 1975). G/SPLINES has advantages over MARS in that it requires fewer least-squares computations, is easily extendable to non-spline basis functions, may discover models inaccessible to local-variable selection algorithms, and allows significantly larger problems to be considered. These issues are discussed in (Rogers, 1991). This paper begins with a discussion of linear regression models, followed by a description of the G/SPLINES algorithm, and finishes with a series of experiments illustrating its performance, robustness, and analysis capabilities.

This paper explores the use of a model neural network for motor learning. Steinbuch and Taylor presented neural network designs to do nearest neighbor lookup in the early 1960s. In this paper their nearest neighbor network is augmented with a local model network, which fits a local model to a set of nearest neighbors. The network design is equivalent to local regression. This network architecture can represent smooth nonlinear functions, yet has simple training rules with a single global optimum.

This paper explores the use of a model neural network for motor learning. Steinbuch and Taylor presented neural network designs to do nearest neighbor lookup in the early 1960s. In this paper their nearest neighbor network is augmented with a local model network, which fits a local model to a set of nearest neighbors. The network design is equivalent to local regression. This network architecture can represent smooth nonlinear functions, yet has simple training rules with a single global optimum.

This paper explores the use of a model neural network for motor learning. Steinbuch and Taylor presented neural network designs to do nearest neighbor lookup in the early 1960s. In this paper their nearest neighbor network is augmented with a local model network, which fits a local model to a set of nearest neighbors. The network design is equivalent to local regression. This network architecture can represent smooth nonlinear functions, yet has simple training rules with a single global optimum.