Transform Learning Based Function Approximation for Regression and Forecasting

Abstract

Regression and forecasting can be viewed as learning the functions with the appropriate input and output variables from the data. To capture the complex relationship among the variables, different techniques like, kernelized dictionary learning are being explored in the existing literature. In this paper, the transform learning based function approximation is presented which has computational and performance advantages over dictionary based techniques. Apart from providing the formulation and derivation of the necessary update steps, the performance results obtained with both synthetic and real data are presented in the paper. The initial results obtained with both the basic and kernelized versions demonstrate the usefulness of the proposed technique for regression and forecasting tasks.