Chapter 8

Linear regression

8.1 Introduction

Parametric regression is the most direct instantiation of the idea of a parametric model representation, in which the model is represented by a finite number of parameters with a fixed functional form assumed. This is also the most frequently used approach to the regression task, to which such a representation is particularly well suited. Parametric regression algorithms can deliver successful regression models by themselves or in combination with other techniques, including those borrowed from algorithms used for the classification task.

Linear regression is the simplest approach to the regression task based on a parametric model representation. Despite its obvious and unquestionable linearity limitation (being capable of directly approximating linear target functions only), it deserves particular attention due to its algorithmic and computational advantages. Interestingly, it is possible, at least to some extent, to overcome the limitation while retaining the advantages. This chapter covers both plain linear regression and augmented versions thereof, breaking the linearity limitation. The presented discussion of model representation and creation techniques maintains a higher level of generality whenever possible, presenting the particular linear representation as an instantiation of the more general parametric regression approach. Linear model representation and gradient-based parameter estimation have already appeared in Chapter ...

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