# Machine Learning Lesson of the Day – Introduction to Linear Basis Function Models

March 10, 2014 Leave a comment

Given a supervised learning problem of using inputs () to predict a continuous target , the simplest model to use would be linear regression. However, what if we know that the relationship between the inputs and the target is **non-linear**, but we are unsure of exactly what form this relationship has?

One way to overcome this problem is to use **linear basis function models**. These models assume that the target is a **linear combination** of a set of **basis functions**.

This is a generalization of linear regression that essentially replaces each input with a function of the input. (A linear basis function model that uses the identity function is just linear regression.)

The type of basis functions (i.e. the type of function given by ) is chosen to suitably model the non-linearity in the relationship between the inputs and the target. It also needs to be chosen so that the computation is efficient. I will discuss variations of linear basis function models in a later Machine Learning Lesson of the Day.

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