A learning model that summarizes data with a set of parameters of fixed size (independent of the number of training examples) is called a parametric model. No matter how much data you throw at a parametric model, it won’t change its mind about how many parameters it needs.

The algorithms involve two steps:

- Select a form for the function.
- Learn the coefficients for the function from the training data.

An easy to understand functional form for the mapping function is a line, as is used in linear regression:

b0 + b1*x1 + b2*x2 = 0

Where b0, b1 and b2 are the coefficients of the line that control the intercept and slope, and x1 and x2 are two input variables.

Assuming the functional form of a line greatly simplifies the learning process. Now, all we need to do is estimate the coefficients of the line equation and we have a predictive model for the problem.

Often the assumed functional form is a linear combination of the input variables and as such parametric machine learning algorithms are often also called “linear machine learning algorithms“.