Function approximation

[2] Function approximations are used where theoretical models are unavailable or hard to compute.

[3] Second, the target function, call it g, may be unknown; instead of an explicit formula, only a set of points of the form (x, g(x)) is provided.

[citation needed] Depending on the structure of the domain and codomain of g, several techniques for approximating g may be applicable.

For example, if g is an operation on the real numbers, techniques of interpolation, extrapolation, regression analysis, and curve fitting can be used.

[4] To some extent, the different problems (regression, classification, fitness approximation) have received a unified treatment in statistical learning theory, where they are viewed as supervised learning problems.

Several approximations of a step function
Several progressively more accurate approximations of the step function .
An asymmetrical Gaussian function fit to a noisy curve using regression.
An asymmetrical Gaussian function fit to a noisy curve using regression.