# 1.15. Isotonic regression¶

The class `IsotonicRegression`

fits a non-decreasing function to data.
It solves the following problem:

minimize \(\sum_i w_i (y_i - \hat{y}_i)^2\)

subject to \(\hat{y}_{min} = \hat{y}_1 \le \hat{y}_2 ... \le \hat{y}_n = \hat{y}_{max}\)

where each \(w_i\) is strictly positive and each \(y_i\) is an arbitrary real number. It yields the vector which is composed of non-decreasing elements the closest in terms of mean squared error. In practice this list of elements forms a function that is piecewise linear.