# 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.