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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.