1.15. Isotonic regressionΒΆ

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.

../_images/plot_isotonic_regression_001.png