1.15. Isotonic regression

The class IsotonicRegression fits a non-decreasing real function to 1-dimensional data. It solves the following problem:

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

subject to \hat{y}_i \le \hat{y}_j whenever X_i \le X_j,

where the weights w_i are strictly positive, and both X and y are arbitrary real quantities.

The increasing parameter changes the constraint to \hat{y}_i \ge \hat{y}_j whenever X_i \le X_j. Setting it to ‘auto’ will automatically choose the constraint based on Spearman’s rank correlation coefficient.

IsotonicRegression produces a series of predictions \hat{y}_i for the training data which are the closest to the targets y in terms of mean squared error. These predictions are interpolated for predicting to unseen data. The predictions of IsotonicRegression thus form a function that is piecewise linear:

../_images/sphx_glr_plot_isotonic_regression_0011.png