doc/modules/isotonic.rst
.. _isotonic:
.. currentmodule:: sklearn.isotonic
The class :class:IsotonicRegression fits a non-decreasing real function to
1-dimensional data. It solves the following problem:
.. math:: \min \sum_i w_i (y_i - \hat{y}_i)^2
subject to :math:\hat{y}_i \le \hat{y}_j whenever :math:X_i \le X_j,
where the weights :math:w_i are strictly positive, and both X and y are
arbitrary real quantities.
The increasing parameter changes the constraint to
:math:\hat{y}_i \ge \hat{y}_j whenever :math:X_i \le X_j. Setting it to
'auto' will automatically choose the constraint based on Spearman's rank correlation coefficient <https://en.wikipedia.org/wiki/Spearman%27s_rank_correlation_coefficient>_.
:class:IsotonicRegression produces a series of predictions
:math:\hat{y}_i for the training data which are the closest to the targets
:math:y in terms of mean squared error. These predictions are interpolated
for predicting to unseen data. The predictions of :class:IsotonicRegression
thus form a function that is piecewise linear:
.. figure:: ../auto_examples/miscellaneous/images/sphx_glr_plot_isotonic_regression_001.png :target: ../auto_examples/miscellaneous/plot_isotonic_regression.html :align: center
.. rubric:: Examples
sphx_glr_auto_examples_miscellaneous_plot_isotonic_regression.py