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doc/modules/isotonic.rst
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Adrin Jalali
DOC use pydata-sphinx-theme for the website (#29038)
20 май 2024, 20:36
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20 май 2024, 20:36
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.. _isotonic: =================== Isotonic regression =================== .. 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 * :ref:`sphx_glr_auto_examples_miscellaneous_plot_isotonic_regression.py`