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