Isotonic Regression#

An illustration of the isotonic regression on generated data (non-linear monotonic trend with homoscedastic uniform noise).

The isotonic regression algorithm finds a non-decreasing approximation of a function while minimizing the mean squared error on the training data. The benefit of such a non-parametric model is that it does not assume any shape for the target function besides monotonicity. For comparison a linear regression is also presented.

The plot on the right-hand side shows the model prediction function that results from the linear interpolation of thresholds points. The thresholds points are a subset of the training input observations and their matching target values are computed by the isotonic non-parametric fit.

# Authors: The scikit-learn developers
# SPDX-License-Identifier: BSD-3-Clause
importmatplotlib.pyplotasplt
importnumpyasnp
frommatplotlib.collectionsimport LineCollection
fromsklearn.isotonicimport IsotonicRegression
fromsklearn.linear_modelimport LinearRegression
fromsklearn.utilsimport check_random_state
n = 100
x = np.arange (n)
rs = check_random_state (0)
y = rs.randint(-50, 50, size=(n,)) + 50.0 * np.log1p (np.arange (n))

Fit IsotonicRegression and LinearRegression models:

ir = IsotonicRegression (out_of_bounds="clip")
y_ = ir.fit_transform(x, y)
lr = LinearRegression ()
lr.fit(x[:, np.newaxis ], y) # x needs to be 2d for LinearRegression

LinearRegression()