77 lines
2.6 KiB
Python
77 lines
2.6 KiB
Python
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"""
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===================
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Isotonic Regression
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===================
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An illustration of the isotonic regression on generated data (non-linear
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monotonic trend with homoscedastic uniform noise).
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The isotonic regression algorithm finds a non-decreasing approximation of a
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function while minimizing the mean squared error on the training data. The
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benefit of such a non-parametric model is that it does not assume any shape for
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the target function besides monotonicity. For comparison a linear regression is
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also presented.
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The plot on the right-hand side shows the model prediction function that
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results from the linear interpolation of thresholds points. The thresholds
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points are a subset of the training input observations and their matching
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target values are computed by the isotonic non-parametric fit.
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"""
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# Author: Nelle Varoquaux <nelle.varoquaux@gmail.com>
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# Alexandre Gramfort <alexandre.gramfort@inria.fr>
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# License: BSD
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import matplotlib.pyplot as plt
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import numpy as np
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from matplotlib.collections import LineCollection
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from sklearn.isotonic import IsotonicRegression
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from sklearn.linear_model import LinearRegression
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from sklearn.utils import check_random_state
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n = 100
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x = np.arange(n)
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rs = check_random_state(0)
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y = rs.randint(-50, 50, size=(n,)) + 50.0 * np.log1p(np.arange(n))
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# %%
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# Fit IsotonicRegression and LinearRegression models:
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ir = IsotonicRegression(out_of_bounds="clip")
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y_ = ir.fit_transform(x, y)
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lr = LinearRegression()
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lr.fit(x[:, np.newaxis], y) # x needs to be 2d for LinearRegression
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# %%
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# Plot results:
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segments = [[[i, y[i]], [i, y_[i]]] for i in range(n)]
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lc = LineCollection(segments, zorder=0)
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lc.set_array(np.ones(len(y)))
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lc.set_linewidths(np.full(n, 0.5))
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fig, (ax0, ax1) = plt.subplots(ncols=2, figsize=(12, 6))
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ax0.plot(x, y, "C0.", markersize=12)
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ax0.plot(x, y_, "C1.-", markersize=12)
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ax0.plot(x, lr.predict(x[:, np.newaxis]), "C2-")
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ax0.add_collection(lc)
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ax0.legend(("Training data", "Isotonic fit", "Linear fit"), loc="lower right")
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ax0.set_title("Isotonic regression fit on noisy data (n=%d)" % n)
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x_test = np.linspace(-10, 110, 1000)
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ax1.plot(x_test, ir.predict(x_test), "C1-")
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ax1.plot(ir.X_thresholds_, ir.y_thresholds_, "C1.", markersize=12)
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ax1.set_title("Prediction function (%d thresholds)" % len(ir.X_thresholds_))
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plt.show()
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# %%
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# Note that we explicitly passed `out_of_bounds="clip"` to the constructor of
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# `IsotonicRegression` to control the way the model extrapolates outside of the
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# range of data observed in the training set. This "clipping" extrapolation can
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# be seen on the plot of the decision function on the right-hand.
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