Pushing the docs to dev/ for branch: master, commit acb8ac5145cfd88fdbd2d381b34883b2c212c8c5

Author: sklearn-ci

dev/_downloads/3409d9766d352cc9f9b169d4a799a87a/auto_examples_python.zip

@@ -3,12 +3,19 @@
 Isotonic Regression
 ===================
 
-An illustration of the isotonic regression on generated data. The
-isotonic regression finds a non-decreasing approximation of a function
-while minimizing the mean squared error on the training data. The benefit
-of such a model is that it does not assume any form for the target
-function such as linearity. For comparison a linear regression is also
-presented.
+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.
 
 """
 print(__doc__)
@@ -30,29 +37,41 @@
 rs = check_random_state(0)
 y = rs.randint(-50, 50, size=(n,)) + 50. * np.log1p(np.arange(n))
 
-# #############################################################################
-# Fit IsotonicRegression and LinearRegression models
-
-ir = IsotonicRegression()
+# %%
+# 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
 
-# #############################################################################
-# Plot result
+# %%
+# Plot results:
 
 segments = [[[i, y[i]], [i, y_[i]]] for i in range(n)]
 lc = LineCollection(segments, zorder=0)
 lc.set_array(np.ones(len(y)))
 lc.set_linewidths(np.full(n, 0.5))
 
-fig = plt.figure()
-plt.plot(x, y, 'r.', markersize=12)
-plt.plot(x, y_, 'b.-', markersize=12)
-plt.plot(x, lr.predict(x[:, np.newaxis]), 'b-')
-plt.gca().add_collection(lc)
-plt.legend(('Data', 'Isotonic Fit', 'Linear Fit'), loc='lower right')
-plt.title('Isotonic regression')
+fig, (ax0, ax1) = plt.subplots(ncols=2, figsize=(12, 6))
+
+ax0.plot(x, y, 'C0.', markersize=12)
+ax0.plot(x, y_, 'C1.-', markersize=12)
+ax0.plot(x, lr.predict(x[:, np.newaxis]), 'C2-')
+ax0.add_collection(lc)
+ax0.legend(('Training data', 'Isotonic fit', 'Linear fit'), loc='lower right')
+ax0.set_title('Isotonic regression fit on noisy data (n=%d)' % n)
+
+x_test = np.linspace(-10, 110, 1000)
+ax1.plot(x_test, ir.predict(x_test), 'C1-')
+ax1.plot(ir.X_thresholds_, ir.y_thresholds_, 'C1.', markersize=12)
+ax1.set_title("Prediction function (%d thresholds)" % len(ir.X_thresholds_))
+
 plt.show()
+
+# %%
+# Note that we explicitly passed `out_of_bounds="clip"` to the constructor of
+# `IsotonicRegression` to control the way the model extrapolates outside of the
+# range of data observed in the training set. This "clipping" extrapolation can
+# be seen on the plot of the decision function on the right-hand.

dev/_downloads/8209ef76ac59bf01aad3721a522859ef/plot_isotonic_regression.py

@@ -15,7 +15,7 @@
       "cell_type": "markdown",
       "metadata": {},
       "source": [
-        "\n# Isotonic Regression\n\n\nAn illustration of the isotonic regression on generated data. The\nisotonic regression finds a non-decreasing approximation of a function\nwhile minimizing the mean squared error on the training data. The benefit\nof such a model is that it does not assume any form for the target\nfunction such as linearity. For comparison a linear regression is also\npresented.\n"
+        "\n# Isotonic Regression\n\n\nAn illustration of the isotonic regression on generated data (non-linear\nmonotonic trend with homoscedastic uniform noise).\n\nThe isotonic regression algorithm finds a non-decreasing approximation of a\nfunction while minimizing the mean squared error on the training data. The\nbenefit of such a non-parametric model is that it does not assume any shape for\nthe target function besides monotonicity. For comparison a linear regression is\nalso presented.\n\nThe plot on the right-hand side shows the model prediction function that\nresults from the linear interpolation of thresholds points. The thresholds\npoints are a subset of the training input observations and their matching\ntarget values are computed by the isotonic non-parametric fit.\n"
       ]
     },
     {
@@ -26,7 +26,50 @@
       },
       "outputs": [],
       "source": [
-        "print(__doc__)\n\n# Author: Nelle Varoquaux <[email protected]>\n#         Alexandre Gramfort <[email protected]>\n# License: BSD\n\nimport numpy as np\nimport matplotlib.pyplot as plt\nfrom matplotlib.collections import LineCollection\n\nfrom sklearn.linear_model import LinearRegression\nfrom sklearn.isotonic import IsotonicRegression\nfrom sklearn.utils import check_random_state\n\nn = 100\nx = np.arange(n)\nrs = check_random_state(0)\ny = rs.randint(-50, 50, size=(n,)) + 50. * np.log1p(np.arange(n))\n\n# #############################################################################\n# Fit IsotonicRegression and LinearRegression models\n\nir = IsotonicRegression()\n\ny_ = ir.fit_transform(x, y)\n\nlr = LinearRegression()\nlr.fit(x[:, np.newaxis], y)  # x needs to be 2d for LinearRegression\n\n# #############################################################################\n# Plot result\n\nsegments = [[[i, y[i]], [i, y_[i]]] for i in range(n)]\nlc = LineCollection(segments, zorder=0)\nlc.set_array(np.ones(len(y)))\nlc.set_linewidths(np.full(n, 0.5))\n\nfig = plt.figure()\nplt.plot(x, y, 'r.', markersize=12)\nplt.plot(x, y_, 'b.-', markersize=12)\nplt.plot(x, lr.predict(x[:, np.newaxis]), 'b-')\nplt.gca().add_collection(lc)\nplt.legend(('Data', 'Isotonic Fit', 'Linear Fit'), loc='lower right')\nplt.title('Isotonic regression')\nplt.show()"
+        "print(__doc__)\n\n# Author: Nelle Varoquaux <[email protected]>\n#         Alexandre Gramfort <[email protected]>\n# License: BSD\n\nimport numpy as np\nimport matplotlib.pyplot as plt\nfrom matplotlib.collections import LineCollection\n\nfrom sklearn.linear_model import LinearRegression\nfrom sklearn.isotonic import IsotonicRegression\nfrom sklearn.utils import check_random_state\n\nn = 100\nx = np.arange(n)\nrs = check_random_state(0)\ny = rs.randint(-50, 50, size=(n,)) + 50. * np.log1p(np.arange(n))"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Fit IsotonicRegression and LinearRegression models:\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "ir = IsotonicRegression(out_of_bounds=\"clip\")\ny_ = ir.fit_transform(x, y)\n\nlr = LinearRegression()\nlr.fit(x[:, np.newaxis], y)  # x needs to be 2d for LinearRegression"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Plot results:\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "segments = [[[i, y[i]], [i, y_[i]]] for i in range(n)]\nlc = LineCollection(segments, zorder=0)\nlc.set_array(np.ones(len(y)))\nlc.set_linewidths(np.full(n, 0.5))\n\nfig, (ax0, ax1) = plt.subplots(ncols=2, figsize=(12, 6))\n\nax0.plot(x, y, 'C0.', markersize=12)\nax0.plot(x, y_, 'C1.-', markersize=12)\nax0.plot(x, lr.predict(x[:, np.newaxis]), 'C2-')\nax0.add_collection(lc)\nax0.legend(('Training data', 'Isotonic fit', 'Linear fit'), loc='lower right')\nax0.set_title('Isotonic regression fit on noisy data (n=%d)' % n)\n\nx_test = np.linspace(-10, 110, 1000)\nax1.plot(x_test, ir.predict(x_test), 'C1-')\nax1.plot(ir.X_thresholds_, ir.y_thresholds_, 'C1.', markersize=12)\nax1.set_title(\"Prediction function (%d thresholds)\" % len(ir.X_thresholds_))\n\nplt.show()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Note that we explicitly passed `out_of_bounds=\"clip\"` to the constructor of\n`IsotonicRegression` to control the way the model extrapolates outside of the\nrange of data observed in the training set. This \"clipping\" extrapolation can\nbe seen on the plot of the decision function on the right-hand.\n\n"
       ]
     }
   ],