Pushing the docs to dev/ for branch: master, commit 57c04f4e8d488352f020f9a89e516eda9fb88190

Author: sklearn-ci

dev/_downloads/auto_examples_jupyter.zip

@@ -0,0 +1,54 @@
+{
+  "cells": [
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "%matplotlib inline"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "\n# Curve Fitting with Bayesian Ridge Regression\n\n\nComputes a Bayesian Ridge Regression of Sinusoids.\n\nSee `bayesian_ridge_regression` for more information on the regressor.\n\nIn general, when fitting a curve with a polynomial by Bayesian ridge\nregression, the selection of initial values of\nthe regularization parameters (alpha, lambda) may be important.\nThis is because the regularization parameters are determined by an iterative\nprocedure that depends on initial values.\n\nIn this example, the sinusoid is approximated by a polynomial using different\npairs of initial values.\n\nWhen starting from the default values (alpha_init = 1.90, lambda_init = 1.),\nthe bias of the resulting curve is large, and the variance is small.\nSo, lambda_init should be relatively small (1.e-3) so as to reduce the bias.\n\nAlso, by evaluating log marginal likelihood (L) of\nthese models, we can determine which one is better.\nIt can be concluded that the model with larger L is more likely.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "print(__doc__)\n\n# Author: Yoshihiro Uchida <[email protected]>\n\nimport numpy as np\nimport matplotlib.pyplot as plt\n\nfrom sklearn.linear_model import BayesianRidge\n\n\ndef func(x): return np.sin(2*np.pi*x)\n\n\n# #############################################################################\n# Generate sinusoidal data with noise\nsize = 25\nrng = np.random.RandomState(1234)\nx_train = rng.uniform(0., 1., size)\ny_train = func(x_train) + rng.normal(scale=0.1, size=size)\nx_test = np.linspace(0., 1., 100)\n\n\n# #############################################################################\n# Fit by cubic polynomial\nn_order = 3\nX_train = np.vander(x_train, n_order + 1, increasing=True)\nX_test = np.vander(x_test, n_order + 1, increasing=True)\n\n# #############################################################################\n# Plot the true and predicted curves with log marginal likelihood (L)\nreg = BayesianRidge(tol=1e-6, fit_intercept=False, compute_score=True)\nfig, axes = plt.subplots(1, 2, figsize=(8, 4))\nfor i, ax in enumerate(axes):\n    # Bayesian ridge regression with different initial value pairs\n    if i == 0:\n        init = [1 / np.var(y_train), 1.]  # Default values\n    elif i == 1:\n        init = [1., 1e-3]\n        reg.set_params(alpha_init=init[0], lambda_init=init[1])\n    reg.fit(X_train, y_train)\n    ymean, ystd = reg.predict(X_test, return_std=True)\n\n    ax.plot(x_test, func(x_test), color=\"blue\", label=\"sin($2\\\\pi x$)\")\n    ax.scatter(x_train, y_train, s=50, alpha=0.5, label=\"observation\")\n    ax.plot(x_test, ymean, color=\"red\", label=\"predict mean\")\n    ax.fill_between(x_test, ymean-ystd, ymean+ystd,\n                    color=\"pink\", alpha=0.5, label=\"predict std\")\n    ax.set_ylim(-1.3, 1.3)\n    ax.legend()\n    title = \"$\\\\alpha$_init$={:.2f},\\\\ \\\\lambda$_init$={}$\".format(\n            init[0], init[1])\n    if i == 0:\n        title += \" (Default)\"\n    ax.set_title(title, fontsize=12)\n    text = \"$\\\\alpha={:.1f}$\\n$\\\\lambda={:.3f}$\\n$L={:.1f}$\".format(\n           reg.alpha_, reg.lambda_, reg.scores_[-1])\n    ax.text(0.05, -1.0, text, fontsize=12)\n\nplt.tight_layout()\nplt.show()"
+      ]
+    }
+  ],
+  "metadata": {
+    "kernelspec": {
+      "display_name": "Python 3",
+      "language": "python",
+      "name": "python3"
+    },
+    "language_info": {
+      "codemirror_mode": {
+        "name": "ipython",
+        "version": 3
+      },
+      "file_extension": ".py",
+      "mimetype": "text/x-python",
+      "name": "python",
+      "nbconvert_exporter": "python",
+      "pygments_lexer": "ipython3",
+      "version": "3.6.8"
+    }
+  },
+  "nbformat": 4,
+  "nbformat_minor": 0
+}

dev/_downloads/auto_examples_python.zip

@@ -0,0 +1,86 @@
+"""
+============================================
+Curve Fitting with Bayesian Ridge Regression
+============================================
+
+Computes a Bayesian Ridge Regression of Sinusoids.
+
+See :ref:`bayesian_ridge_regression` for more information on the regressor.
+
+In general, when fitting a curve with a polynomial by Bayesian ridge
+regression, the selection of initial values of
+the regularization parameters (alpha, lambda) may be important.
+This is because the regularization parameters are determined by an iterative
+procedure that depends on initial values.
+
+In this example, the sinusoid is approximated by a polynomial using different
+pairs of initial values.
+
+When starting from the default values (alpha_init = 1.90, lambda_init = 1.),
+the bias of the resulting curve is large, and the variance is small.
+So, lambda_init should be relatively small (1.e-3) so as to reduce the bias.
+
+Also, by evaluating log marginal likelihood (L) of
+these models, we can determine which one is better.
+It can be concluded that the model with larger L is more likely.
+"""
+print(__doc__)
+
+# Author: Yoshihiro Uchida <[email protected]>
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+from sklearn.linear_model import BayesianRidge
+
+
+def func(x): return np.sin(2*np.pi*x)
+
+
+# #############################################################################
+# Generate sinusoidal data with noise
+size = 25
+rng = np.random.RandomState(1234)
+x_train = rng.uniform(0., 1., size)
+y_train = func(x_train) + rng.normal(scale=0.1, size=size)
+x_test = np.linspace(0., 1., 100)
+
+
+# #############################################################################
+# Fit by cubic polynomial
+n_order = 3
+X_train = np.vander(x_train, n_order + 1, increasing=True)
+X_test = np.vander(x_test, n_order + 1, increasing=True)
+
+# #############################################################################
+# Plot the true and predicted curves with log marginal likelihood (L)
+reg = BayesianRidge(tol=1e-6, fit_intercept=False, compute_score=True)
+fig, axes = plt.subplots(1, 2, figsize=(8, 4))
+for i, ax in enumerate(axes):
+    # Bayesian ridge regression with different initial value pairs
+    if i == 0:
+        init = [1 / np.var(y_train), 1.]  # Default values
+    elif i == 1:
+        init = [1., 1e-3]
+        reg.set_params(alpha_init=init[0], lambda_init=init[1])
+    reg.fit(X_train, y_train)
+    ymean, ystd = reg.predict(X_test, return_std=True)
+
+    ax.plot(x_test, func(x_test), color="blue", label="sin($2\\pi x$)")
+    ax.scatter(x_train, y_train, s=50, alpha=0.5, label="observation")
+    ax.plot(x_test, ymean, color="red", label="predict mean")
+    ax.fill_between(x_test, ymean-ystd, ymean+ystd,
+                    color="pink", alpha=0.5, label="predict std")
+    ax.set_ylim(-1.3, 1.3)
+    ax.legend()
+    title = "$\\alpha$_init$={:.2f},\\ \\lambda$_init$={}$".format(
+            init[0], init[1])
+    if i == 0:
+        title += " (Default)"
+    ax.set_title(title, fontsize=12)
+    text = "$\\alpha={:.1f}$\n$\\lambda={:.3f}$\n$L={:.1f}$".format(
+           reg.alpha_, reg.lambda_, reg.scores_[-1])
+    ax.text(0.05, -1.0, text, fontsize=12)
+
+plt.tight_layout()
+plt.show()