Pushing the docs to dev/ for branch: master, commit 075d4245681110386cb4312cbdbd0c82776290ac

Author: sklearn-ci

dev/_downloads/055e50ba9fa8c7dcf45dc8f1f32a0243/plot_nnls.py

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+"""
+==========================
+Non-negative least squares
+==========================
+
+In this example, we fit a linear model with positive constraints on the
+regression coefficients and compare the estimated coefficients to a classic
+linear regression.
+"""
+print(__doc__)
+import numpy as np
+import matplotlib.pyplot as plt
+from sklearn.metrics import r2_score
+
+# %%
+# Generate some random data
+np.random.seed(42)
+
+n_samples, n_features = 200, 50
+X = np.random.randn(n_samples, n_features)
+true_coef = 3 * np.random.randn(n_features)
+# Threshold coefficients to render them non-negative
+true_coef[true_coef < 0] = 0
+y = np.dot(X, true_coef)
+
+# Add some noise
+y += 5 * np.random.normal(size=(n_samples, ))
+
+# %%
+# Split the data in train set and test set
+from sklearn.model_selection import train_test_split
+
+X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.5)
+
+# %%
+# Fit the Non-Negative least squares.
+from sklearn.linear_model import LinearRegression
+
+reg_nnls = LinearRegression(positive=True)
+y_pred_nnls = reg_nnls.fit(X_train, y_train).predict(X_test)
+r2_score_nnls = r2_score(y_test, y_pred_nnls)
+print("NNLS R2 score", r2_score_nnls)
+
+# %%
+# Fit an OLS.
+reg_ols = LinearRegression()
+y_pred_ols = reg_ols.fit(X_train, y_train).predict(X_test)
+r2_score_ols = r2_score(y_test, y_pred_ols)
+print("OLS R2 score", r2_score_ols)
+
+
+# %%
+# Comparing the regression coefficients between OLS and NNLS, we can observe
+# they are highly correlated (the dashed line is the identity relation),
+# but the non-negative constraint shrinks some to 0.
+# The Non-Negative Least squares inherently yield sparse results.
+
+fig, ax = plt.subplots()
+ax.plot(reg_ols.coef_, reg_nnls.coef_, linewidth=0, marker=".")
+
+low_x, high_x = ax.get_xlim()
+low_y, high_y = ax.get_ylim()
+low = max(low_x, low_y)
+high = min(high_x, high_y)
+ax.plot([low, high], [low, high], ls="--", c=".3", alpha=.5)
+ax.set_xlabel("OLS regression coefficients", fontweight="bold")
+ax.set_ylabel("NNLS regression coefficients", fontweight="bold")

dev/_downloads/3409d9766d352cc9f9b169d4a799a87a/auto_examples_python.zip

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+{
+  "cells": [
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "%matplotlib inline"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "\n# Non-negative least squares\n\n\nIn this example, we fit a linear model with positive constraints on the\nregression coefficients and compare the estimated coefficients to a classic\nlinear regression.\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "print(__doc__)\nimport numpy as np\nimport matplotlib.pyplot as plt\nfrom sklearn.metrics import r2_score"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Generate some random data\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "np.random.seed(42)\n\nn_samples, n_features = 200, 50\nX = np.random.randn(n_samples, n_features)\ntrue_coef = 3 * np.random.randn(n_features)\n# Threshold coefficients to render them non-negative\ntrue_coef[true_coef < 0] = 0\ny = np.dot(X, true_coef)\n\n# Add some noise\ny += 5 * np.random.normal(size=(n_samples, ))"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Split the data in train set and test set\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "from sklearn.model_selection import train_test_split\n\nX_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.5)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Fit the Non-Negative least squares.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "from sklearn.linear_model import LinearRegression\n\nreg_nnls = LinearRegression(positive=True)\ny_pred_nnls = reg_nnls.fit(X_train, y_train).predict(X_test)\nr2_score_nnls = r2_score(y_test, y_pred_nnls)\nprint(\"NNLS R2 score\", r2_score_nnls)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Fit an OLS.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "reg_ols = LinearRegression()\ny_pred_ols = reg_ols.fit(X_train, y_train).predict(X_test)\nr2_score_ols = r2_score(y_test, y_pred_ols)\nprint(\"OLS R2 score\", r2_score_ols)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Comparing the regression coefficients between OLS and NNLS, we can observe\nthey are highly correlated (the dashed line is the identity relation),\nbut the non-negative constraint shrinks some to 0.\nThe Non-Negative Least squares inherently yield sparse results.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "fig, ax = plt.subplots()\nax.plot(reg_ols.coef_, reg_nnls.coef_, linewidth=0, marker=\".\")\n\nlow_x, high_x = ax.get_xlim()\nlow_y, high_y = ax.get_ylim()\nlow = max(low_x, low_y)\nhigh = min(high_x, high_y)\nax.plot([low, high], [low, high], ls=\"--\", c=\".3\", alpha=.5)\nax.set_xlabel(\"OLS regression coefficients\", fontweight=\"bold\")\nax.set_ylabel(\"NNLS regression coefficients\", fontweight=\"bold\")"
+      ]
+    }
+  ],
+  "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": "3.8.5"
+    }
+  },
+  "nbformat": 4,
+  "nbformat_minor": 0
+}