{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "\n# Non-negative least squares\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": [
        "# Authors: The scikit-learn developers\n# SPDX-License-Identifier: BSD-3-Clause\n\nimport matplotlib.pyplot as plt\nimport numpy as np\n\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=0.5)\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",
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      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
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