labs/linear-models/decision-surfaces.ipynb

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   "source": [
    "# Plotting decision surfaces for linear models"
   ]
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   "metadata": {},
   "source": [
    "## Goal\n",
    "\n",
    "Understanding the mathematics of linear models is important, but to lock that in, it's a good idea to draw model decision surfaces for yourself.  In this lab, you will use sklearn to train linear regression and logistic regression models but extract to the model parameters and draw the surfaces and then compare to the `predict()` and `predict_proba()` results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "from sklearn.linear_model import LinearRegression, LogisticRegression\n",
    "from sklearn.datasets import load_wine, load_boston\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "%config InlineBackend.figure_format = 'retina'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Boston data set 1-var regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
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       "      CRIM    ZN  INDUS  CHAS    NOX     RM   AGE     DIS  RAD    TAX  \\\n",
       "0  0.00632  18.0   2.31   0.0  0.538  6.575  65.2  4.0900  1.0  296.0   \n",
       "1  0.02731   0.0   7.07   0.0  0.469  6.421  78.9  4.9671  2.0  242.0   \n",
       "\n",
       "   PTRATIO      B  LSTAT  \n",
       "0     15.3  396.9   4.98  \n",
       "1     17.8  396.9   9.14  "
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   "source": [
    "boston = load_boston()\n",
    "X = pd.DataFrame(boston.data, columns=boston.feature_names)\n",
    "y = boston.target\n",
    "X.head(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Check feature importance**\n",
    "\n",
    "You'll need to do `pip install rfpimp`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
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      "text/plain": [
       "<rfpimp.PimpViz at 0x7faba1141b20>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm = LinearRegression()\n",
    "lm.fit(X, y)\n",
    "\n",
    "from rfpimp import * # See https://explained.ai/rf-importance/index.html\n",
    "I = importances(lm, X, y)\n",
    "plot_importances(I)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**1. Split off validation/test set**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, shuffle=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2. Pick most important single var**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train = X_train[['LSTAT']] # pick single feature for 1-var regression\n",
    "X_test = X_test[['LSTAT']]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**3. Train LinearRegression model on (X_train, y_train); use variable lm**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm = LinearRegression()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details>\n",
    "<summary>Solution</summary>\n",
    "<pre>\n",
    "lm = LinearRegression()\n",
    "lm.fit(X_train, y_train)\n",
    "</pre>\n",
    "</details>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Being able to visualize data sets is important in machine learning. Let's display the training and test sets using a scatterplot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'y')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 216x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 153,
       "width": 215
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(3,2))\n",
    "plt.scatter(X_train, y_train, s=15, alpha=.3)\n",
    "plt.scatter(X_test, y_test, s=15, alpha=.5, c='orange')\n",
    "plt.xlabel('LSTAT')\n",
    "plt.ylabel('y')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**4. Create function plotting line for $(\\beta_0,\\beta_1)$ and extract betas from model**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def line(beta, x):\n",
    "    return ..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details>\n",
    "<summary>Solution</summary>\n",
    "<pre>\n",
    "def line(beta, x):\n",
    "    return beta[0] + beta[1]*x\n",
    "</pre>\n",
    "</details>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "beta = np.array([...])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details>\n",
    "<summary>Solution</summary>\n",
    "<pre>\n",
    "beta = np.array([lm.intercept_, lm.coef_[0]])\n",
    "</pre>\n",
    "</details>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**5. Plot regression line using coefficients in beta**\n",
    "\n",
    "It should look like:\n",
    "\n",
    "<img src=\"boston-linreg.png\" width=\"200\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.figure(figsize=(3,2))\n",
    "plt.scatter(X_train, y_train, s=15, alpha=.3)\n",
    "plt.scatter(X_test, y_test, s=15, alpha=.5, c='orange')\n",
    "plt.xlabel('LSTAT')\n",
    "plt.ylabel('y')\n",
    "\n",
    "lx = np.arange(np.min(X_train['LSTAT']), np.max(X_train['LSTAT'])).reshape(-1,1)\n",
    "y_pred = ...\n",
    "plt.plot(lx, y_pred, '--',color='red', linewidth=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details>\n",
    "<summary>Solution</summary>\n",
    "<pre>\n",
    "y_pred = line(beta,lx)\n",
    "</pre>\n",
    "</details>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**6. Verify that the model predictions give the same line**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.figure(figsize=(3,2))\n",
    "plt.scatter(X_train, y_train, s=15, alpha=.3)\n",
    "plt.scatter(X_test, y_test, s=15, alpha=.5, c='orange')\n",
    "plt.xlabel('LSTAT')\n",
    "plt.ylabel('y')\n",
    "\n",
    "y_pred = ...\n",
    "plt.plot(lx, y_pred, '.', color='red', linewidth=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details>\n",
    "<summary>Solution</summary>\n",
    "<pre>\n",
    "y_pred = lm.predict(lx)\n",
    "</pre>\n",
    "</details>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**7. How good is that fit? Compare your belief with $R^2$ computed on the test set**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "r2 = lm.score(...)\n",
    "print(f\"R^2 = {r2:.3f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details>\n",
    "<summary>Solution</summary>\n",
    "<pre>\n",
    "r2 = lm.score(X_test, y_test)\n",
    "</pre>\n",
    "</details>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**8. Compare the $R^2$ computed on the test set and training set**\n",
    "\n",
    "It should be about the same because there is a clear linear relationship to exploit and the training and test sets look similar."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "r2_train = lm.score(...)\n",
    "print(f\"R^2 = {r2_train:.3f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details>\n",
    "<summary>Solution</summary>\n",
    "<pre>\n",
    "r2_train = lm.score(X_train, y_train)\n",
    "</pre>\n",
    "</details>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Wine data set 2-class logistic regression\n",
    "\n",
    "The wine data set has three categories or classes of wine, but we can strip out one of the categories to get a two class problem for simple logistic regression. (We'll drop class 0, but then rename classes 1,2 as 0,1.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "wine = load_wine()\n",
    "df_wine = pd.DataFrame(data=wine.data, columns=wine.feature_names)\n",
    "df_wine['y'] = wine.target\n",
    "df_wine = df_wine[df_wine['y']>=1] # Only do 2-class problem, classes {1,2}\n",
    "df_wine['y'] -= 1                  # rename classes as {0,1}\n",
    "X = df_wine['color_intensity']\n",
    "y = df_wine['y']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot12(X,y):\n",
    "    X_0 = X[y==0] # separate class 0, 1 to color differently\n",
    "    X_1 = X[y==1]\n",
    "\n",
    "    plt.figure(figsize=(4.8,1.5))\n",
    "    plt.scatter(X_0, [0]*len(X_0), s=20, alpha=.8, label='class1')\n",
    "    plt.scatter(X_1, [1]*len(X_1), s=20, alpha=.8, label='class2')\n",
    "    plt.xlabel('color_intensity')\n",
    "    plt.ylabel('class')\n",
    "    plt.legend(loc='upper left', fontsize=9)\n",
    "    plt.title(\"1D wine data set, classes 1,2\", fontsize=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**1. Split off validation/test set**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, shuffle=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot12(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2. Train and test logistic regression model**\n",
    "\n",
    "Note that `fit()` requires a matrix so you cannot pass in a one-dimensional numpy array. Use `X.values.reshape(-1,1)` to convert a vector `X` into an nx1 matrix. Also, be aware that `LogisticRegression` does regularized logistic regression by default so your model will performing better than vanilla logistic regression would do."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "lg = ...  # (Use arg solver='lbfgs' to get rid of a warning)\n",
    "lg.fit(...)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details>\n",
    "<summary>Solution</summary>\n",
    "<pre>\n",
    "lg = LogisticRegression(solver='lbfgs')\n",
    "lg.fit(X_train.values.reshape(-1,1), y_train)\n",
    "</pre>\n",
    "</details>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check accuracy:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(f\"{100*lg.score(X_train.values.reshape(-1,1), y_train):.2f}% accurate on training set\")\n",
    "print(f\"{100*lg.score(X_test.values.reshape(-1,1), y_test):.2f}% accurate on test set\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**3. Create sigmoid function and extract betas from the model**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(z):\n",
    "    return ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "beta = np.array([...])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details>\n",
    "<summary>Solution</summary>\n",
    "<pre>\n",
    "def sigmoid(z):\n",
    "    return 1 / (1 + np.exp(-z))\n",
    "    \n",
    "beta = np.array([lg.intercept_[0], lg.coef_[0][0]])\n",
    "</pre>\n",
    "</details>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**4. Plot regression line using coefficients from model**\n",
    "\n",
    "You'll have to create the predictions manually. Recall that logistic regression predicts the probability of class 1 given a feature vector. That probability is just the sigmoid of the linear equation.  It should look like:\n",
    "\n",
    "<img src=\"wine-logreg.png\" width=\"400\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot12(X,y)\n",
    "\n",
    "lx = np.arange(np.min(X_train), np.max(X_train), step=.1).reshape(-1,1)\n",
    "y_pred = ...\n",
    "plt.plot(lx, y_pred, '--', c='red', lw=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details>\n",
    "<summary>Solution</summary>\n",
    "<pre>\n",
    "y_pred = sigmoid(line(beta, lx))\n",
    "</pre>\n",
    "</details>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**5. Verify that the model predictions give the same line**\n",
    "\n",
    "Here we don't want classification; we want the probabilities so use function `predict_proba()` not `predict()`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot12(X,y)\n",
    "y_pred = ...\n",
    "plt.plot(lx, y_pred, '--', c='red', lw=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details>\n",
    "<summary>Solution</summary>\n",
    "<pre>\n",
    "y_pred = lg.predict_proba(lx)[:,1]\n",
    "</pre>\n",
    "</details>"
   ]
  }
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