03_linear_model_for_regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Methods for Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* A linear regression model assumes that the regression function $E(Y|X)$ is\n",
    "linear in the coeficients $B_1, ..., B_p$.\n",
    "\n",
    "* They are simple and often provide an adequate and interpretable description of how the inputs affect the output.\n",
    "\n",
    "* For prediction purposes they can sometimes outperform fancier nonlinear models, especially in situations with small numbers of training cases, low signal-to-noise ratio or sparse data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Regression Models and Least Squares"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have an input vector $X^T = (X_1, X_2, ..., X_p)$,\n",
    "and want to predict a real-valued output $Y$ . The linear regression model\n",
    "has the form\n",
    "$$f(x)=B_0 + \\sum_{j = 2}^pX_jB_j$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$B_j$'s are unknown parameters or coefficients, and the variables $X_j$ can come\n",
    "from different sources:\n",
    "\n",
    "* quantitative inputs;\n",
    "* transformations of quantitative inputs, such as log, square-root or\n",
    "square;\n",
    "* basis expansions, such as $X_2 = X_{1}^{2}$, $X_3 = X_{1}^{3}$, leading to a polynomial\n",
    "representation\n",
    "* dummy coding of the levels of qualitative inputs.\n",
    "* interactions between variables, for example, $X_3 = X_1 X_2$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given a set of training data $(x_1, y_1) ... (x_N , y_N)$ from which\n",
    "to estimate the parameters $\\beta$. Each $x_i = (x_{i1}, x_{i2}, ... , x_{ip})^T$ is a vector\n",
    "of feature measurements for the ith case. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The most popular estimation method is least squares, in which we pick the coefficients $β = (β_0, β_1, . . . , β_p)T$\n",
    "to minimize the residual sum of squares.\n",
    "\n",
    "$$RSS(\\beta)= \\sum_{i=1}^{N} (y_i - \\beta_0 - \\sum_{j=1}^{p}x_{ij}\\beta_j)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From a statistical point of view, this criterion is reasonable if $X_1, ... , X_n$ are independent r.v.s sample.\n",
    "\n",
    "Even if the $x_i$'s were not drawn randomly, the criterion is still valid if the $y_i’s$ are conditionally independent given the inputs $x_i$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import norm, uniform\n",
    "from matplotlib import cm\n",
    "import os, glob"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We simulate X's features. 2 features\n",
    "# We make a linear transformation.\n",
    "# Recall, Z ~ N(0, 1) -> X ~ N(1.6, 64)\n",
    "\n",
    "sample_size = 500\n",
    "z = np.random.randn(sample_size, 2)\n",
    "sigma = 8\n",
    "mu = 1.6\n",
    "x = sigma*z + mu\n",
    "\n",
    "# Betas: b = [B0, B1]\n",
    "b = np.array([1.6, 0.8])\n",
    "\n",
    "# Error: e ~ N(0, 1) \n",
    "e = np.random.randn(sample_size)\n",
    "\n",
    "# Function: f = B0 + B1.X1 + B2.X2 \n",
    "f = 1.5 + np.sum(b*x, axis=1)\n",
    "\n",
    "# Output: y = B0 + B1.X1 + B2.X2 + e\n",
    "y = f + e"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The quantity of betas have effects on $y$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Grid \n",
    "x1_range = np.linspace(x[:,0].min(), x[:,0].max(), sample_size)\n",
    "x2_range = np.linspace(x[:,1].min(), x[:,1].max(), sample_size)\n",
    "x1, x2 = np.meshgrid(x1_range, x2_range)\n",
    "\n",
    "# f in 2d\n",
    "f_sorted,_ = np.meshgrid(np.sort(f), np.sort(f))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12, 6))\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "ax.scatter(x[:,0], x[:,1], y, alpha = 0.5, color = 'k')\n",
    "ax.plot_surface(x1, x2, f_sorted, alpha = 0.5, cmap = cm.cividis)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Denote by $X$ the $N × (p + 1)$ matrix with each row an input vector (with a 1 in the first position), and similarly let\n",
    "y be the $N$-vector of outputs in the training set. Then we can write the\n",
    "residual sum-of-squares as"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$RSS(β) = (y − Xβ)^T (y − Xβ)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a quadratic function in the $p + 1$ parameters. Differentiating with\n",
    "respect to $β$ we obtain:\n",
    "\n",
    "$$\\frac{∂RSS}{∂β} = −2X^T (y − Xβ)$$\n",
    "\n",
    "$$\\frac{∂^2RSS}{∂∂β^T} = 2X^T X$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We suppose that $X$ has full column rank, and hence $X^TX$\n",
    "is positive definite. The derivative is equal to 0. This result in \n",
    "$$\\hat{β} = (X^TX)^{−1}X^T y$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The predicted values are:\n",
    "$$\\hat{y} = X\\hat{β} = X(X^TX)^{−1}X^Ty$$\n",
    "\n",
    "where the matrix $H = X(X^T X)^{−1}X^T$ is called hat\n",
    "\n",
    "When minimize $RSS(β) = ||y − Xβ||^2$ by choosing $\\hat{β}$ so that the residual vector $y − \\hat{y}$ is orthogonal to this subspace"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It might happen that the columns of $X$ are not linearly independent, so that $X$\n",
    " is not of full rank However, the fitted values $\\hat{y} = X\\hat{β}$ are still the projection of $y$ onto the column space of $X$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Property of $\\hat{β}$\n",
    "\n",
    "* $Var(\\hat{β}) = (X^TX)^{−1}σ^2$\n",
    "\n",
    "Estimates of the variance $\\sigma^2$ by\n",
    "\n",
    "* $\\sigma^2 = \\frac{1}{N − p − 1} \\sum_{i =1}^{N}(y_i − \\hat{y}_i)^2.$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To draw inferences about the parameters and the model, additional assumptions are needed \n",
    "\n",
    "$$Y = B_0 + \\sum_{j = 2}^pX_jB_j + \\epsilon$$\n",
    "\n",
    "where $\\epsilon$ ~ $N(0, \\sigma^2)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can show\n",
    "$$\\hat{β} ∼ N(β, (X^TX)^{−1}σ^2)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a multivariate normal distribution with mean vector and variance–\n",
    "covariance matrix as shown. \n",
    "\n",
    "Also $(N − p − 1)σ^2$ ~ $σ^2χ^2_{N−p−1}$ a chi-squared distribution with $N − p − 1$ degrees of freedom. \n",
    "\n",
    "We use these distributional properties to form tests of hypothesis and confidence intervals for the parameters $β_j$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To test the hypothesis that a particular coefficient $β_j = 0$, we form the standardized coefficient or $Z-score$\n",
    "\n",
    "$$z_i = \\frac{β_j}{\\hat{σ}\\sqrt{v_j}}$$\n",
    "\n",
    "Where $v_j$ is the $jth$ diagonal element of $(X^T X)^{−1}$. Under the null hypothesis that $β_j = 0$, $z_j$ is distributed as $t_{N−p−1}$ (a t distribution with $N − p − 1$ degrees of freedom), and hence a large (absolute) value of $z_j$ will lead to rejection of this null hypothesis. \n",
    "\n",
    "The difference between the tail quantiles of a t-distribution and a standard normal become negligible\n",
    "as the sample size increases"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Often we need to test for the significance of groups of coefficients simultaneously.\n",
    "\n",
    "Here we use the $F$ statistic\n",
    "\n",
    "$$F = \\frac{(RSS_0 − RSS_1)/(p_1 − p_0)}{RSS_1/(N − p_1 − 1)}$$\n",
    "\n",
    "the $F$ statistic will have a $F_{p_1−p_0, N − p_1−1}$ distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similarly, we can isolate $β_j$ in (3.10) to obtain a $1−2α$ confidence interval for $β_j$. \n",
    "$$(\\hat{β_j} − z^{(1−α)}v_j^{1/2}\\hat{σ}, \\hat{β_j} + z^{(1−α)}v_j^{1/2}\\hat{σ})$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here $z^{(1−α)}$ is the $1 − α$ percentile of the normal distribution:\n",
    "* $z^{(1−0.025)} = 1.96$,\n",
    "* $z^{(1−.05)} = 1.645$, etc."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hence the standard practice of reporting $\\hat{β} ± 2 · se(\\hat{β})$ amounts to an approximate 95% confidence interval. Even if the Gaussian error assumption does not hold, this interval will be approximately correct, with its coverage approaching $1 − 2α$ as the sample size $N → ∞.$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.read_stata('MLB1.dta')\n",
    "\n",
    "features = ['years', 'gamesyr', 'bavg', 'hrunsyr', 'rbisyr']\n",
    "target = 'salary'\n",
    "\n",
    "X = data.get(features)\n",
    "y = np.log(data.get(target))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Model:\n",
    "\n",
    "$$log(salary)  = B_0 + B_1years + B_2gamesyr + B_3bavg + B_4hrunsyr + B_5rbisyr + u$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                 salary   R-squared:                       0.628\n",
      "Model:                            OLS   Adj. R-squared:                  0.622\n",
      "Method:                 Least Squares   F-statistic:                     117.1\n",
      "Date:                Sat, 02 Apr 2022   Prob (F-statistic):           2.94e-72\n",
      "Time:                        15:00:21   Log-Likelihood:                -385.11\n",
      "No. Observations:                 353   AIC:                             782.2\n",
      "Df Residuals:                     347   BIC:                             805.4\n",
      "Df Model:                           5                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "years          0.0689      0.012      5.684      0.000       0.045       0.093\n",
      "gamesyr        0.0126      0.003      4.742      0.000       0.007       0.018\n",
      "bavg           0.0010      0.001      0.887      0.376      -0.001       0.003\n",
      "hrunsyr        0.0144      0.016      0.899      0.369      -0.017       0.046\n",
      "rbisyr         0.0108      0.007      1.500      0.134      -0.003       0.025\n",
      "const         11.1924      0.289     38.752      0.000      10.624      11.760\n",
      "==============================================================================\n",
      "Omnibus:                        6.816   Durbin-Watson:                   1.265\n",
      "Prob(Omnibus):                  0.033   Jarque-Bera (JB):               10.197\n",
      "Skew:                          -0.068   Prob(JB):                      0.00610\n",
      "Kurtosis:                       3.821   Cond. No.                     2.09e+03\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 2.09e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "# using Statsmodels\n",
    "\n",
    "import statsmodels.api as sm\n",
    "\n",
    "# we need to add a constant\n",
    "X = sm.add_constant(X, prepend=False)\n",
    "mod = sm.OLS(y, X)\n",
    "res = mod.fit()\n",
    "\n",
    "print(res.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we can compute the *test hypothesis* individual and join. \n",
    "\n",
    "*Subset Selection*. This can be achieved searching the subset of features in which the model maximize some criterior of information, like Akaike. That is, it is the best combination of features that maximize some criterium of information.\n",
    "\n",
    "This can decrease the error, that is loss function reducing the biased."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import cross_val_score\n",
    "from sklearn import metrics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "log(salary) = 11.1924 + 0.0689 years + 0.0126 gamesyr + 0.001 bavg + 0.0144 hrunsyr + 0.0108 rbisyr\n"
     ]
    }
   ],
   "source": [
    "# Using Sklearn\n",
    "\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "\n",
    "X = data.get(features)\n",
    "y = np.log(data.get(target))\n",
    "\n",
    "lin_reg = LinearRegression()\n",
    "# don't need add constant\n",
    "lin_reg.fit(X, y)\n",
    "\n",
    "def model_print(model, target_print:str):\n",
    "    print(f'{target_print} = ' + str(round(model.intercept_, 4)) + ' + '+\\\n",
    "          ('{} '+' + {} '.join(list(model.feature_names_in_))).format(*model.coef_.round(4)))\n",
    "\n",
    "model_print(lin_reg, 'log(salary)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [],
   "source": [
    "def metrics_model(y_true, model, X):\n",
    "    mape = metrics.mean_absolute_percentage_error(y_true, model.predict(X))\n",
    "    print(f'The Mean Absolute Error is {mape:.2}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Mean Absolute Error is 0.041\n"
     ]
    }
   ],
   "source": [
    "metrics_model(y, lin_reg, X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Shrinkage Methods"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ridge Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\hat{\\beta}^{ridge} = argmin\\{\\sum_{1}^{N} (y_i - B_0 - \\sum_{j = 1}^{p}x_{ij}\\beta_j)^2 + (\\lambda \\sum_{j = 1}^{p}\\beta_j^2))\\}$$\n",
    "\n",
    "$$Or$$\n",
    "\n",
    "$$\\hat{\\beta}^{ridge} = argmin\\{\\sum_{1}^{N} (y_i - B_0 - \\sum_{j = 1}^{p}x_{ij}\\beta_j)^2\\}$$\n",
    "$$ subject to(\\lambda \\sum_{j = 1}^{p}\\beta_j^2)<t$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here λ ≥ 0 is a complexity parameter that controls the amount of shrinkage: the larger the value of λ, the greater the amount of shrinkage."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* When there are many correlated variables in a linear regression model, their coefficients can become poorly determined and exhibit high variance.\n",
    "* A wildly large positive coefficient on one variable can be canceled by asimilarly large negative coefficient on its correlated cousin.\n",
    "* By imposing a size constraint on the coefficients, as in (3.42), this problem is alleviated"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Whe We include $\\lambda \\sum_{j = 1}^{p}\\beta_j^2$ (regularization term) in Loss function this called **L1 Regularization**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Lasso\n",
    "The lasso is a shrinkage method like ridge, with subtle but important differences. The lasso estimate is defined by"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\hat{\\beta}^{lasso} = argmin \\sum_{i = 1}^{N} (y_i - B_0 - \\sum_{j = 1}^{p} x_{ij}\\beta_{j})^2$$\n",
    "\n",
    "$$subject\\: to$$\n",
    "\n",
    "$$ \\lambda \\sum_{j = 1}^{p}|\\beta_j|<t$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "When we include $ \\lambda \\sum_{j = 1}^{p}|\\beta_j|<t$ (regularization term) in Loss function this called **L2 Regularization**\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import Lasso, LassoCV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "log(salary) = 11.429 + 0.0 years + 0.0161 gamesyr + 0.0005 bavg + 0.0 hrunsyr + 0.0138 rbisyr\n"
     ]
    }
   ],
   "source": [
    "# alpha by default is 1\n",
    "\n",
    "lasso_model = Lasso()\n",
    "lasso_model.fit(X, y)\n",
    "model_print(lasso_model, 'log(salary)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Mean Absolute Error is 0.045\n"
     ]
    }
   ],
   "source": [
    "metrics_model(y, lasso_model, X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Mean Absolute Error is 0.041\n"
     ]
    }
   ],
   "source": [
    "# cross validation for alpha \n",
    "\n",
    "lasso_model_cv = LassoCV(cv=5, alphas= np.linspace(0.000001, 5, 50))\n",
    "lasso_model_cv.fit(X, y)\n",
    "metrics_model(y, lasso_model_cv, X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Alpha chossen 1e-06\n"
     ]
    }
   ],
   "source": [
    "print(f'Alpha chossen {lasso_model_cv.alpha_}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Resources:\n",
    "\n",
    "* The Elements of Statistical Learning Data Mining, Inference, and Prediction - Second Edition - Trevor Hastie - Robert Tibshirani - Jerome Friedman. Springer.\n",
    "\n",
    "* Data Page: https://hastie.su.domains/ElemStatLearn/\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "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": "3.9.7"
  },
  "vscode": {
   "interpreter": {
    "hash": "7679c2132d3f6ce38c9df14d554b39c06862b36a4e6689c81f9ae15bd0911d7d"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}