{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ridge-Lasso Regression\n",
    "\n",
    "> In this post, We will review the way of generalization, especially on Ridge and Lasso.\n",
    "\n",
    "- toc: true \n",
    "- badges: true\n",
    "- comments: true\n",
    "- author: Chanseok Kang\n",
    "- categories: [Python, Machine_Learning]\n",
    "- image: images/ridge_reg.png"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.linear_model import lasso_path, Lasso, Ridge\n",
    "np.random.seed(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ridge Penalty"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In logistic Regression, we can define the loss function like this,\n",
    "\n",
    "$$ L(\\beta; \\lambda) = -\\frac{1}{n} \\sum_{i=1}^n (y_i x_i^T \\beta - \\log(1+ \\exp(x_i^T \\beta))) $$\n",
    "\n",
    "For the Regularization, we can add the penalty term. In this case, we added Ridge penalty (also known as L2 error). That is, we measure the squared beta for the penalty.\n",
    "\n",
    "$$ L(\\beta; \\lambda) = -\\frac{1}{n} \\sum_{i=1}^n (y_i x_i^T \\beta - \\log(1+ \\exp(x_i^T \\beta))) + \\lambda \\Vert \\beta \\Vert_2^2 $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = 2\n",
    "lambda_v = 1.5\n",
    "n = 10\n",
    "true_beta = np.array([[1], [-0.5]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So we need to make predictor. In this example, we assume that the sample data is from binomial distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.87327416, 0.50207813, 0.88248512, 0.89334897, 0.60914609,\n",
       "       0.92359167, 0.4674486 , 0.84339584, 0.56623371, 0.43802193])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.random.normal(0, 1, (n, p))\n",
    "prob = 1 / (1 + np.exp(-x @ true_beta))\n",
    "prob = prob.reshape((n,))\n",
    "prob"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1],\n",
       "       [1],\n",
       "       [0],\n",
       "       [1],\n",
       "       [1],\n",
       "       [1],\n",
       "       [0],\n",
       "       [1],\n",
       "       [1],\n",
       "       [0]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = np.random.binomial(np.ones(n, dtype='int32'), prob, n)\n",
    "y = y.reshape((n, 1))\n",
    "y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Currently, we generate the ture data from true beta. So how can we get true beta from initial beta?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.62393741],\n",
       "       [0.30990356],\n",
       "       [0.32781911],\n",
       "       [0.62053095],\n",
       "       [0.50870771],\n",
       "       [0.42579795],\n",
       "       [0.41259797],\n",
       "       [0.50423467],\n",
       "       [0.37165034],\n",
       "       [0.5774989 ]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "beta = np.array([.5, .5]).reshape((p, 1))\n",
    "prob = 1 / (1 + np.exp(-x @ beta))\n",
    "prob"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With Newton raphson method, we differentiate it two times.\n",
    "\n",
    "$$ g = \\frac{\\partial}{\\partial\\beta} L(\\beta; \\lambda) = -\\frac{1}{n} \\sum_{i=1}^n \\big( y_i x_i - \\frac{\\exp(x_i^T \\beta)}{1 + \\exp(x_i^T \\beta)} x_i \\big) + 2 \\lambda \\beta \\\\\n",
    " H = \\frac{\\partial^2}{\\partial \\beta^2} L(\\beta ; \\lambda) = \\frac{1}{n} \\sum_{i=1}^n \\big( \\frac{\\exp(x_i^T \\beta)}{1 + \\exp(x_i^T \\beta)} \\cdot \\frac{1}{1 + \\exp(x_i^T \\beta)} \\big) x_i x_i^T + 2 \\lambda I$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.28165535],\n",
       "       [1.80853325]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grad = np.mean((prob - y) * x, axis=0, keepdims=True).T + 2 * lambda_v * beta\n",
    "grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.23463952, 0.        , 0.        , 0.        , 0.        ],\n",
       "       [0.        , 0.21386334, 0.        , 0.        , 0.        ],\n",
       "       [0.        , 0.        , 0.22035374, 0.        , 0.        ],\n",
       "       [0.        , 0.        , 0.        , 0.23547229, 0.        ],\n",
       "       [0.        , 0.        , 0.        , 0.        , 0.24992418]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D = np.diag((prob * (1 - prob)).reshape(n))\n",
    "D[:5, :5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3.24626658, -0.18603102],\n",
       "       [-0.18603102,  3.32919247]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H = x.T @ D @ x / n + np.diag(np.repeat(2 * lambda_v, p))\n",
    "H"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After we calculate the gradient and hessian matrix of one optimization, we do the one step for the beta update. All we need to do is to repeat these steps until the threshold is reached."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 0 beta:\n",
      "[[ 0.07280789]\n",
      " [-0.0647952 ]] \n",
      "\n",
      "Iteration 1 beta:\n",
      "[[ 0.07283667]\n",
      " [-0.06483139]] \n",
      "\n",
      "Iteration 2 beta:\n",
      "[[ 0.07283667]\n",
      " [-0.06483139]] \n",
      "\n"
     ]
    }
   ],
   "source": [
    "beta = np.zeros((p, 1))\n",
    "beta_0 = []\n",
    "beta_1 = []\n",
    "\n",
    "for i in range(10):\n",
    "    prob = 1 / (1 + np.exp(-x @ beta))\n",
    "    grad = np.mean((prob - y) * x, axis=0, keepdims=True).T + 2 * lambda_v * beta\n",
    "    D = np.diag((prob * (1 - prob)).reshape(n))\n",
    "    H = x.T @ D @ x / n + np.diag(np.repeat(2 * lambda_v, p))\n",
    "    \n",
    "    beta_new = beta - np.linalg.inv(H) @ grad\n",
    "    beta_0.append(beta_new[0])\n",
    "    beta_1.append(beta_new[1])\n",
    "    \n",
    "    if np.sum(np.abs(beta_new - beta)) < 1e-8:\n",
    "        beta = beta_new\n",
    "        print('Iteration {} beta:'.format(i))\n",
    "        print(beta, '\\n')\n",
    "        break\n",
    "    else:\n",
    "        beta = beta_new\n",
    "        print('Iteration {} beta:'.format(i))\n",
    "        print(beta, '\\n')    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We almost found the solution for beta. So does this solution satisfy the optimality? Or Is the gradient of 0 at this beta? One way to check this is to apply [Karush-Kuhn-Tucker (KKT) condition](https://en.wikipedia.org/wiki/Karush%E2%80%93Kuhn%E2%80%93Tucker_conditions)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2.77555756e-17],\n",
       "       [0.00000000e+00]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob = 1 / (1 + np.exp(-x @ beta))\n",
    "grad = np.mean((prob - y) * x, axis=0, keepdims=True).T + 2 * lambda_v * beta\n",
    "grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.all(np.abs(grad) < 1e-8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this time, we will use Lasso and Ridge Regression implemented in scikit-learn. \n",
    "\n",
    "At first, we need to find solution path for each lambda.\n",
    "\n",
    "Note that, Ridge penalty can be expressed like this,\n",
    "\n",
    "$$ \\beta(\\lambda) = \\arg\\min_{\\beta} \\frac{1}{2} \\Vert Y - X \\beta \\Vert^2 + \\lambda \\Vert \\beta \\Vert^2 $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_lambdas = 50\n",
    "lambda_vec = np.linspace(0, 100, n_lambdas)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.30933704, -0.3050756 ],\n",
       "       [ 0.27101754, -0.28508068],\n",
       "       [ 0.2436212 , -0.26489766],\n",
       "       [ 0.22216416, -0.24649493],\n",
       "       [ 0.2045881 , -0.23010196],\n",
       "       [ 0.18979669, -0.21556417]])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coefs = []\n",
    "for lambda_v in lambda_vec:\n",
    "    ridge = Ridge(alpha=lambda_v, fit_intercept=False)\n",
    "    ridge.fit(x, y)\n",
    "    coefs.append(ridge.coef_)\n",
    "coefs = np.squeeze(np.array(coefs))\n",
    "coefs[:6, :]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(16, 10))\n",
    "colors = ['b', 'r', 'g']\n",
    "lstyles = ['-', '--', '-.', ':']\n",
    "\n",
    "for i in range(p):\n",
    "    l = plt.plot(lambda_vec, coefs[:, i], linestyle=lstyles[i], c=colors[i])\n",
    "plt.xscale('log')\n",
    "plt.axis('tight')\n",
    "plt.xlabel('lambda')\n",
    "plt.ylabel('beta')\n",
    "plt.title('Ridge Regression Solution Path')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, when the $\\lambda$ is increased, $\\beta$ is closed to 0, which means the **'shrinkage'** of the beta.\n",
    "\n",
    "Unlike Ridge, Lasso uses absolute beta for the penalty.\n",
    "\n",
    "$$ \\beta(\\lambda) = \\arg\\min_{\\beta} \\frac{1}{2} \\Vert Y - X \\beta \\Vert^2 + \\lambda \\vert \\beta \\vert $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,\n",
       "         0.00000000e+00,  0.00000000e+00],\n",
       "       [-5.27325648e-17, -2.47515217e-02, -4.82132055e-02,\n",
       "        -7.04522666e-02, -9.15324179e-02]])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eps = 5e-3\n",
    "\n",
    "lambdas_lasso, coefs_lasso, _ = lasso_path(x, y, eps=eps, fit_intercept=False)\n",
    "coefs_lasso = np.squeeze(coefs_lasso)\n",
    "coefs_lasso[:, :5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(16, 10))\n",
    "colors = ['b', 'r', 'g']\n",
    "lstyles = ['-', '--', '-.', ':']\n",
    "\n",
    "for coef, c, l in zip(coefs_lasso, colors, lstyles):\n",
    "    l = plt.plot(lambdas_lasso, coef, linestyle=l, c=c)\n",
    "plt.axis('tight')\n",
    "plt.xlabel('lambda')\n",
    "plt.ylabel('beta')\n",
    "plt.title('Lasso Regression Solution Path')\n",
    "plt.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": "3.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}