NEandBGD-Video/main.ipynb

{
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  {
   "cell_type": "markdown",
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   "source": [
    "# Linear regression\n",
    "\n",
    "The linear regression is a training procedure based on a linear model. The model makes a prediction by simply computing a weighted sum of the input features, plus a constant term called the bias term (also called the intercept term):\n",
    "\n",
    "$$ \\hat{y}=\\theta_0 x_0 + \\theta_1 x_1 + \\theta_2 x_2 + \\cdots + \\theta_n x_n$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This can be writen more easy by using vector notation form for $m$ values. Therefore, the model will become:\n",
    "\n",
    "$$ \n",
    "    \\begin{bmatrix}\n",
    "    \\hat{y}^0 \\\\ \n",
    "    \\hat{y}^1\\\\\n",
    "    \\hat{y}^2\\\\\n",
    "    \\vdots \\\\\n",
    "    \\hat{y}^m\n",
    "    \\end{bmatrix}\n",
    "    =\n",
    "    \\begin{bmatrix}\n",
    "    1 &  x_0^0  & x_1^0 & \\cdots x_n^0\\\\\n",
    "    1 &  x_0^1  & x_1^1 & \\cdots x_n^1\\\\\n",
    "    \\vdots & \\vdots \\\\\n",
    "    1 & x_0^m  & x_1^m & \\cdots x_n^m\n",
    "    \\end{bmatrix}\n",
    "    \\begin{bmatrix}\n",
    "    \\theta_0 \\\\\n",
    "    \\theta_1 \\\\\n",
    "     \\theta_2 \\\\\n",
    "    \\vdots \\\\\n",
    "    \\theta_n\n",
    "    \\end{bmatrix}\n",
    "$$\n",
    "Resulting:\n",
    "\n",
    "$$\\hat{y}= h_\\theta(x) = x \\theta $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Now that we have our mode, how do we train it?**\n",
    "\n",
    "Please, consider that training the model means adjusting the parameters to reduce the error or minimizing the cost function. The most common performance measure of a regression model is the Mean Square Error (MSE). Therefore, to train a Linear Regression model, you need to find the value of θ that minimizes the MSE:\n",
    "\n",
    "$$ MSE(X,h_\\theta) = \\frac{1}{m} \\sum_{i=1}^{m} \\left(\\hat{y}^{(i)}-y^{(i)} \\right)^2$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ MSE(X,h_\\theta) = \\frac{1}{m} \\sum_{i=1}^{m} \\left(  x^{(i)}\\theta-y^{(i)} \\right)^2$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ MSE(X,h_\\theta) = \\frac{1}{m}  \\left(  x\\theta-y \\right)^T \\left(  x\\theta-y \\right)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The normal equation\n",
    "\n",
    "To find the value of $\\theta$ that minimizes the cost function, there is a closed-form solution that gives the result directly. This is called the **Normal Equation**; and can be find it by derivating the *MSE* equation as a function of $\\theta$ and making it equals to zero:\n",
    "\n",
    "\n",
    "$$\\hat{\\theta} = (X^T X)^{-1} X^{T} y $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ Temp = \\theta_0 + \\theta_1 * t $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
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       "\n",
       "[300 rows x 1 columns]"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "df = pd.read_csv('data.csv')\n",
    "df "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "y = df['0']\n",
    "n = 300\n",
    "t = np.linspace(0,n-1,n)\n",
    "X = np.c_[np.ones(len(t)), t]\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([25.70275643,  0.07850281])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(y)\n",
    "theta "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1.        ,   0.        ],\n",
       "       [  1.        ,  15.78947368],\n",
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       "       [  1.        , 284.21052632],\n",
       "       [  1.        , 300.        ]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "Xnew1 = np.linspace(0,300, 20)\n",
    "Xnew = np.c_[np.ones(len(Xnew1)), Xnew1]\n",
    "Xnew"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ypre = Xnew.dot(theta)\n",
    "plt.plot(Xnew1, ypre, '*-r', label='model')\n",
    "plt.plot(t,y, '.k', label='data')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Polynomial model \n",
    "$$ Temp = \\theta_0 + \\theta_1 * t + \\theta_2 * t^2$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.28848082e+01,  1.35240024e-01, -1.89756565e-04])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = np.c_[np.ones(len(t)), t, t*t]\n",
    "theta = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(y)\n",
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Xnew1 = np.linspace(0,300,50)\n",
    "Xnew = np.c_[np.ones(len(Xnew1)), Xnew1, Xnew1*Xnew1]\n",
    "ypred = Xnew.dot(theta)\n",
    "plt.plot(Xnew1, ypred, '*-r', label='model')\n",
    "plt.plot(t,y, '.g', label='data')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Batch Gradient Descent\n",
    "\n",
    "$$\\theta_{new} = \\theta_{old}-\\eta \\nabla_{\\theta} $$\n",
    "\n",
    "$$\\nabla_{\\theta} =  \\frac{2}{m} X^T (X \\theta -y) $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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       "       [43.135],\n",
       "       [43.103],\n",
       "       [43.038],\n",
       "       [43.135],\n",
       "       [43.264],\n",
       "       [43.425],\n",
       "       [43.328],\n",
       "       [43.328],\n",
       "       [43.457],\n",
       "       [43.457],\n",
       "       [43.521],\n",
       "       [43.683],\n",
       "       [43.779],\n",
       "       [43.683],\n",
       "       [43.683],\n",
       "       [43.715],\n",
       "       [43.973],\n",
       "       [43.94 ],\n",
       "       [44.102],\n",
       "       [44.005],\n",
       "       [44.005],\n",
       "       [44.005],\n",
       "       [44.23 ],\n",
       "       [44.359],\n",
       "       [44.424],\n",
       "       [44.392],\n",
       "       [44.327],\n",
       "       [44.327],\n",
       "       [44.424],\n",
       "       [44.521],\n",
       "       [43.779],\n",
       "       [44.682],\n",
       "       [44.714],\n",
       "       [44.649],\n",
       "       [44.649],\n",
       "       [44.746],\n",
       "       [44.778],\n",
       "       [44.907],\n",
       "       [44.972],\n",
       "       [42.2  ],\n",
       "       [44.939],\n",
       "       [45.036],\n",
       "       [44.907],\n",
       "       [44.327],\n",
       "       [43.876],\n",
       "       [45.004],\n",
       "       [45.197],\n",
       "       [45.294],\n",
       "       [45.358],\n",
       "       [45.326],\n",
       "       [45.229],\n",
       "       [45.358],\n",
       "       [45.101],\n",
       "       [45.423],\n",
       "       [45.391],\n",
       "       [45.713],\n",
       "       [45.681],\n",
       "       [45.616],\n",
       "       [45.713],\n",
       "       [45.616],\n",
       "       [45.713],\n",
       "       [45.713],\n",
       "       [45.713],\n",
       "       [45.745],\n",
       "       [45.648],\n",
       "       [45.971],\n",
       "       [45.938],\n",
       "       [45.938],\n",
       "       [45.938],\n",
       "       [46.067],\n",
       "       [45.971],\n",
       "       [46.035],\n",
       "       [46.132],\n",
       "       [46.196],\n",
       "       [45.938],\n",
       "       [46.164],\n",
       "       [46.261],\n",
       "       [46.261],\n",
       "       [46.229],\n",
       "       [46.261],\n",
       "       [46.229],\n",
       "       [46.229],\n",
       "       [46.357],\n",
       "       [46.551],\n",
       "       [46.519],\n",
       "       [46.551],\n",
       "       [46.583]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = np.array(df['0']).reshape(300,1)\n",
    "n = 300\n",
    "t = np.linspace(0,n-1,n)\n",
    "X = np.c_[np.ones(len(t)), t]\n",
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  8.40650403],\n",
       "       [-13.57147156]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(82)\n",
    "eta = 0.00001 #lerning rate\n",
    "n_iteration = 1000000\n",
    "m = len(y)\n",
    "theta = np.random.randn(2,1)*10\n",
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[25.5895366 ],\n",
       "       [ 0.07906986]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "for iterations in range(n_iteration):\n",
    "    gradient = 2/m * X.T.dot(X.dot(theta)- y)\n",
    "    theta = theta - eta*gradient\n",
    "theta\n",
    "#array([25.70275643,  0.07850281])\n",
    "#array([[25.53711216],[ 0.07933242]]) -> 42\n",
    "#array([[25.53941259],[ 0.0793209 ]]) -> 82"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# BGD Visualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_gradient_descent(eta):\n",
    "    m =len(y)\n",
    "    theta = np.random.randn(2,1)\n",
    "    plt.plot(t,y,'.b')\n",
    "    n_iteration = 1000000\n",
    "    Xnew1 = np.linspace(0,n-1,n)\n",
    "    Xnew = np.c_[np.ones(len(Xnew1)), Xnew1]\n",
    "    for iterations in range(n_iteration):\n",
    "        if iterations % 100000 == 0:\n",
    "            #print(iterations)\n",
    "            ypre = Xnew.dot(theta)\n",
    "            style = '-r' if iterations > 0 else 'g--'\n",
    "            plt.plot(Xnew1, ypre, style)\n",
    "        gradient = 2/m * Xnew.T.dot(Xnew.dot(theta)- y)\n",
    "        theta = theta - eta*gradient\n",
    "    plt.xlabel('$x_1$', fontsize=18)\n",
    "    #plt.axis([0,300, 15,50])\n",
    "    plt.title(r'$\\eta$ = {}'.format(eta), fontsize=16) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[25.5895366 ],\n",
       "       [ 0.07906986]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(112)\n",
    "plot_gradient_descent(eta=0.000001)\n",
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1443cc2f0>]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t,y,'.b')\n",
    "Xnew1 = np.linspace(0,n-1,n)\n",
    "Xnew = np.c_[np.ones(len(Xnew1)), Xnew1]\n",
    "ypre = Xnew.dot(theta)\n",
    "plt.plot(Xnew1, ypre, '-r')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,4))\n",
    "plt.subplot(131)\n",
    "np.random.seed(112)\n",
    "plot_gradient_descent(eta=0.000001)\n",
    "plt.subplot(132)\n",
    "np.random.seed(112)\n",
    "plot_gradient_descent(eta=0.001)\n",
    "plt.subplot(133)\n",
    "np.random.seed(112)\n",
    "plot_gradient_descent(eta=0.00000001)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": ".venv",
   "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": "3.12.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}