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Diffstat (limited to 'ft_linear_regression_notebook.ipynb')
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diff --git a/ft_linear_regression_notebook.ipynb b/ft_linear_regression_notebook.ipynb new file mode 100644 index 0000000..5f14eea --- /dev/null +++ b/ft_linear_regression_notebook.ipynb @@ -0,0 +1,471 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# ft_linear_regression\n", + "\n", + "Project in which I need to build a linear regression model for a simple dataset." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "\n", + "data = np.genfromtxt('../data.csv', delimiter=',')[1:]\n", + "km = data[:, 0]\n", + "price = data[:, 1]" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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C3FeW9wDXlVFslwAvlm64vcCmiFhVBhBsKmWSpIapsnttDfC5iGh/zh9l5p9FxEPAPRFxA/AE8L6y/ReAK4FJ4AfA9QCZeSQiPgo8VLb7SGYeqbDekqSKRObg/fwxOjqa4+Pjva6GJDVKRBzomN5SCa9IIEmqjaEjSaqNoSNJqo2hI0mqjaEjSaqNoSNJqo2hI0mqjaEjSaqNoSNJqo2hI0mqjaEjSaqNoSNJqo2hI0mqjaEjSaqNoSNJqk2VN3GTpNdt98Epduyd4OmjM5w3PMTWsQ1s3jjS62rpFBk6kvrO7oNTbN91iJmXjwEwdXSG7bsOARg8DWfoSANmEM4QduydOB44bTMvH2PH3onGfRedyNCRBsignCE8fXRmSeVqDgcSSANkoTOEJjlveGhJ5WoOQ0caIINyhrB1bANDp604oWzotBVsHdvQoxqpWwwdaYAMyhnC5o0jfOzqtzEyPEQAI8NDfOzqtzWqi1Bz8zcdaYBsHdtwwm860NwzhM0bRwyZAWToSAOk/Ue66aPXNLgMHWnAeIagfuZvOpKk2hg6kqTaGDqSpNoYOpKk2hg6kqTaGDqSpNoYOpKk2hg6kqTaVB46EbEiIg5GxP8qr9dHxIMRMRkRd0fE6aX8jPJ6sqxf1/Ee20v5RESMVV1nSVI16jjT+RXgax2vPw58IjN/DHgBuKGU3wC8UMo/UbYjIi4ErgXeClwO/I+IOPHys5KkRqg0dCJiLfDPgd8vrwN4D3Bv2eROYHNZvqq8pqy/rGx/FXBXZr6Umd8EJoF3VllvSVI1qj7T+a/ArwOvltdnA0cz85Xy+imgfZGoEeBJgLL+xbL98fI59pEkNUhloRMRPwM8n5kHqvqMWZ93Y0SMR8T49PR0HR8pSVqiKs90LgV+NiK+BdxFq1vtd4DhiGhf3XotMFWWp4DzAcr6NwPf7SyfY5/jMnNnZo5m5ujq1au7/20kSaesstDJzO2ZuTYz19EaCLA/M38eeAC4pmy2BbivLO8prynr92dmlvJry+i29cAFwJerqrckqTq9uJ/Oh4C7IuK3gIPA7aX8duAzETEJHKEVVGTmYxFxD/A48ApwU2Ye+//fVpLU76J1MjFYRkdHc3x8vNfVkKRGiYgDmTla5Wd4RQJJUm28XbXUh3YfnGLH3gmePjrDecNDbB3b4C2oNRAMHanP7D44xfZdh5h5ufXT5dTRGbbvOgRg8Kjx7F6T+syOvRPHA6dt5uVj7Ng70aMaSd1j6Eh95umjM0sql5rE0JH6zHnDQ0sql5rE0JH6zNaxDQydduKF1IdOW8HWsQ09qpHUPQ4kkPpMe7CAo9e0FE0Z8WjoSH1o88aRvvyDof7UpBGPdq9JUsM1acSjoSNJDdekEY+GjiQ1XJNGPBo6ktRwTRrx6EACSWq4Jo14NHQkaQA0ZcSj3WuSpNoYOpKk2hg6kqTaGDqSpNoYOpKk2kRm9roOXRcR08ATva5HBc4BvtPrSvQh22VutsvcbJe5nQOcmZmrq/yQgQydQRUR45k52ut69BvbZW62y9xsl7nV1S52r0mSamPoSJJqY+g0y85eV6BP2S5zs13mZrvMrZZ28TcdSVJtPNORJNXG0OmBiPhWRByKiIcjYryUnRUR+yLicHleVcojIm6NiMmIeCQiLup4ny1l+8MRsaWj/B3l/SfLvlH/tzy5iLgjIp6PiEc7yipvh/k+o1/M0y6/GRFT5Zh5OCKu7Fi3vXzHiYgY6yi/vJRNRsS2jvL1EfFgKb87Ik4v5WeU15Nl/bp6vvHiRMT5EfFARDweEY9FxK+U8mV9zCzQLv15zGSmj5ofwLeAc2aV/SdgW1neBny8LF8J/CkQwCXAg6X8LOBvy/OqsryqrPty2TbKvlf0+jvP0w7vBi4CHq2zHeb7jH55zNMuvwn82hzbXgh8FTgDWA98A1hRHt8A3gKcXra5sOxzD3BtWf4k8Etl+QPAJ8vytcDdvW6LWd/1XOCisvwm4G/K91/Wx8wC7dKXx0zPG2w5Ppg7dCaAczsOoomy/Cng/bO3A94PfKqj/FOl7Fzg6x3lJ2zXbw9gHSf+ca28Heb7jH56zNEu8/0B2Q5s73i9F/ip8tg7e7vyx/Q7wMpSfny79r5leWXZLnrdFgu00X3Aez1m5m2Xvjxm7F7rjQT+PCIORMSNpWxNZj5Tlp8F1pTlEeDJjn2fKmULlT81R3lT1NEO831Gv/vl0k10R0f3zlLb5WzgaGa+Mqv8hPcq618s2/ed0o2zEXgQj5njZrUL9OExY+j0xrsy8yLgCuCmiHh358ps/bNh2Q8rrKMdGtTWtwH/CHg78Azwn3tbnd6JiL8H/E/gg5n5vc51y/mYmaNd+vKYMXR6IDOnyvPzwOeAdwLPRcS5AOX5+bL5FHB+x+5rS9lC5WvnKG+KOtphvs/oW5n5XGYey8xXgd+jdczA0tvlu8BwRKycVX7Ce5X1by7b942IOI3WH9Y/zMxdpXjZHzNztUu/HjOGTs0i4syIeFN7GdgEPArsAdqjaLbQ6pellF9XRuJcArxYTvP3ApsiYlU5bd5Eq5/1GeB7EXFJGXlzXcd7NUEd7TDfZ/St9h+84l/QOmag9V2uLaOI1gMX0Pox/CHggjLq6HRaP/LuKf9KfwC4puw/u43b7XINsL9s3xfKf8fbga9l5n/pWLWsj5n52qVvj5le/+i13B60RoZ8tTweAz5cys8G7gcOA18EzirlAfwurVElh4DRjvf6BWCyPK7vKB8tB9g3gP9On/4YDHyW1mn/y7T6iW+oox3m+4x+eczTLp8p3/uR8j/6uR3bf7h8xwk6RirSGr31N2Xdh2cdg18u7fXHwBml/A3l9WRZ/5Zet8WsdnkXrW6tR4CHy+PK5X7MLNAufXnMeEUCSVJt7F6TJNXG0JEk1cbQkSTVxtCRJNXG0JEk1cbQkSoQEeui4yrRkloMHUlSbVaefBNJpyIi3kLrEiV/BFwKnElrFvhv07qE/L8EXgKuzMwjvaqnVAfPdKQKRcQGWoHzr4Bp4CeBq4F/CvxH4AeZuRH4P7QuuyINNENHqs5qWteo+vnM/GopeyAz/29mTtO6DPyflPJDtO6hIw00Q0eqzovAt2ldG6vtpY7lVztev4rd3VoGPMil6vyQ1tV990bE3/W6MlI/8ExHqlBmfh/4GeBXgb/f4+pIPedVpiVJtfFMR5JUG0NHklQbQ0eSVBtDR5JUG0NHklQbQ0eSVBtDR5JUG0NHklSb/weNO61A3jp7CQAAAABJRU5ErkJggg==\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "def plot_data():\n", + " plt.scatter(km, price)\n", + " plt.xlabel(\"km\")\n", + " plt.ylabel(\"price\")\n", + "plot_data()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This dataset contains information about cars, their cost and the the number of kilometers they've made.\n", + "\n", + "We can see just by looking at the data that their is a **linear relationship**, when the distance made diminish, the price rize.\n", + "\n", + "We can try to trace an approximate line which goes *through* the data." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plot_data()\n", + "plt.plot([200_000, 20_000], [3_500, 8_500], color='r')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can use this hypothetical line to predict new data, for example predict the price of a car knowing only it's distance traveled.\n", + "\n", + "The equation of a line is in the form:\n", + "\n", + "$$\n", + "\\boxed {\n", + " y = \\theta_1 x + \\theta_0\n", + "}\n", + "$$\n", + "\n", + "Where $\\theta_1$ is the slope of the line and $\\theta_0$ the y-intercept. If we managed to tweak those values correctly we can find the best fitting line for our data (or at least very close to it).\n", + "\n", + "If we switch to a function, we get $h(x) = \\theta_1 x + \\theta_0$, $h$ is our **hypothesis function**." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "def h(x, theta1, theta0):\n", + " return x * theta1 + theta0\n", + "\n", + "theta1 = -0.03\n", + "theta0 = 9000\n", + "\n", + "line_xs = [km.min(), km.max()]\n", + "line_ys = [h(x, theta1, theta0) for x in line_xs]\n", + "plt.plot(line_xs, line_ys, color='r')\n", + "\n", + "plot_data()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can adjust our prediction by changing $\\theta_1$ and $\\theta_0$.\n", + "\n", + "Now, we need a way to know if our line correctly predicts the data or not, so that if not, we can slightly change it to better fit the data.\n", + "\n", + "Introducing the **error function** $J$ (also called cost function):\n", + "\n", + "$$\n", + "\\begin{align}\n", + "J(\\theta_1, \\theta_0) &= \\frac{1}{2n} \\sum_{i=1}^{n}(h(x_i) - y_i)^2 \\\\\n", + " &= \\frac{1}{2n} \\sum_{i=1}^{n}((\\theta_1 x_i + \\theta_0) - y_i)^2\n", + "\\end{align}\n", + "$$\n", + "\n", + "It's the sum of the square of the distance between what we predicted and the actual data.\n", + "$n$ is the number of entry we got, we divide by it to normalize the result." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "def error_function(xs, ys, theta1, theta0):\n", + " return (1 / (2 * len(xs))) * sum(\n", + " [(h(x, theta1, theta0) - y) ** 2\n", + " for x, y in zip(xs, ys)])" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "386217.6189791666\n" + ] + } + ], + "source": [ + "xs = km\n", + "ys = price\n", + "\n", + "print(error_function(xs, ys, theta1, theta0))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The error value is pretty high, this means that the approximated line is garbage.\n", + "\n", + "The process of learning will be done by reducing this error function. To make that happen, we need to know *how* we are going to change $\\theta_1$ and $\\theta_0$.\n", + "\n", + "Here comes partial derivatives:\n", + "\n", + "$$\n", + "\\begin{align}\n", + " \\theta_1 &:= \\theta_1 - \\alpha \\frac{\\partial}{\\partial \\theta_1} J(\\theta_1, \\theta_0) \\\\\n", + " \\theta_0 &:= \\theta_0 - \\alpha \\frac{\\partial}{\\partial \\theta_0} J(\\theta_1, \\theta_0)\n", + "\\end{align}\n", + "$$\n", + "\n", + "First of all $\\alpha$ is the **learning rate** we multiply the change we want to make by it, it describes how *fast* we are changing the hypothesis component.\n", + "\n", + "The partial derivative of $J$ by regard to $\\theta_1$ for example is how the error function changes if we consider $\\theta_0$ has a constant.\n", + "\n", + "We compute the *next* $\\theta_0$ by subtracting learning rate * partial derivative from it.\n", + "\n", + "Lets expand theses partial derivatives:\n", + "\n", + "$$\n", + "\\newcommand{\\partialthetazero}{\\frac{\\partial}{\\partial \\theta_0}}\n", + "\\begin{align}\n", + " & \\partialthetazero \\left[ J(\\theta_1, \\theta_0) \\right] \\\\\n", + " =& \\partialthetazero \\left[ \\frac{1}{2n} \\sum_{i=1}^{n}((\\theta_1 x_i + \\theta_0) - y_i)^2 \\right] \\\\\n", + " =& \\frac{1}{2n} \\sum_{i=1}^{n} \\partialthetazero \\left[ ((\\theta_1 x_i + \\theta_0) - y_i)^2 \\right] \\\\\n", + " =& \\frac{1}{2n} \\sum_{i=1}^{n} 2((\\theta_1 x_i + \\theta_0) - y_i) \\partialthetazero \\left[ ((\\theta_1 x_i + \\theta_0) - y_i) \\right] \\\\\n", + " =& \\boxed{ \\frac{1}{n} \\sum_{i=1}^{n} ((\\theta_1 x_i + \\theta_0) - y_i) }\n", + "\\end{align}\n", + "$$\n", + "\n", + "And for $\\theta_1$:\n", + "\n", + "$$\n", + "\\newcommand{\\partialthetaone}{\\frac{\\partial}{\\partial \\theta_1}}\n", + "\\begin{align}\n", + " & \\partialthetaone \\left[ J(\\theta_1, \\theta_0) \\right] \\\\\n", + " =& \\partialthetaone \\left[ \\frac{1}{2n} \\sum_{i=1}^{n}((\\theta_1 x_i + \\theta_0) - y_i)^2 \\right] \\\\\n", + " =& \\frac{1}{2n} \\sum_{i=1}^{n} \\partialthetaone \\left[ ((\\theta_1 x_i + \\theta_0) - y_i)^2 \\right] \\\\\n", + " =& \\frac{1}{2n} \\sum_{i=1}^{n} 2((\\theta_1 x_i + \\theta_0) - y_i) \\partialthetaone \\left[ ((\\theta_1 x_i + \\theta_0) - y_i) \\right] \\\\\n", + " =& \\boxed { \\frac{1}{n} \\sum_{i=1}^{n} ((\\theta_1 x_i + \\theta_0) - y_i) x_i }\n", + "\\end{align}\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "def theta0_partial(xs, ys, theta1, theta0):\n", + " return sum([h(x, theta1, theta0) - y\n", + " for x, y in zip(xs, ys)]) / len(xs)\n", + "\n", + "def theta1_partial(xs, ys, theta1, theta0):\n", + " return sum([(h(x, theta1, theta0) - y) * x\n", + " for x, y in zip(xs, ys)]) / len(xs)\n", + "\n", + "\n", + "def gradient_descent(xs, ys, theta1, theta0, alpha, iterations):\n", + " for _ in range(iterations):\n", + " next_theta1 = theta1 - alpha * theta1_partial(xs, ys, theta1, theta0)\n", + " next_theta0 = theta0 - alpha * theta0_partial(xs, ys, theta1, theta0)\n", + " theta1 = next_theta1\n", + " theta0 = next_theta0\n", + " return theta1, theta0\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The gradient descent work by repeating the formula above a certain amount of times.\n", + "\n", + "But before actually running the algorithm, the data need to be normalized. This means that they will be in a range like 0 < x < 1 but they will keep their relative distance to each other.\n", + "\n", + "If we don't do this, our values will go to infinity or some do some sneaky floating point arithmetic stuff.\n", + "\n", + "Here is how we normalize:\n", + "\n", + "$$\n", + "X_{normalized} = \\frac{X - X_{min}}{X_{max} - X_{min}}\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1. 0.53846366 0.58774948 0.74910295 0.70520633 0.42330989\n", + " 0.66282974 0.30447119 0.56011257 0.28144044 0.27236171 0.18498763\n", + " 0.23537893 0.34362347 0.20313587 0.24470638 0.11670144 0.3228958\n", + " 0.17526405 0.19702811 0.1432559 0.21004509 0. 0.17913321]\n", + "[240000. 139800. 150500. 185530. 176000. 114800. 166800. 89000. 144500.\n", + " 84000. 82029. 63060. 74000. 97500. 67000. 76025. 48235. 93000.\n", + " 60949. 65674. 54000. 68500. 22899. 61789.]\n" + ] + } + ], + "source": [ + "#from sklearn.preprocessing import normalize\n", + "#X, Y = normalize([xs, ys])\n", + "\n", + "def normalize(x):\n", + " return (x - x.min()) / (x.max() - x.min())\n", + "\n", + "def denormalize(x, x_ref):\n", + " return x * (x_ref.max() - x_ref.min()) + x_ref.min()\n", + "\n", + "X = normalize(xs)\n", + "Y = normalize(ys)\n", + "\n", + "print(X)\n", + "print(denormalize(X, xs))" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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tWN05wLuB70fEc8CVwI5mF1Uz84HMHMnMkWXLls29aknStFoJ90eBDRGxLiLOAG4BdtRfzMxXM3NpZq7NzLXALuDGzLSHniT1yIzPlsnMExFxJ7ATGAAezMwnI+IeYDQzd0z/FaT2spWcNLOWHhyWmY8Aj0w69vkpxn5o/mVJzdlKTmqNd6iqVGwlJ7XGcFep2EpOao3hrlKxlZzUGsNdpWIrufbbvnuMq+/9Luvu+jZX3/tdtu8em/l/pL5nJyaViq3k2ssL1NVluKt0bCXXPtNdoPZ7XG4uy0gLmBeoq8twlxYwL1BXl+EuLWBeoK4u19ylBcwL1NVluEsLnBeoq8llGUmqIMNdkirIcJekCjLcJamCDHdJqiDDXZIqyHCXpAoy3CWpggx3Saogw12SKshwl6QKMtwlqYIMd0mqIMNdkirIcJekCjLcJamCDHdJqiDDXZIqyHCXpApqKdwj4rqI2BMReyPiriav/35EPBURP46I70TEmvaXKklq1YzhHhEDwP3A9cClwK0RcemkYbuBkcz8l8DfAP+13YVKklrXypn75cDezNyXmW8CDwFbGgdk5vcy81jt013AyvaWKUmajVbCfQXwQsPnB2rHpnI78HfzKUqSND+L2/nFIuI2YAT44BSv3wHcAbB69ep2vrUkqUErZ+5jwKqGz1fWjk0QEdcAnwNuzMw3mn2hzHwgM0cyc2TZsmVzqVeS1IJWztwfBTZExDqKUL8F+GTjgIjYBPwZcF1mvtT2KiX1le27x9i2cw8Hj46zfGiQrZuHuWnTdKu16rYZwz0zT0TEncBOYAB4MDOfjIh7gNHM3AFsA94O/HVEAOzPzBs7WLekHtm+e4y7H36c8eMnARg7Os7dDz8OYMD3kZbW3DPzEeCRScc+3/DxNW2uS1Kf2rZzzy+CvW78+Em27dxjuPeRtl5QldSaMi9rHDw6Pqvj6g0fPyB1WX1ZY+zoOMmpZY3tu0/bp9CXlg8Nzuq4esNwl7psumWNMti6eZjBJQMTjg0uGWDr5uEeVaRmXJaRuqzsyxr15aOyListFIa71GXLhwYZaxLkZVrWuGnTCsO8z7ksI3WZyxrqBs/cpS5zWUPdYLhLPeCyhjrNZRlJqiDDXZIqyHCXpAoy3CWpggx3Saogw12SKshwl6QKMtwlqYIMd0mqIMNdkirIcJekCjLcJamCDHdJqiDDXZIqyHCXpAoy3CWpggx3SaogOzFJc7R995it8tS3DHdpDrbvHuPuhx9n/PhJAMaOjnP3w48DGPDqCy7LSHOwbeeeXwR73fjxk2zbuadHFUkTGe7SHBw8Oj6r41K3Ge7SHCwfGpzVcanbDHdpDrZuHmZwycCEY4NLBti6ebhHFUkTtXRBNSKuA74EDABfy8x7J71+JvBN4H3AK8AnMvO59pYq9Y/6RVN3y2gmvdpVNWO4R8QAcD9wLXAAeDQidmTmUw3DbgeOZObFEXELcB/wiU4ULPWLmzatMMw1rV7uqmplWeZyYG9m7svMN4GHgC2TxmwBvlH7+G+Aj0ZEtK9MSSqfXu6qaiXcVwAvNHx+oHas6ZjMPAG8Crxj8heKiDsiYjQiRg8dOjS3iiWpJHq5q6qrF1Qz84HMHMnMkWXLlnXzrSWp63q5q6qVcB8DVjV8vrJ2rOmYiFgMnEdxYVWSFqxe7qpqJdwfBTZExLqIOAO4BdgxacwO4N/UPv7XwHczM9tXpiSVz02bVvDFX3sPK4YGCWDF0CBf/LX39Mdumcw8ERF3AjsptkI+mJlPRsQ9wGhm7gD+B/DnEbEXOEzxfwCStOD1aldVS/vcM/MR4JFJxz7f8PHrwM3tLU2SNFfeoSpJFWS4S1IFGe6SVEGGuyRVkOEuSRUUvdqOHhGHgOfb8KWWAi+34euUhfOtroU0V3C+c7UmM2e8xb9n4d4uETGamSO9rqNbnG91LaS5gvPtNJdlJKmCDHdJqqAqhPsDvS6gy5xvdS2kuYLz7ajSr7lLkk5XhTN3SdIkpQn3iLguIvZExN6IuKvJ62dGxF/VXv9RRKztfpXt08J8fz8inoqIH0fEdyJiTS/qbIeZ5tow7tcjIiOi1DssWplvRPxG7ef7ZET8RbdrbKcWfpdXR8T3ImJ37ff5hl7U2Q4R8WBEvBQRT0zxekTEn9a+Fz+OiMs6Vkxm9v0fikcNPwusB84A/hG4dNKYfwd8pfbxLcBf9bruDs/3w8DZtY9/t6zzbWWutXHnAD8AdgEjva67wz/bDcBu4Jdqn1/Q67o7PN8HgN+tfXwp8Fyv657HfD8AXAY8McXrNwB/BwRwJfCjTtVSljP3hdake8b5Zub3MvNY7dNdFB2yyqiVny3AHwL3Aa93s7gOaGW+vw3cn5lHADLzpS7X2E6tzDeBc2sfnwcc7GJ9bZWZP6DoaTGVLcA3s7ALGIqICztRS1nCvW1Nukuilfk2up3ibKCMZpxr7T9dV2Xmt7tZWIe08rPdCGyMiB9GxK6IuK5r1bVfK/P9AnBbRByg6Bvxe90prSdm+297zlpq1qH+FRG3ASPAB3tdSydExCLgT4BP9biUblpMsTTzIYr/IvtBRLwnM4/2tKrOuRX4emb+cURcRdHV7d2Z+VavCyuzspy5L7Qm3a3Ml4i4BvgccGNmvtGl2tptprmeA7wb+H5EPEexTrmjxBdVW/nZHgB2ZObxzPwJ8DRF2JdRK/O9HfgWQGb+PXAWxXNYqqilf9vtUJZwX2hNumecb0RsAv6MItjLvCY77Vwz89XMXJqZazNzLcX1hRszc7Q35c5bK7/L2ynO2omIpRTLNPu6WWQbtTLf/cBHASLiEopwP9TVKrtnB/BbtV0zVwKvZuaLHXmnXl9dnsVV6BsozmCeBT5XO3YPxT90KH4h/hrYC/xfYH2va+7wfP838M/AP9T+7Oh1zZ2a66Sx36fEu2Va/NkGxVLUU8DjwC29rrnD870U+CHFTpp/AD7W65rnMde/BF4EjlP8F9jtwGeAzzT8bO+vfS8e7+TvsneoSlIFlWVZRpI0C4a7JFWQ4S5JFWS4S1IFGe6SVEGGuyRVkOEuSRVkuEtSBf1/H/TNgC+CQloAAAAASUVORK5CYII=\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "theta1, theta0 = np.random.random(2)\n", + "\n", + "line_xs = [X.min(), X.max()]\n", + "line_ys = [h(x, theta1, theta0) for x in line_xs]\n", + "plt.plot(line_xs, line_ys, color='r')\n", + "\n", + "plt.scatter(X, Y)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "error before: 0.06228371667961022\n" + ] + } + ], + "source": [ + "print(\"error before: \", error_function(X, Y, theta1, theta0))" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-1.0035757423970153 0.9393189294497459\n", + "error after: 0.010349594165039607\n" + ] + } + ], + "source": [ + "alpha = 0.1\n", + "iterations = 20000\n", + "\n", + "theta1, theta0 = gradient_descent(X, Y, theta1, theta0, alpha, iterations)\n", + "\n", + "print(theta1, theta0)\n", + "print(\"error after: \", error_function(X, Y, theta1, theta0))" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "line_xs = [X.min(), X.max()]\n", + "line_ys = [h(x, theta1, theta0) for x in line_xs]\n", + "plt.plot(line_xs, line_ys, color='r')\n", + "\n", + "plt.scatter(X, Y)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-1.0035757423970153 0.9393189294497459\n", + "-50177.847800921314\n" + ] + } + ], + "source": [ + "#t1 = theta1 * (xs.max() - xs.min()) + xs.min()\n", + "#t0 = theta0 * (xs.max() - xs.min()) + xs.min()\n", + "\n", + "#print(t1, t0)\n", + "\n", + "t1 = denormalize(theta1, )\n", + "print(h(50_000, theta1, theta0))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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": "3.7.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} |