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Diffstat (limited to 'notebook/ft_linear_regression_notebook.ipynb')
| -rw-r--r-- | notebook/ft_linear_regression_notebook.ipynb | 434 |
1 files changed, 0 insertions, 434 deletions
diff --git a/notebook/ft_linear_regression_notebook.ipynb b/notebook/ft_linear_regression_notebook.ipynb deleted file mode 100644 index 8515c65..0000000 --- a/notebook/ft_linear_regression_notebook.ipynb +++ /dev/null @@ -1,434 +0,0 @@ -{ - "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": 9, - "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": 10, - "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 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": 11, - "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": 12, - "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": 13, - "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": 14, - "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": 15, - "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." - ] - }, - { - "cell_type": "code", - "execution_count": 25, - "metadata": {}, - "outputs": [], - "source": [ - "from sklearn.preprocessing import normalize\n", - "\n", - "X, Y = normalize([xs, ys])\n", - "#Y = normalize([ys])[0]" - ] - }, - { - "cell_type": "code", - "execution_count": 26, - "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": [ - "theta1, theta0 = np.random.randn(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": 27, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "error before: 0.7480087502767399\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": [ - "-0.3765733088322758 0.26847436709506317\n", - "error after: 0.00022231908719401474\n" - ] - } - ], - "source": [ - "alpha = 1\n", - "iterations = 1000\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": 30, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "-18828.396967246696\n" - ] - } - ], - "source": [ - "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": "3.7.5" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} |