{ "cells": [ { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# All imports and setups \n", "\n", "%run ../../../common_functions/import_all.py\n", "\n", "import sys\n", "sys.path.append('../../')\n", "\n", "import statsmodels.api as sm\n", "from scipy.spatial.distance import euclidean\n", "\n", "from common_functions.setup_notebook import *\n", "\n", "config_ipython()\n", "setup_matplotlib()\n", "set_css_style()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# The Gradient Descent method" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Standard Gradient Descent: finding the minumum of a function" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Minimizing a 1D parabola with Standard Gradient Descent" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": { "image/png": { "height": 380, "width": 607 } }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Local min of function is 1.666702\n" ] }, { "data": { "image/png": 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" ] }, "metadata": { "image/png": { "height": 396, "width": 627 } }, "output_type": "display_data" } ], "source": [ "# Choose the x points\n", "x = np.array([i for i in range(-1000, 1000)])\n", "\n", "# Define the function and its derivative\n", "def f1(x):\n", " return 3*x**2 - 10*x + 4\n", "\n", "def f1_der(x):\n", " return 6*x - 10\n", "\n", "# Plot the function\n", "plt.ylim(-10,100)\n", "plt.xlim(-10,10)\n", "plt.plot(x, f1(x), label='$f$', lw=3)\n", "plt.plot(x, f1_der(x), label=\"$f'$\", lw=3)\n", "plt.legend(loc=2)\n", "plt.xlabel('$x$')\n", "plt.show()\n", "\n", "# Running the Gradient Descent\n", "\n", "x0 = 7 # starting point for the descent\n", "alpha = .1 # step size (learning rate)\n", "p = .0001 # chosen precision\n", "\n", "former_min = x0\n", "iterative_mins = [former_min]\n", "while True:\n", " x_min = former_min - alpha * f1_der(former_min)\n", " iterative_mins.append(x_min)\n", " if abs(former_min - x_min) <= p:\n", " break\n", " else:\n", " former_min = x_min\n", " \n", "print('Local min of function is %f' %x_min)\n", "\n", "plt.plot(x, f1(x), lw=3)\n", "plt.ylim(-10,100)\n", "plt.xlim(-10,10)\n", "plt.title('Iterative descent to minimum')\n", "plt.xlabel('$x$')\n", "plt.ylabel('$f(x)$')\n", "plt.plot(iterative_mins, f1(np.array(iterative_mins)), marker='o')\n", "plt.show();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Minimizing a 2D parabola with Standard Gradient Descent\n", "\n", "The we do the same but for a paraboloid in 3 dimensions." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Local min of function is [ 0.00036538 0.00036538]\n" ] } ], "source": [ "def f2(x, y):\n", " return x**2 + y**2\n", "\n", "def f2_der(x, y):\n", " return np.array([2*x, 2*y])\n", "\n", "#Running the Gradient Descent\n", "\n", "x0 = 50 # starting point for the descent\n", "y0 = 50 # starting point for the descent\n", "alpha = .1 # step size (learning rate)\n", "p = .0001 # chosen precision\n", "\n", "former_min = np.array([x0, y0])\n", "iterative_mins = [former_min]\n", "while True:\n", " x_min = former_min - alpha * f2_der(former_min[0], former_min[1])\n", " iterative_mins.append(x_min)\n", " if abs(former_min[0] - x_min[0]) <= p and abs(former_min[1] - x_min[1]) <= p:\n", " break\n", " else:\n", " former_min = x_min\n", " \n", "print('Local min of function is', x_min)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Standard Gradient Descent: implementing a Linear Regression" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we said, this method is used in a Ordinary Least Squares calculation in a Linear Regression to find the line which best fits a series of observation points. Let's \"manually\" implement it." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Minimizing an objective function for Linear Regression with Standard Gradient Descent" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true } }, "outputs": [], "source": [ "# The experimental points (observations)\n", "x = np.array([1, 2, 2.5, 3, 3.5, 4.5, 4.7, 5.2, 6.1, 6.1, 6.8])\n", "y = np.array([1.5, 1, 2, 2, 3.7, 3, 5, 4, 5.8, 5, 5.7])\n", "\n", "alpha = 0.001 # learning rate\n", "p = .001 # precision\n", "\n", "def f(x, w):\n", " \"\"\"A line y = wx, to be intended as w0 + w1x (x0 = 1)\"\"\"\n", " return np.dot(x, w)\n", "\n", "def diff(a, b):\n", " return a - b\n", "\n", "def squared_diff(a, b):\n", " return (a - b)**2\n", "\n", "def obj_f(w, x, y):\n", " \"\"\"The objective function: sum of squared diffs between observations and line predictions\"\"\"\n", " return sum([squared_diff(f(np.array([1, x[i]]), w), y[i]) for i in range(len(x))])" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Found parameters (intercept, slope): [ 0.26961873 0.79783026]\n" ] }, { "data": { "image/png": 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CwgytxWazGXp/AAAAoCPef/99paWladu2bZKkiy++WJmZmRo3bpzBlQHehWAJ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\n509/+hO9evVi5syZlJSUcPHFF/Piiy8yfPhwSyVJkiRpP1VrxlJhYSH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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 359, "width": 587 } }, "output_type": "display_data" } ], "source": [ "def obj_f_der(w, x, y):\n", " \"\"\"Gradient of the objective function in the parameters\"\"\"\n", " return sum([np.dot(2 * np.array([1, x[i]]), diff(f(np.array([1, x[i]]), w), y[i])) for i in range(len(x))])\n", "\n", "# Perform a Standard Gradient Descent to get the parameters of the fitting line\n", "former_w = np.array([10, 5]) # the chosen starting point for the descent\n", "while True:\n", " w = former_w - alpha * obj_f_der(former_w, x, y)\n", " if euclidean(former_w, w) <= p:\n", " break\n", " else:\n", " former_w = w\n", " \n", "print('Found parameters (intercept, slope):', w)\n", "\n", "plt.scatter(x, y, marker='o', label='points')\n", "plt.plot([i for i in range(0,11)], [w[0] + w[1] * i for i in range(0, 11)], label='fitting line', c='k', lw=1)\n", "plt.legend(loc=2)\n", "plt.show();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Stochastic Gradient Descent" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Minimizing an objective function for Linear Regression with Stochastic Gradient Descent\n", "\n", "Using the same dataset, same learning rate and same precision as above, we re-implement an OLS, this time using a Stochastic Gradient Descent, and looking at the difference in the result we obtain." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2000\n", "Found parameters (intercept, slope): [ 0.22687683 0.80406405]\n" ] }, { "data": { "image/png": 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gWwiWgD4sPz9fUVFRkqQ5c+YYWktVVZWh9wcAAAA88fXXX8tisejVV1+VJI0Y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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 359, "width": 587 } }, "output_type": "display_data" } ], "source": [ "def obj_f_der_point(w, obs_x, obs_y):\n", " \"\"\"Addend of the gradient of the objective function in the parameters\"\"\"\n", " return np.dot(2 * np.array([1, obs_x]), diff(f(np.array([1, obs_x]), w), obs_y))\n", "\n", "# Perform a Stochastic Gradient Descent to get the parameters of the fitting line\n", "training_set = [(x[i], y[i]) for i in range(len(x))]\n", "\n", "epoch = 1\n", "former_w = np.array([10, 5]) # the chosen starting point for the descent\n", "#while epoch < 2000:\n", "\n", "found = False\n", "max_epochs = 2000\n", "while epoch < max_epochs:\n", " random.shuffle(training_set)\n", " for point in training_set:\n", " w = former_w - alpha * obj_f_der_point(former_w, point[0], point[1])\n", " if euclidean(former_w, w) <= p:\n", " break\n", " else:\n", " former_w = w\n", " \n", " epoch +=1 \n", " \n", "print(epoch)\n", "print('Found parameters (intercept, slope):', w)\n", "\n", "plt.scatter(x, y, marker='o', label='points')\n", "plt.plot([i for i in range(0,11)], [w[0] + w[1] * i for i in range(0, 11)], label='fitting line', c='k', lw=1)\n", "plt.legend(loc=2)\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": "3.7.6" } }, "nbformat": 4, "nbformat_minor": 4 }