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@peterroelants
Created May 21, 2017 07:55
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Matplotlib Gradient Descent Animation
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from __future__ import division, print_function, absolute_import, unicode_literals\n",
"\n",
"# Python imports\n",
"import numpy # Matrix and vector computation package\n",
"import matplotlib.pyplot as plt # Plotting library\n",
"import seaborn\n",
"# Allow matplotlib to plot inside this notebook\n",
"%matplotlib inline\n",
"# Set the seed of the numpy random number generator so that the tutorial is reproducable\n",
"numpy.random.seed(seed=1)\n",
"\n",
"from matplotlib import animation, rc\n",
"from IPython.display import HTML, Image\n",
"\n",
"# equivalent to rcParams['animation.html'] = 'html5'\n",
"rc('animation', html='html5')"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Define the vector of input samples as x, with 20 values sampled from a uniform distribution\n",
"# between 0 and 1\n",
"x = numpy.random.uniform(0, 1, 20)\n",
"\n",
"# Generate the target values t from x with small gaussian noise so the estimation won't\n",
"# be perfect.\n",
"# Define a function f that represents the line that generates t without noise\n",
"def f(x): return x * 2\n",
"\n",
"# Create the targets t with some gaussian noise\n",
"noise_variance = 0.2 # Variance of the gaussian noise\n",
"# Gaussian noise error for each sample in x\n",
"noise = numpy.random.randn(x.shape[0]) * noise_variance\n",
"# Create targets t\n",
"t = f(x) + noise"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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O7Oysp7e37p2JExVYal/co7/2Bq4AJgGbzGwusARY4+4JM1sKPGJmG4DfAz9196SZPW5m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\ngg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f14643ab6a0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Plot the target t versus the input x\n",
"plt.plot(x, t, 'bo', label='target: t')\n",
"plt.xlabel('input: $x$', fontsize=15)\n",
"plt.ylabel('target: $t$', fontsize=15)\n",
"plt.ylim([0,2])\n",
"plt.xlim([0,1])\n",
"plt.title('Labelled data', fontsize=18)\n",
"plt.legend(loc=2)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Define the neural network function y = x * w\n",
"def nn(x, w): return x * w\n",
"\n",
"# Define the cost function\n",
"def cost(y, t): return ((t - y)**2).sum()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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7X0G0iT45rVRNyJp0Dy6/n+LxEyAry+44KaNaRcQY80NNBVGVyMmheMRIcm6+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\nXeW0/VzGcvqAmVg3q33AbUATHPZvvQo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"text/plain": [
"<matplotlib.figure.Figure at 0x7f1460ce47f0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Plot the cost vs the given weight w\n",
"\n",
"# Define a vector of weights for which we want to plot the cost\n",
"ws = numpy.linspace(0, 4, num=100) # weight values\n",
"cost_ws = numpy.vectorize(lambda w: cost(nn(x, w) , t))(ws) # cost for each weight in ws\n",
"\n",
"# Plot\n",
"plt.plot(ws, cost_ws, 'r-', label='cost')\n",
"plt.ylim([0,14])\n",
"plt.xlim([0,4])\n",
"plt.xlabel('parameter: $p$', fontsize=15)\n",
"plt.ylabel('cost: $\\sum |t-y|^2$', fontsize=15)\n",
"plt.title('Cost function', fontsize=18)\n",
"plt.legend(loc=2)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"# Animation functions\n",
"# Uses the Matplotlib animation module: http://matplotlib.org/api/animation_api.html\n",
"# More examples: http://matplotlib.org/examples/animation/\n",
"\n",
"def init_fig():\n",
" \"\"\"Initialise figure\"\"\"\n",
" fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12,5))\n",
" # Line vs data plot\n",
" # Plot the fitted line agains the target line\n",
" # Plot the target t versus the input x\n",
" ax2.plot(x, t, 'bo', label='target: t')\n",
" ax2.set_xlim([0, 1])\n",
" ax2.set_ylim([0, 2])\n",
" ax2.set_xlabel('input: $x$', fontsize=15)\n",
" ax2.set_ylabel('target: $t$', fontsize=15)\n",
" ax2.yaxis.set_label_position('right')\n",
" ax2.set_title('Labelled data & model output', fontsize=18)\n",
" line2, = ax2.plot([], [], 'k-', label='fitted line: $y=x*p$')\n",
" ax2.legend(loc=2)\n",
" # Cost function plot\n",
" ax1.plot(ws, cost_ws, 'r-', label='cost')\n",
" ax1.set_ylim([0, 14])\n",
" ax1.set_xlim([0, 4])\n",
" ax1.set_xlabel('parameter: $p$', fontsize=15)\n",
" ax1.set_ylabel('cost: $\\sum |t-y|^2$', fontsize=15)\n",
" cost_text = ax1.set_title('Cost at step {}'.format(0), fontsize=18)\n",
" line1, = ax1.plot([], [], 'k:', label='derivative at $p$')\n",
" pc_dots, = ax1.plot([], [], 'ko')\n",
" ax1.legend(loc=2)\n",
" return fig, ax1, ax2, line1, line2, pc_dots, cost_text\n",
"\n",
"\n",
"def get_anim(fig, ax1, ax2, line1, line2, pc_dots, cost_text, weights):\n",
" \"\"\"Return animation function.\"\"\"\n",
" xs = numpy.linspace(0, 4, num=100) # weight values\n",
" #(w, dw, cost)\n",
" def anim(i):\n",
" \"\"\"Animate step i\"\"\"\n",
" if i == 0:\n",
" return [line1, line2, pc_dots, cost_text]\n",
" (w, dw, cost) = weights[i-1]\n",
" cost_text.set_text('Cost at step {} = {:.3f}'.format(i, cost))\n",
" ws, _, cs = zip(*weights[0:i])\n",
" pc_dots.set_xdata(ws)\n",
" pc_dots.set_ydata(cs)\n",
" abline_values = [dw * (x-w) + cost for x in xs]\n",
" line1.set_xdata(xs)\n",
" line1.set_ydata(abline_values)\n",
" # Plot fit\n",
" # plot the fitted line\n",
" line2.set_xdata([0, 1])\n",
" line2.set_ydata([0*w, 1*w])\n",
" ax2.legend(loc=2)\n",
" return [line1, line2, pc_dots, cost_text]\n",
" return anim"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"# define the gradient function. Remember that y = nn(x, w) = x * w\n",
"def gradient(w, x, t): \n",
" return 2 * x * (nn(x, w) - t)\n",
"\n",
"# define the update function delta w\n",
"def delta_w(w_k, x, t, learning_rate):\n",
" return learning_rate * gradient(w_k, x, t).sum()\n",
"\n",
"# Set the initial weight parameter\n",
"w = 0.3\n",
"# Set the learning rate\n",
"learning_rate = 0.05\n",
"\n",
"# Start performing the gradient descent updates, and print the weights and cost:\n",
"nb_of_iterations = 11 # number of gradient descent updates\n",
"w_cost = [(w, cost(nn(x, w), t))] # List to store the weight,costs values\n",
"weights = [(w, gradient(w, x, t).sum(), cost(nn(x, w), t))]\n",
"for i in range(nb_of_iterations):\n",
" dw = delta_w(w, x, t, learning_rate) # Get the delta w update\n",
" w = w - dw # Update the current weight parameter\n",
" gw = gradient(w, x, t).sum()\n",
" c = cost(nn(x, w), t)\n",
" w_cost.append((w, c)) # Add weight,cost to list\n",
" weights.append((w, gw, c))"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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7jx+0e/euCvc/fPh1e9f/61/vJhAIsHHjerZv386tt97J2Wd3iMn3Uym3eP74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\nJfvpJ8l+6p9kvf4qOXMfJ2fu499fPjeXSGEhkYJCIuEwodpaQjU1hFa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"text/plain": [
"<matplotlib.figure.Figure at 0x7f1460cfae80>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Create animation (uses ffmpeg)\n",
"fig, ax1, ax2, line1, line2, pc_dots, cost_text = init_fig()\n",
"animate = get_anim(fig, ax1, ax2, line1, line2, pc_dots, cost_text, weights)\n",
"\n",
"anim = animation.FuncAnimation(fig, animate, frames=len(weights)+1, interval=800, blit=True)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
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" <source type=\"video/mp4\" src=\"data:video/mp4;base64,AAAAHGZ0eXBNNFYgAAACAGlzb21pc28yYXZjMQAAAAhmcmVlAADNFG1kYXQAAAKtBgX//6ncRem9\n",
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"\">\n",
" Your browser does not support the video tag.\n",
"</video>"
],
"text/plain": [
"<matplotlib.animation.FuncAnimation at 0x7f1460b30ac8>"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"anim"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<img src=\"./gradient_descent.gif\"/>"
],
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Create gif from animation (uses ImageMagick)\n",
"gif_path = './gradient_descent.gif'\n",
"anim.save('./gradient_descent.gif', writer='imagemagick', fps=1000/800)\n",
"Image(url=gif_path)"
]
}
],
"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": "3.6.1"
},
"widgets": {
"state": {},
"version": "1.1.2"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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