{ "cells": [ { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "np.random.seed(seed=1)\n", "plt.xkcd()" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "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 = np.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 = np.random.randn(x.shape[0]) * noise_variance\n", "# Create targets t\n", "t = f(x) + noise" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "image/png": 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cjEaj3Q2URHHhFA83BnXgcDwWo5FNJW7ShAlLWBiwfj2we7d7hIXZZN93OkKl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\n5RERyb/z/PnziYjo+PHjBIDat2+fMPujZfr06fK4UUFBAWVmZpLX66X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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot the target t versus the input x\n", "plt.plot(x, t, 'o', label='t')\n", "# Plot the initial line\n", "plt.plot([0, 1], [f(0), f(1)], 'b-', label='f(x)')\n", "plt.xlabel('$x$', fontsize=15)\n", "plt.ylabel('$t$', fontsize=15)\n", "plt.ylim([0,2])\n", "plt.title('inputs (x) vs targets (t)')\n", "plt.grid()\n", "plt.legend(loc=2)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 40, "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": 41, "metadata": {}, "outputs": [ { "data": { "image/png": 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kSeCjj3i+iIPOeIEUeVORBcV4eqUzt9tdcztt1QoYMoQPVMrKqrn9EkJql6VL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\no0ePYujQobjooouwaNEi9OjRQ+6wiIJs2LABb77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"text/plain": [ "" ] }, "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 = np.linspace(0, 4, num=100) # weight values\n", "cost_ws = np.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-')\n", "plt.xlabel('$w$', fontsize=15)\n", "plt.ylabel('$\\\\xi$', fontsize=15)\n", "plt.title('cost vs. weight')\n", "plt.grid()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "w(0): 0.1000 \t cost: 13.6197\n", "w(1): 1.5277 \t cost: 1.1239\n", "w(2): 1.8505 \t cost: 0.4853\n", "w(3): 1.9234 \t cost: 0.4527\n", "w(4): 1.9399 \t cost: 0.4510\n" ] } ], "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 = 0.1\n", "# Set the learning rate\n", "learning_rate = 0.1\n", "\n", "# Start performing the gradient descent updates, and print the weights and cost:\n", "nb_of_iterations = 4 # number of gradient descent updates\n", "w_cost = [(w, cost(nn(x, w), t))] # List to store the weight,costs values\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", " w_cost.append((w, cost(nn(x, w), t))) # Add weight,cost to list\n", "\n", "# Print the final w, and cost\n", "for i in range(0, len(w_cost)):\n", " print('w({}): {:.4f} \\t cost: {:.4f}'.format(i, w_cost[i][0], w_cost[i][1]))" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "image/png": 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u3DiKioqiGzdu0Nq1a+mzzz4jiURC3t7eeg6l75KQkEDNmjUjsVhMT5480bs/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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot the first 2 gradient descent updates\n", "plt.plot(ws, cost_ws, 'r-') # Plot the error curve\n", "# Plot the updates\n", "for i in range(0, len(w_cost)-2):\n", " w1, c1 = w_cost[i]\n", " w2, c2 = w_cost[i+1]\n", " plt.plot(w1, c1, 'bo')\n", " plt.plot([w1, w2],[c1, c2], 'b-')\n", " plt.text(w1, c1+0.5, '$w({})$'.format(i)) \n", "# Show figure\n", "plt.xlabel('$w$', fontsize=15)\n", "plt.ylabel('$\\\\xi$', fontsize=15)\n", "plt.title('Gradient descent updates plotted on cost function')\n", "plt.grid()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": true }, "outputs": [], "source": [ "w = 0\n", "# Start performing the gradient descent updates\n", "nb_of_iterations = 10 # number of gradient descent updates\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" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "image/png": 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PV3UhadGiBTt37lQJmcoA5ZEoSovTCa+9JrMUJiXBnXfKJSC6iKxfLwdLvvji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\nfcsPxnI6MYscxyVjlW13suJgLMfj0rk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UiYCAsutbLks090wJSfXi822nceRLuONwCU4n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\n6vsXWK1W0tPTsVqt5OXlYbVayczMJD09nZycHGw2G3a7HbvdjsPhID8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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot the fitted line agains the target line\n", "# Plot the target t versus the input x\n", "plt.plot(x, t, 'o', label='t')\n", "# Plot the initial line\n", "plt.plot([0, 1], [f(0), f(1)], 'b-', label='f(x)')\n", "# plot the fitted line\n", "plt.plot([0, 1], [0*w, 1*w], 'r-', label='fitted line')\n", "plt.xlabel('input x')\n", "plt.ylabel('target t')\n", "plt.ylim([0,2])\n", "plt.title('input vs. target')\n", "plt.grid()\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": "3.6.1" } }, "nbformat": 4, "nbformat_minor": 2 }