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Use @ operator, fix animation (shorten, improve code, and zoom)

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Aurélien Geron 2021-11-23 18:21:10 +13:00
parent 0cdac2f683
commit 84c512121d
1 changed files with 60 additions and 51 deletions
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extra_gradient_descent_comparison.ipynb
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@ -20,10 +20,10 @@
"source": [ "source": [
"<table align=\"left\">\n", "<table align=\"left\">\n",
" <td>\n", " <td>\n",
" <a href=\"https://colab.research.google.com/github/ageron/handson-ml2/blob/master/extra_gradient_descent_comparison.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>\n", " <a href=\"https://colab.research.google.com/github/ageron/handson-ml3/blob/main/extra_gradient_descent_comparison.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>\n",
" </td>\n", " </td>\n",
" <td>\n", " <td>\n",
" <a target=\"_blank\" href=\"https://kaggle.com/kernels/welcome?src=https://github.com/ageron/handson-ml2/blob/master/extra_gradient_descent_comparison.ipynb\"><img src=\"https://kaggle.com/static/images/open-in-kaggle.svg\" /></a>\n", " <a target=\"_blank\" href=\"https://kaggle.com/kernels/welcome?src=https://github.com/ageron/handson-ml3/blob/main/extra_gradient_descent_comparison.ipynb\"><img src=\"https://kaggle.com/static/images/open-in-kaggle.svg\" /></a>\n",
" </td>\n", " </td>\n",
"</table>" "</table>"
] ]
@ -34,11 +34,11 @@
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
"import numpy as np\n", "import matplotlib\n",
"\n",
"%matplotlib nbagg\n",
"import matplotlib.pyplot as plt\n", "import matplotlib.pyplot as plt\n",
"from matplotlib.animation import FuncAnimation" "from matplotlib.animation import FuncAnimation\n",
"\n",
"matplotlib.rc('animation', html='jshtml')"
] ]
}, },
{ {
@ -47,10 +47,12 @@
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
"import numpy as np\n",
"\n",
"m = 100\n", "m = 100\n",
"X = 2*np.random.rand(m, 1)\n", "X = 2 * np.random.rand(m, 1)\n",
"X_b = np.c_[np.ones((m, 1)), X]\n", "X_b = np.c_[np.ones((m, 1)), X]\n",
"y = 4 + 3*X + np.random.rand(m, 1)" "y = 4 + 3 * X + np.random.rand(m, 1)"
] ]
}, },
{ {
@ -65,8 +67,8 @@
" thetas = np.random.randn(2, 1)\n", " thetas = np.random.randn(2, 1)\n",
" thetas_path = [thetas]\n", " thetas_path = [thetas]\n",
" for i in range(n_iterations):\n", " for i in range(n_iterations):\n",
" gradients = 2*X_b.T.dot(X_b.dot(thetas) - y)/m\n", " gradients = 2 * X_b.T @ (X_b @ thetas - y) / m\n",
" thetas = thetas - learning_rate*gradients\n", " thetas = thetas - learning_rate * gradients\n",
" thetas_path.append(thetas)\n", " thetas_path.append(thetas)\n",
"\n", "\n",
" return thetas_path" " return thetas_path"
@ -88,9 +90,9 @@
" random_index = np.random.randint(m)\n", " random_index = np.random.randint(m)\n",
" xi = X_b[random_index:random_index+1]\n", " xi = X_b[random_index:random_index+1]\n",
" yi = y[random_index:random_index+1]\n", " yi = y[random_index:random_index+1]\n",
" gradients = 2*xi.T.dot(xi.dot(thetas) - yi)\n", " gradients = 2 * xi.T @ (xi @ thetas - yi)\n",
" eta = learning_schedule(epoch*m + i, t0, t1)\n", " eta = learning_schedule(epoch * m + i, t0, t1)\n",
" thetas = thetas - eta*gradients\n", " thetas = thetas - eta * gradients\n",
" thetas_path.append(thetas)\n", " thetas_path.append(thetas)\n",
"\n", "\n",
" return thetas_path" " return thetas_path"
@ -115,11 +117,11 @@
" y_shuffled = y[shuffled_indices]\n", " y_shuffled = y[shuffled_indices]\n",
" for i in range(0, m, minibatch_size):\n", " for i in range(0, m, minibatch_size):\n",
" t += 1\n", " t += 1\n",
" xi = X_b_shuffled[i:i+minibatch_size]\n", " xi = X_b_shuffled[i : i + minibatch_size]\n",
" yi = y_shuffled[i:i+minibatch_size]\n", " yi = y_shuffled[i : i + minibatch_size]\n",
" gradients = 2*xi.T.dot(xi.dot(thetas) - yi)/minibatch_size\n", " gradients = 2 * xi.T @ (xi @ thetas - yi) / minibatch_size\n",
" eta = learning_schedule(t, t0, t1)\n", " eta = learning_schedule(t, t0, t1)\n",
" thetas = thetas - eta*gradients\n", " thetas = thetas - eta * gradients\n",
" thetas_path.append(thetas)\n", " thetas_path.append(thetas)\n",
"\n", "\n",
" return thetas_path" " return thetas_path"
@ -132,7 +134,7 @@
"outputs": [], "outputs": [],
"source": [ "source": [
"def compute_mse(theta):\n", "def compute_mse(theta):\n",
" return np.sum((np.dot(X_b, theta) - y)**2)/m" " return ((X_b @ theta - y) ** 2).sum() / m"
] ]
}, },
{ {
@ -142,7 +144,7 @@
"outputs": [], "outputs": [],
"source": [ "source": [
"def learning_schedule(t, t0, t1):\n", "def learning_schedule(t, t0, t1):\n",
" return t0/(t+t1)" " return t0 / (t + t1)"
] ]
}, },
{ {
@ -166,7 +168,7 @@
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
"exact_solution = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y)\n", "exact_solution = np.linalg.inv(X_b.T @ X_b) @ X_b.T @ y\n",
"bgd_thetas = np.array(batch_gradient_descent())\n", "bgd_thetas = np.array(batch_gradient_descent())\n",
"sgd_thetas = np.array(stochastic_gradient_descent())\n", "sgd_thetas = np.array(stochastic_gradient_descent())\n",
"mbgd_thetas = np.array(mini_batch_gradient_descent())" "mbgd_thetas = np.array(mini_batch_gradient_descent())"
@ -194,9 +196,38 @@
"data_ax = fig.add_subplot(121)\n", "data_ax = fig.add_subplot(121)\n",
"cost_ax = fig.add_subplot(122)\n", "cost_ax = fig.add_subplot(122)\n",
"\n", "\n",
"data_ax.plot(X, y, 'k.')\n",
"\n",
"cost_ax.plot(exact_solution[0,0], exact_solution[1,0], 'y*')\n", "cost_ax.plot(exact_solution[0,0], exact_solution[1,0], 'y*')\n",
"cost_img = cost_ax.pcolor(theta0, theta1, cost_map)\n", "cost_ax.pcolor(theta0, theta1, cost_map, shading='auto')\n",
"fig.colorbar(cost_img)" "\n",
"i = -1\n",
"[bgd_data_plot] = data_ax.plot(X, X_b @ bgd_thetas[i,:], 'r-')\n",
"[bgd_cost_plot] = cost_ax.plot(bgd_thetas[:i,0], bgd_thetas[:i,1], 'r--')\n",
"\n",
"[sgd_data_plot] = data_ax.plot(X, X_b @ sgd_thetas[i,:], 'g-')\n",
"[sgd_cost_plot] = cost_ax.plot(sgd_thetas[:i,0], sgd_thetas[:i,1], 'g--')\n",
"\n",
"[mbgd_data_plot] = data_ax.plot(X, X_b @ mbgd_thetas[i,:], 'b-')\n",
"[mbgd_cost_plot] = cost_ax.plot(mbgd_thetas[:i,0], mbgd_thetas[:i,1], 'b--')\n",
"\n",
"data_ax.set_xlim([0, 2])\n",
"data_ax.set_ylim([0, 15])\n",
"cost_ax.set_xlim([3, 5])\n",
"cost_ax.set_ylim([2, 5])\n",
"\n",
"data_ax.set_xlabel(r'$x_1$')\n",
"data_ax.set_ylabel(r'$y$', rotation=0)\n",
"cost_ax.set_xlabel(r'$\\theta_0$')\n",
"cost_ax.set_ylabel(r'$\\theta_1$')\n",
"\n",
"data_ax.legend(('Data', 'BGD', 'SGD', 'MBGD'), loc=\"upper left\")\n",
"cost_ax.legend(('Normal Equation', 'BGD', 'SGD', 'MBGD'), loc=\"upper left\")\n",
"\n",
"cost_ax.plot(exact_solution[0,0], exact_solution[1,0], 'y*')\n",
"cost_img = cost_ax.pcolor(theta0, theta1, cost_map, shading='auto')\n",
"fig.colorbar(cost_img)\n",
"plt.show()"
] ]
}, },
{ {
@ -206,35 +237,14 @@
"outputs": [], "outputs": [],
"source": [ "source": [
"def animate(i):\n", "def animate(i):\n",
" data_ax.cla()\n", " bgd_data_plot.set_data(X, X_b @ bgd_thetas[i,:])\n",
" cost_ax.cla()\n", " bgd_cost_plot.set_data(bgd_thetas[:i,0], bgd_thetas[:i,1])\n",
"\n", "\n",
" data_ax.plot(X, y, 'k.')\n", " sgd_data_plot.set_data(X, X_b @ sgd_thetas[i,:])\n",
" sgd_cost_plot.set_data(sgd_thetas[:i,0], sgd_thetas[:i,1])\n",
"\n", "\n",
" cost_ax.plot(exact_solution[0,0], exact_solution[1,0], 'y*')\n", " mbgd_data_plot.set_data(X, X_b @ mbgd_thetas[i,:])\n",
" cost_ax.pcolor(theta0, theta1, cost_map)\n", " mbgd_cost_plot.set_data(mbgd_thetas[:i,0], mbgd_thetas[:i,1])"
"\n",
" data_ax.plot(X, X_b.dot(bgd_thetas[i,:]), 'r-')\n",
" cost_ax.plot(bgd_thetas[:i,0], bgd_thetas[:i,1], 'r--')\n",
"\n",
" data_ax.plot(X, X_b.dot(sgd_thetas[i,:]), 'g-')\n",
" cost_ax.plot(sgd_thetas[:i,0], sgd_thetas[:i,1], 'g--')\n",
"\n",
" data_ax.plot(X, X_b.dot(mbgd_thetas[i,:]), 'b-')\n",
" cost_ax.plot(mbgd_thetas[:i,0], mbgd_thetas[:i,1], 'b--')\n",
"\n",
" data_ax.set_xlim([0, 2])\n",
" data_ax.set_ylim([0, 15])\n",
" cost_ax.set_xlim([0, 5])\n",
" cost_ax.set_ylim([0, 5])\n",
"\n",
" data_ax.set_xlabel(r'$x_1$')\n",
" data_ax.set_ylabel(r'$y$', rotation=0)\n",
" cost_ax.set_xlabel(r'$\\theta_0$')\n",
" cost_ax.set_ylabel(r'$\\theta_1$')\n",
"\n",
" data_ax.legend(('Data', 'BGD', 'SGD', 'MBGD'), loc=\"upper left\")\n",
" cost_ax.legend(('Normal Equation', 'BGD', 'SGD', 'MBGD'), loc=\"upper left\")"
] ]
}, },
{ {
@ -243,8 +253,7 @@
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
"animation = FuncAnimation(fig, animate, frames=n_iter)\n", "FuncAnimation(fig, animate, frames=n_iter // 3)"
"plt.show()"
] ]
}, },
{ {