Skip to content

Instantly share code, notes, and snippets.

@kiwamizamurai
Created April 21, 2019 22:06
Show Gist options
  • Star 0 You must be signed in to star a gist
  • Fork 0 You must be signed in to fork a gist
  • Save kiwamizamurai/b6c8879fe01f141651bcdc5798a29e1a to your computer and use it in GitHub Desktop.
Save kiwamizamurai/b6c8879fe01f141651bcdc5798a29e1a to your computer and use it in GitHub Desktop.
Display the source blob
Display the rendered blob
Raw
{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "minibatch_gd",
"version": "0.3.2",
"provenance": []
},
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
}
},
"cells": [
{
"metadata": {
"id": "_XuWmiBbY9Z2",
"colab_type": "code",
"colab": {}
},
"cell_type": "code",
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"import seaborn as sns\n",
"sns.set()\n",
"\n",
"from pylab import rcParams\n",
"rcParams['figure.figsize'] = 12, 6\n",
"rcParams['font.size'] = 20\n",
"\n",
"np.random.seed(7)"
],
"execution_count": 0,
"outputs": []
},
{
"metadata": {
"id": "3YaEIonqY9aF",
"colab_type": "text"
},
"cell_type": "markdown",
"source": [
"\n",
"\\begin{equation} \\beta_0= 2 \\end{equation} \n",
"\\begin{equation} \\beta_1= -3 \\end{equation} \n",
"\n",
"\\begin{equation} \\hat{y} = \\beta_0 + \\beta_1 x \\end{equation} \n",
"\\begin{equation} y = \\hat{y} + \\epsilon \\end{equation} "
]
},
{
"metadata": {
"id": "6uZUKbTJY9aG",
"colab_type": "code",
"colab": {}
},
"cell_type": "code",
"source": [
"N = 100\n",
"X = 4*np.random.rand(N,1)\n",
"y = 2 - 3*X + 1.6*np.random.randn(N,1)"
],
"execution_count": 0,
"outputs": []
},
{
"metadata": {
"id": "hGwW_tP3Y9aM",
"colab_type": "code",
"outputId": "406270b4-6fe9-443e-df27-2f637fb92b41",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 410
}
},
"cell_type": "code",
"source": [
"plt.plot(X,y,'b.')\n",
"plt.title(\"data\")"
],
"execution_count": 42,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"Text(0.5, 1.0, 'data')"
]
},
"metadata": {
"tags": []
},
"execution_count": 42
},
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAtIAAAF4CAYAAAB5BR6/AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
"text/plain": [
"<Figure size 864x432 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"metadata": {
"id": "Iu-naihzY9aR",
"colab_type": "text"
},
"cell_type": "markdown",
"source": [
"# Linear Regression\n",
"\n",
"$$ \n",
"\\beta=\\left(X^{T} X\\right)^{-1} X^{T} y\n",
" $$"
]
},
{
"metadata": {
"id": "myA1zAnBY9aS",
"colab_type": "code",
"outputId": "b81becaf-e233-45c7-8949-1fc84d2cb9aa",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 51
}
},
"cell_type": "code",
"source": [
"XX = np.c_[np.ones((100,1)), X]\n",
"theta_best = np.linalg.inv(XX.T.dot(XX)).dot(XX.T).dot(y)\n",
"print(theta_best)"
],
"execution_count": 43,
"outputs": [
{
"output_type": "stream",
"text": [
"[[ 1.75402391]\n",
" [-2.87915842]]\n"
],
"name": "stdout"
}
]
},
{
"metadata": {
"id": "ORr_MxoXY9al",
"colab_type": "text"
},
"cell_type": "markdown",
"source": [
"# Gradient Descent"
]
},
{
"metadata": {
"id": "0F0hkmH2Y9am",
"colab_type": "text"
},
"cell_type": "markdown",
"source": [
"\n",
"$$\n",
"\\begin{array}{c}\n",
"{\\frac{1}{2}\\|y-X \\beta\\|^{2}=\\frac{1}{2}(y-X \\beta)^{T}(y-X \\beta)}\n",
"\\end{array}\n",
"$$\n",
"\n",
"$$\n",
"\\begin{array}{c}\n",
" {\\frac{1}{2}\\|y-X \\beta\\|^{2}=\\frac{1}{2}\\left(\\beta^{T} X^{T} X \\beta-2 y^{T} X \\beta+y^{T} y\\right)} \n",
" \\end{array}\n",
"$$\n",
" \n",
" $$\n",
"\\begin{array}{c}\n",
" {\\nabla_{\\beta} \\frac{1}{2}\\|y-X \\beta\\|^{2}=\\left(X^{T} X+\\left(X^{T} X\\right)^{T}\\right) \\beta-2 X^{T} y}\\end{array}$$"
]
},
{
"metadata": {
"id": "KdAHnLQKY9ao",
"colab_type": "code",
"colab": {}
},
"cell_type": "code",
"source": [
"def cost(theta, X, y):\n",
" m = len(y)\n",
" predictions = X.dot(theta)\n",
" cost = (1/2*m) * np.sum(np.square(predictions-y))\n",
" return cost"
],
"execution_count": 0,
"outputs": []
},
{
"metadata": {
"id": "ea8UaAOCY9as",
"colab_type": "code",
"colab": {}
},
"cell_type": "code",
"source": [
"def gradient_descent(X, y, theta, alpha=0.01, iter=100):\n",
" m = len(y)\n",
" cost_history = np.zeros(iter)\n",
" theta_history = np.zeros((iter, 2))\n",
" for i in range(iter):\n",
" prediction = np.dot(X,theta)\n",
" theta = theta -(1/m)*alpha*(X.T.dot((prediction-y)))\n",
" theta_history[i, :] = theta.T\n",
" cost_history[i] = cost(theta, X, y)\n",
" return theta, cost_history, theta_history"
],
"execution_count": 0,
"outputs": []
},
{
"metadata": {
"id": "Rh60XqBnY9ax",
"colab_type": "code",
"outputId": "e73b4ce3-8945-4f87-ce24-1fd426c20b36",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 451
}
},
"cell_type": "code",
"source": [
"lr =0.01\n",
"n_iter = 300\n",
"\n",
"theta = np.random.randn(2,1)\n",
"\n",
"X_b = np.c_[np.ones((len(X), 1)), X]\n",
"theta, gd_cost_history, gd_theta_history = gradient_descent(X_b, y, theta, lr, n_iter)\n",
"\n",
"\n",
"print('beta0: {0:>7.3f} \\nbeta1: {0:>7.3f}'.format(theta[0][0], theta[1][0]))\n",
"\n",
"plt.plot(gd_cost_history)\n",
"plt.xlabel(\"iteration\")\n",
"plt.ylabel(\"cost\")"
],
"execution_count": 53,
"outputs": [
{
"output_type": "stream",
"text": [
"beta0: 0.841 \n",
"beta1: 0.841\n"
],
"name": "stdout"
},
{
"output_type": "execute_result",
"data": {
"text/plain": [
"Text(0, 0.5, 'cost')"
]
},
"metadata": {
"tags": []
},
"execution_count": 53
},
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAu8AAAF/CAYAAAD5DSePAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTkSuQmCC\n",
"text/plain": [
"<Figure size 864x432 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"metadata": {
"id": "UBx-2txOY9cM",
"colab_type": "text"
},
"cell_type": "markdown",
"source": [
"# Stochastic Gradient Descent"
]
},
{
"metadata": {
"id": "s6VcRoNfY9ck",
"colab_type": "code",
"colab": {}
},
"cell_type": "code",
"source": [
"def stocashtic_gradient_descent(X, y, theta, alpha=0.01, iter=10):\n",
" m = len(y)\n",
" cost_history = np.zeros(iter)\n",
" theta_history = np.zeros((iter*m, 2))\n",
" \n",
" for it in range(iter):\n",
" costt = 0.0\n",
" for i in range(m):\n",
" rand_ind = np.random.randint(0, m)\n",
" X_i = X[rand_ind, :].reshape(1, X.shape[1])\n",
" y_i = y[rand_ind].reshape(1, 1)\n",
" prediction = np.dot(X_i, theta)\n",
"\n",
" theta = theta -(1/m)*alpha*(X_i.T.dot((prediction-y_i)))\n",
" theta_history[i, :] = theta.T\n",
" costt += cost(theta, X_i, y_i)\n",
" cost_history[it] = costt\n",
" \n",
" return theta, cost_history, theta_history"
],
"execution_count": 0,
"outputs": []
},
{
"metadata": {
"id": "Kq2aMN3FY9co",
"colab_type": "code",
"outputId": "29fbd675-a000-49f9-ad39-7afe64832f39",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 451
}
},
"cell_type": "code",
"source": [
"lr =0.5\n",
"n_iter = 300\n",
"\n",
"theta = np.random.randn(2,1)\n",
"\n",
"X_b = np.c_[np.ones((len(X),1)),X]\n",
"theta, sgd_cost_history, sgd_theta_history = stocashtic_gradient_descent(X_b,y,theta,lr,n_iter)\n",
"\n",
"\n",
"print('beta0: {0:>7.3f} \\nbeta1: {0:>7.3f}'.format(theta[0][0],theta[1][0]))\n",
"plt.plot(sgd_cost_history)\n",
"plt.xlabel(\"iteration\")\n",
"plt.ylabel(\"cost\")"
],
"execution_count": 56,
"outputs": [
{
"output_type": "stream",
"text": [
"beta0: 1.676 \n",
"beta1: 1.676\n"
],
"name": "stdout"
},
{
"output_type": "execute_result",
"data": {
"text/plain": [
"Text(0, 0.5, 'cost')"
]
},
"metadata": {
"tags": []
},
"execution_count": 56
},
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAuEAAAF/CAYAAADnxBc8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
"text/plain": [
"<Figure size 864x432 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"metadata": {
"id": "x6pQsDGvY9cv",
"colab_type": "text"
},
"cell_type": "markdown",
"source": [
"# Mini Batch Gradient Descent"
]
},
{
"metadata": {
"id": "XQd6KV8oY9cw",
"colab_type": "code",
"colab": {}
},
"cell_type": "code",
"source": [
"def minibatch_gradient_descent(X, y, theta, alpha=0.01, iter=10, batch_size=20):\n",
" m = len(y)\n",
" cost_history = np.zeros(iter)\n",
" n_batches = int(m/batch_size)\n",
" theta_history = np.zeros((iter*m, 2))\n",
" \n",
" for it in range(iter):\n",
" costt = 0.0\n",
" indices = np.random.permutation(m)\n",
" X = X[indices]\n",
" y = y[indices]\n",
" for i in range(0, m, batch_size):\n",
" X_i = X[i:i+batch_size]\n",
" y_i = y[i:i+batch_size]\n",
" \n",
" X_i = np.c_[np.ones(len(X_i)), X_i] \n",
" prediction = np.dot(X_i, theta)\n",
"\n",
" theta = theta -(1/m)*alpha*(X_i.T.dot((prediction-y_i)))\n",
" theta_history[i, :] = theta.T\n",
" costt += cost(theta, X_i, y_i)\n",
" cost_history[it] = costt\n",
" \n",
" return theta, cost_history, theta_history"
],
"execution_count": 0,
"outputs": []
},
{
"metadata": {
"id": "erQifW90Y9cy",
"colab_type": "code",
"outputId": "d89ee929-8371-43fb-e867-a5864ef861db",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 451
}
},
"cell_type": "code",
"source": [
"lr =0.1\n",
"n_iter = 300\n",
"b_size = 10\n",
"\n",
"theta = np.random.randn(2,1)\n",
"\n",
"\n",
"theta, mini_cost_history, mini_theta_history = minibatch_gradient_descent(X, y, theta, lr, n_iter, b_size)\n",
"\n",
"\n",
"print('beta0: {0:>7.3f} \\nbeta1: {0:>7.3f}'.format(theta[0][0],theta[1][0]))\n",
"plt.plot(mini_cost_history)\n",
"plt.xlabel(\"iteration\")\n",
"plt.ylabel(\"cost\")"
],
"execution_count": 58,
"outputs": [
{
"output_type": "stream",
"text": [
"beta0: 1.741 \n",
"beta1: 1.741\n"
],
"name": "stdout"
},
{
"output_type": "execute_result",
"data": {
"text/plain": [
"Text(0, 0.5, 'cost')"
]
},
"metadata": {
"tags": []
},
"execution_count": 58
},
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAugAAAF/CAYAAAAb0Tz2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nH9XDuRT/AAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 864x432 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"metadata": {
"id": "c3AWJuvqY9c3",
"colab_type": "code",
"outputId": "fe5bafdd-161b-4f58-d4fe-9a9625760074",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 400
}
},
"cell_type": "code",
"source": [
"transform_gf = np.log(gd_cost_history)\n",
"transform_sgd = np.log(sgd_cost_history)\n",
"transform_mini = np.log(mini_cost_history)\n",
"\n",
"plt.plot(transform_gf, label='GD')\n",
"plt.plot(transform_sgd, label='SGD')\n",
"plt.plot(transform_mini, label='mini-batch')\n",
"\n",
"plt.legend()"
],
"execution_count": 59,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7efcf74efeb8>"
]
},
"metadata": {
"tags": []
},
"execution_count": 59
},
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAskAAAFuCAYAAABzxIUmAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQhjJAoFAIBAIBAJBFP8fcSmUbR1Nh44AAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 864x432 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"metadata": {
"id": "V4g1IcVuaE8C",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 400
},
"outputId": "47d15c96-cf1e-4dd4-975c-8cb66fbbc613"
},
"cell_type": "code",
"source": [
"plt.plot(mini_theta_history[:,0], mini_theta_history[:,1], label=\"mini-batch\")\n",
"plt.plot(gd_theta_history[:,0], gd_theta_history[:,1], label=\"GD\")\n",
"plt.plot(sgd_theta_history[:,0], sgd_theta_history[:,1], label=\"SGD\")\n",
"\n",
"plt.legend()"
],
"execution_count": 60,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7efcf74e3358>"
]
},
"metadata": {
"tags": []
},
"execution_count": 60
},
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAtYAAAFuCAYAAAClYV9DAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 864x432 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"metadata": {
"id": "a11-Iib662LO",
"colab_type": "code",
"colab": {}
},
"cell_type": "code",
"source": [
""
],
"execution_count": 0,
"outputs": []
}
]
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment