Skip to content

Instantly share code, notes, and snippets.

@jupp0r
Last active April 13, 2017 06:52
Show Gist options
  • Save jupp0r/5b5cd269bc5b39b30a76cdf2b25b7546 to your computer and use it in GitHub Desktop.
Save jupp0r/5b5cd269bc5b39b30a76cdf2b25b7546 to your computer and use it in GitHub Desktop.
coursera_machine_learning_python
Display the source blob
Display the rendered blob
Raw
Loading
Sorry, something went wrong. Reload?
Sorry, we cannot display this file.
Sorry, this file is invalid so it cannot be displayed.
Display the source blob
Display the rendered blob
Raw
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Exercise 2: Logistic Regression"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Reading data\n",
"Let's input and plot the data"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAArcAAAIrCAYAAAD1ObFPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fe45f386bd0>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"<ggplot: (8788675546397)>"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"from ggplot import *\n",
"\n",
"# read data\n",
"ex2data1 = np.genfromtxt('ex2data1.txt', delimiter=',')\n",
"\n",
"# plot data\n",
"ggplot(pd.DataFrame({\"score_test1\": ex2data1[:,0], \\\n",
" \"score_test2\": ex2data1[:,1], \\\n",
" \"admitted\": [ \"true\" if x > 0 else \"false\" for x in ex2data1[:,2] ] \\\n",
" }), aes(x=\"score_test1\", y=\"score_test2\", color=\"admitted\")) + geom_point()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Cost function\n",
"We will now implement the cost function for logistic regression\n",
"\n",
"$$ J(\\theta) = \\frac{1}{m}\\,\\sum^{m}_{i=1}\\left[ -y^{(i)} \\log(h_{\\theta}(x^{(i)}))-(1-y^{(i)})\\log(1-h_{\\theta}(x^{(i)})) \\right] $$\n",
"\n",
"and its partial derivatives\n",
"\n",
"$$ \\frac{\\partial J(\\theta)}{\\partial \\theta_j} = \\frac{1}{m}\\,\\sum^{m}_{i=1}\\left( h_{\\theta}(x^{(i)})-y^{(i)}\\right) x_j^{(i)} $$"
]
},
{
"cell_type": "code",
"execution_count": 121,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Cost at initial theta (zeros):\n",
"0.69314718056\n",
"Expected cost (approx): 0.693\n",
"Gradient at initial theta (zeros):\n",
"[ -0.1 -12.00921659 -11.26284221]\n",
"Expected gradients (approx):[-0.1000, -12.0092, -11.2628]\n",
"Cost at test theta:\n",
"0.218330193827\n",
"Expected cost (approx): 0.218\n",
"Gradient at test theta:\n",
"[ 0.04290299 2.56623412 2.64679737]\n",
"Expected gradients (approx): [0.043, 2.566, 2.647]\n"
]
}
],
"source": [
"from scipy.special import expit\n",
"\n",
"def compute_cost(theta, x, y):\n",
" m = y.shape[0]\n",
" j = 0.0\n",
" grad = np.zeros(x.shape[1])\n",
" for i in range(m):\n",
" hx = expit(theta.dot(x[i,:]))\n",
" j = j + (-y[i]*np.log(hx)-(1-y[i])*np.log(1-hx))\n",
" grad = grad + (hx-y[i])*(x[i,:]);\n",
" j = j/m\n",
" grad = grad/m\n",
" return j, grad\n",
"\n",
"# extend x by intercept terms\n",
"x = np.c_[np.ones(ex2data1.shape[0]), ex2data1[:,0:2]]\n",
"y = ex2data1[:,2]\n",
"initial_theta = np.zeros(x.shape[1])\n",
"\n",
"j, grad = compute_cost(initial_theta, x, y)\n",
"print('Cost at initial theta (zeros):')\n",
"print(j)\n",
"print('Expected cost (approx): 0.693')\n",
"print('Gradient at initial theta (zeros):')\n",
"print(grad)\n",
"print('Expected gradients (approx):[-0.1000, -12.0092, -11.2628]')\n",
"\n",
"test_theta = np.array([-24, 0.2, 0.2])\n",
"j, grad = compute_cost(test_theta, x, y)\n",
"\n",
"print('Cost at test theta:')\n",
"print(j)\n",
"print('Expected cost (approx): 0.218')\n",
"print('Gradient at test theta:')\n",
"print(grad)\n",
"print('Expected gradients (approx): [0.043, 2.566, 2.647]');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Optimizing using library functions instead of gradient descent\n",
"In the original coursera course, Octave's `fminunc` is used instead of gradient descent to find the $\\theta$ which minimizes $J(\\theta)$. We'll be using `fmin` from `scipi` instead."
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Optimization terminated successfully.\n",
" Current function value: 0.203498\n",
" Iterations: 157\n",
" Function evaluations: 287\n",
"Cost at theta found by fmin:\n",
"0.20349770159\n",
"Expected cost (approx): 0.203\n",
"theta:\n",
"[-25.16130062 0.20623142 0.20147143]\n",
"Expected theta (approx):\n",
"[ -25.161, 0.206, 0.201]\n"
]
}
],
"source": [
"from scipy.optimize import fmin\n",
"# extract only the cost part from compute_cost\n",
"def cost(theta, x, y):\n",
" r, _ = compute_cost(theta, x, y)\n",
" return r\n",
"\n",
"theta_m = fmin(func=cost, x0=initial_theta, args=(x, y))\n",
"\n",
"print('Cost at theta found by fmin:')\n",
"print(cost(theta_m, x, y))\n",
"print('Expected cost (approx): 0.203')\n",
"print('theta:')\n",
"print(theta_m)\n",
"print('Expected theta (approx):')\n",
"print('[ -25.161, 0.206, 0.201]');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Plotting the boundary\n",
"Now we can plot the boundary we just found. We would expect the boundary line to separate admissions from non-admissions."
]
},
{
"cell_type": "code",
"execution_count": 66,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAArcAAAImCAYAAABJp6KRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n8T8vcg4mvA7lxgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fe45ea4e110>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"<ggplot: (8788675970381)>"
]
},
"execution_count": 66,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"boundary = [ (theta_m[0] + x*theta_m[1])*-1/theta_m[2] for x in ex2data1[:,0] ]\n",
"\n",
"ggplot(pd.DataFrame({\"score_test1\": ex2data1[:,0], \\\n",
" \"score_test2\": ex2data1[:,1], \\\n",
" \"admitted\": [ \"true\" if x > 0 else \"false\" for x in ex2data1[:,2] ],\n",
" \"boundary\": boundary \\\n",
" }), aes(x=\"score_test1\", y=\"score_test2\", color=\"admitted\")) \\\n",
" + geom_point() + geom_line(aes(x=\"score_test1\", y=\"boundary\"), color=\"green\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Performing predictions using the trained model\n",
"We can now use the trained model to predict admissions/non-admissions given a student's test scores."
]
},
{
"cell_type": "code",
"execution_count": 110,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"For a student with scores 45 and 85, we predict an admission probability of\n",
"0.776291590411\n",
"Expected value: 0.775 +/- 0.002\n",
"Train Accuracy:\n",
"89.000000%\n",
"Expected accuracy (approx): 89.0%\n"
]
}
],
"source": [
"def predict(theta, x):\n",
" return np.round(expit(x.dot(theta)))\n",
"\n",
"x = np.c_[np.ones(ex2data1.shape[0]), ex2data1[:,0:2]]\n",
"y = ex2data1[:,2]\n",
"\n",
"prob = expit(np.array([1, 45, 85]).dot(theta_m))\n",
"print('For a student with scores 45 and 85, we predict an admission probability of')\n",
"print(prob)\n",
"print('Expected value: 0.775 +/- 0.002')\n",
"\n",
"p = predict(theta_m, x)\n",
"print('Train Accuracy:')\n",
"print(\"%f%%\" % (np.count_nonzero(p == y)/float(y.shape[0])*100.0))\n",
"print('Expected accuracy (approx): 89.0%')\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Part 2: Regularization\n",
"The second part of the exercise deals with regularization to avoid overfitting. The example data set represents microchip test data. Let's read the data and take a look at it."
]
},
{
"cell_type": "code",
"execution_count": 87,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAr0AAAIrCAYAAADiGyGGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nP+r4uZxNLuABAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fe45f39fa50>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"<ggplot: (8788676681477)>"
]
},
"execution_count": 87,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# read data\n",
"ex2data2 = np.genfromtxt('ex2data2.txt', delimiter=',')\n",
"\n",
"# plot data\n",
"ggplot(pd.DataFrame({\"score_test1\": ex2data2[:,0], \\\n",
" \"score_test2\": ex2data2[:,1], \\\n",
" \"ok\": [ \"true\" if x > 0 else \"false\" for x in ex2data2[:,2] ] \\\n",
" }), aes(x=\"score_test1\", y=\"score_test2\", color=\"ok\")) + geom_point()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Cost function\n",
"Obviously, this data cannot be fitted by first order polynomials. We need to create features representing higher polynomials and include them into the feature matrix."
]
},
{
"cell_type": "code",
"execution_count": 177,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Cost at initial theta (zeros): 0.693147\n",
"Expected cost (approx): 0.693\n",
"Gradient at initial theta (zeros) - first five values only:\n",
"[ 8.47457627e-03 1.87880932e-02 7.77711864e-05 5.03446395e-02\n",
" 1.15013308e-02]\n",
"Expected gradients (approx) - first five values only:\n",
"[ 0.0085, 0.0188, 0.0001, 0.0503, 0.0115]\n",
"Cost at test theta (with lambda = 10):\n",
"3.16450933162\n",
"Expected cost (approx): 3.16\n",
"Gradient at test theta - first five values only:\n",
"[ 0.34604507 0.16135192 0.19479576 0.22686278 0.09218568]\n",
"Expected gradients (approx) - first five values only:\n",
"[ 0.3460, 0.1614, 0.1948, 0.2269, 0.0922]\n"
]
}
],
"source": [
"def include_higher_order_polynomial_features(x1, x2, maxdegree):\n",
" out = np.ones(x1.shape[0])\n",
" # this can probably be written more concisely using list comprehensions\n",
" for i in range(1,maxdegree+1):\n",
" for j in range(0,i+1):\n",
" out = np.c_[out, np.power(x1, i-j)*np.power(x2, j)]\n",
" return out\n",
"\n",
"y = ex2data2[:,2]\n",
"x = include_higher_order_polynomial_features(ex2data2[:,0], ex2data2[:,1], 6)\n",
"\n",
"def cost_function_reg(theta, x, y, lam):\n",
" m = y.shape[0]\n",
" # we'll reuse the cost function we defined for part 1\n",
" j, grad = compute_cost(theta, x, y)\n",
" theta[0] = 0\n",
" j = j + float(lam)/(2*m)*np.sum(np.power(theta,2.))\n",
" grad = grad + (float(lam)/m)*theta\n",
" return j, grad\n",
"\n",
"initial_theta = np.zeros(x.shape[1])\n",
"lam = 1.0\n",
"\n",
"j, grad = cost_function_reg(initial_theta, x, y, lam)\n",
"\n",
"print('Cost at initial theta (zeros): %f' % j)\n",
"print('Expected cost (approx): 0.693')\n",
"print('Gradient at initial theta (zeros) - first five values only:')\n",
"print(grad[0:5])\n",
"print('Expected gradients (approx) - first five values only:')\n",
"print('[ 0.0085, 0.0188, 0.0001, 0.0503, 0.0115]')\n",
"\n",
"j, grad = cost_function_reg(np.ones(x.shape[1]), x, y, 10.)\n",
"print('Cost at test theta (with lambda = 10):')\n",
"print(j)\n",
"print('Expected cost (approx): 3.16')\n",
"print('Gradient at test theta - first five values only:')\n",
"print(grad[0:5])\n",
"print('Expected gradients (approx) - first five values only:')\n",
"print('[ 0.3460, 0.1614, 0.1948, 0.2269, 0.0922]')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Fitting and Regularization\n",
"Let's see how $\\lambda$ influences the fitting curve."
]
},
{
"cell_type": "code",
"execution_count": 231,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Optimization terminated successfully.\n",
" Current function value: 0.224569\n",
" Iterations: 546\n",
" Function evaluations: 547\n",
" Gradient evaluations: 547\n",
"Optimization terminated successfully.\n",
" Current function value: 0.332654\n",
" Iterations: 140\n",
" Function evaluations: 141\n",
" Gradient evaluations: 141\n",
"Optimization terminated successfully.\n",
" Current function value: 0.529003\n",
" Iterations: 47\n",
" Function evaluations: 48\n",
" Gradient evaluations: 48\n",
"Optimization terminated successfully.\n",
" Current function value: 0.648216\n",
" Iterations: 21\n",
" Function evaluations: 22\n",
" Gradient evaluations: 22\n",
"Optimization terminated successfully.\n",
" Current function value: 0.529003\n",
" Iterations: 47\n",
" Function evaluations: 48\n",
" Gradient evaluations: 48\n",
"Train Accuracy:\n",
"83.050847%\n",
"Expected accuracy with lambda=1 (approx): 83.1%\n"
]
},
{
"data": {
"text/plain": [
"<matplotlib.figure.Figure at 0x7fe45704e310>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAiIAAAGGCAYAAABG0epPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fe45704eb50>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from scipy.optimize import fmin_bfgs\n",
"import matplotlib.pyplot as plt\n",
"\n",
"# extract only the cost part from compute_cost\n",
"def cost_reg(theta, x, y, lam):\n",
" r, _ = cost_function_reg(theta, x, y, lam)\n",
" return r\n",
"\n",
"def cost_reg_prime(theta, x, y, lam):\n",
" _, d = cost_function_reg(theta, x, y, lam)\n",
" return d\n",
"\n",
"y = ex2data2[:,2]\n",
"x = include_higher_order_polynomial_features(ex2data2[:,0], ex2data2[:,1], 6)\n",
"\n",
"u = np.linspace(-1.0, 1.5, num=50)\n",
"v = np.linspace(-1.0, 1.5, num=50)\n",
"z = np.zeros((u.size, v.size))\n",
"\n",
"plt.figure()\n",
"_, s = plt.subplots(2,2)\n",
"for (lam, col, sp) in [(0, \"red\", s[0,0]), (0.01, \"blue\", s[0,1]), (1, \"green\", s[1,0]), (10, \"purple\", s[1,1])]:\n",
"\n",
" theta_m = fmin_bfgs(cost_reg, np.zeros(x.shape[1]), args=(x, y, lam), fprime=cost_reg_prime)\n",
"\n",
" for i in range(u.size):\n",
" for j in range(v.size):\n",
" z[i,j] = include_higher_order_polynomial_features(np.array([u[i]]), np.array([v[j]]), 6).dot(theta_m)\n",
" sp.set_title(\"lambda=%f\" % lam)\n",
" sp.scatter(ex2data2[:,0], ex2data2[:,1], c=ex2data2[:,2])\n",
" sp.contour(u, v, z, levels=[0.0], colors=col)\n",
"\n",
"# finally one last test from the Octave exercise\n",
"theta_m = fmin_bfgs(cost_reg, np.zeros(x.shape[1]), args=(x, y, 1.0), fprime=cost_reg_prime)\n",
"p = predict(theta_m, x)\n",
"print('Train Accuracy:')\n",
"print(\"%f%%\" % (np.count_nonzero(p == y)/float(y.shape[0])*100.0))\n",
"print('Expected accuracy with lambda=1 (approx): 83.1%')"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.9"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment