tensorflow-for-deep-learnin.../Notebooks/learning_from_unbalanced_clases.ipynb
2016-09-27 14:31:03 -07:00

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"<img src=\"svds/logo_large.jpg\" alt=\"SVDS\" width=\"590\" align=\"left\">"
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"# Imbalanced Learning with Gaussians\n",
"\n",
"## Tom Fawcett / Silicon Valley Data Science / May 2016\n",
"tom@svds.com\n",
"\n",
"This notebook ([click here for `.ipynb` file](https://github.com/silicon-valley-data-science/learning-from-imbalanced-classes/blob/master/Gaussians.ipynb)) illustrates several approaches to the same problem: learning a classifier that can separate examples from two slightly overlapping Gaussians. This notebook shows the effects of undersampling, oversampling, and class weight adjustment.\n",
"\n",
"(Bits and pieces of this code were taken from everywhere, including the scikit-learn examples. Little of it is mine; I mostly stitched it together.)"
]
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"source": [
"# The usual imports\n",
"\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"%matplotlib inline\n",
"plt.rcParams['figure.figsize'] = (12, 10)\n",
"\n",
"from numpy.random import normal, shuffle\n",
"from sklearn.linear_model import LogisticRegression\n",
"\n",
"from ipywidgets import interact, IntSlider\n",
"from IPython.display import display"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Create two one-dimensional arrays sampled from Gaussians. Both have standard deviation of 1.0. The first is centered at x=1 and the second at x=2."
]
},
{
"cell_type": "code",
"execution_count": 2,
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"source": [
"mu1 = 1\n",
"sigma1 = 0.3\n",
"mu2 = 2\n",
"sigma2 = 0.3\n",
"\n",
"p1_all = normal(loc=mu1, scale=sigma1, size=200)\n",
"p2_all = normal(loc=mu2, scale=sigma2, size=200)\n",
"# Create linear spaces spanning out to 3 sigma on each side.\n",
"linspace1 = np.linspace(mu1-3*sigma1, mu1+3*sigma1, 200)\n",
"linspace2 = np.linspace(mu2-3*sigma2, mu2+3*sigma2, 200)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This is the main driver function. It plots the two gaussians and the points on the _x_ axis. Below you can choose the number of class1 and class2 examples used, as well as the number of random samples retrieved. Each separating line is shown as a black vertical line."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false,
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"source": [
"def plot_samples(class1_examples, class2_examples, samples):\n",
" plt.clf()\n",
" # Plot the Gaussians\n",
" plt.plot(linspace1, 1/(sigma1 * np.sqrt(2 * np.pi)) *\n",
" np.exp( - (linspace1 - mu1)**2 / (2 * sigma1**2) ),\n",
" linewidth=2, color='b', label=\"Class 1\")\n",
" plt.plot(linspace2, 1/(sigma1 * np.sqrt(2 * np.pi)) *\n",
" np.exp( - (linspace2 - mu2)**2 / (2 * sigma1**2) ),\n",
" linewidth=2, color='r', label=\"Class 2 (majority)\")\n",
" for _ in range(samples):\n",
" # Shuffle the examples then trim them to the number desired\n",
" shuffle(p1_all)\n",
" shuffle(p2_all)\n",
" p1 = p1_all[:class1_examples]\n",
" p2 = p2_all[:class2_examples]\n",
" X = np.append(p1, p2)\n",
" y = np.append([0] * len(p1), [1] * len(p2))\n",
" # Train Logistic Regression on X and y\n",
" lr = LogisticRegression(fit_intercept=True, intercept_scaling=1, solver=\"sag\")\n",
" lr.fit(X.reshape(-1,1), y)\n",
" # Plot the examples\n",
" plt.plot(p1, np.zeros(len(p1)), marker=\"o\", markersize=7, color=\"b\")\n",
" plt.plot(p2, np.zeros(len(p2)), marker=\"o\", markersize=7, color=\"r\")\n",
" # Now draw the boundary line found by LR. We don't care about the slope of the LR line.\n",
" # Just drop a vertical line through each x intercept.\n",
" x_weight = lr.coef_[0][0]\n",
" y_intercept = lr.intercept_[0]\n",
" x_intercept = -y_intercept / x_weight\n",
" plt.plot([x_intercept,x_intercept], [0,2], color=\"black\")\n",
" plt.legend()\n",
" plt.xlim(0,3)\n",
" plt.ylim(-0.1, 1.6)\n",
" plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Interactive experiment -- undersampling\n",
"\n",
"Below you can play with sampling these distributions by moving the sliders. Each **sample** is one draw of examples from each class, followed by the generation of a separating line based on those examples. **class1** and **class2_examples** determine how many examples are pulled from each class for one sample.\n",
"\n",
"In general, the more balanced the examples are, the closer the vertical lines should be to the ideal split point (where the Gaussians cross). The more examples you have the narrower the band of separators should be, though there will still be some variance even at the highest (n=100) values. Note that this is **always** undersampling, never oversampling."
]
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XnXfemZL7P336tDp16qRevXrpzTffTMlj1BczxwAQAsy4IQp4HiMVkj1zzIY8AAAAoALJ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\n/mMlYbKyLBvs0CHoiNLGgQfCpEm2aW67DV5+OeiIRDJEy5bW4PbbD15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dOy4iO3sRh/MX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"text/plain": [
"<matplotlib.figure.Figure at 0x114d4ef60>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"v = interact(plot_samples, class1_examples=(5,100,5), class2_examples=(5,100,5), samples=(1,20))\n",
"display(v)"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"# Oversampling\n",
"\n",
"This shows the same problem as above but addressed with **oversampling** (replicating minority instances). As the slider below is moved, the minority instances are randomly duplicated. This mostly has the effect of increasing the penalties for false positives (false classifications of the minority instances)."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": true,
"run_control": {
"frozen": false,
"read_only": false
}
},
"outputs": [],
"source": [
"minority_all = normal(loc=mu1, scale=sigma1, size=10)\n",
"majority_all = normal(loc=mu2, scale=sigma2, size=100)\n",
"\n",
"def plot_samples_oversampling(n_minority_exs=len(minority_all)):\n",
" plt.clf()\n",
" plt.plot(linspace1, 1/(sigma1 * np.sqrt(2 * np.pi)) *\n",
" np.exp( - (linspace1 - mu1)**2 / (2 * sigma1**2) ),\n",
" linewidth=2, color='b', label=\"Class 1 (minority)\")\n",
" plt.plot(linspace2, 1/(sigma1 * np.sqrt(2 * np.pi)) *\n",
" np.exp( - (linspace2 - mu2)**2 / (2 * sigma1**2) ),\n",
" linewidth=2, color='r', label=\"Class 2 (majority)\")\n",
" minority_exs = np.concatenate([minority_all for _ in \n",
" range(0, int(n_minority_exs/len(minority_all))+1)][:n_minority_exs])\n",
" X = np.append(minority_exs, majority_all)\n",
" y = np.append([0] * len(minority_exs), [1] * len(majority_all))\n",
" lr = LogisticRegression(fit_intercept=True, intercept_scaling=1, solver=\"sag\")\n",
" lr.fit(X.reshape(-1,1), y)\n",
" plt.plot(minority_exs, np.zeros(len(minority_exs)), marker=\"o\", markersize=7, color=\"b\")\n",
" plt.plot(majority_all, np.zeros(len(majority_all)), marker=\"o\", markersize=7, color=\"r\")\n",
" x_weight = lr.coef_[0][0]\n",
" y_intercept = lr.intercept_[0]\n",
" x_intercept = -y_intercept / x_weight\n",
"# print(\"X weight =\", x_weight, \", Y intercept = \", y_intercept, \", X intercept =\", x_intercept)\n",
" plt.title(\"Minority sampled %0.1f\" % (n_minority_exs/len(minority_all)))\n",
" plt.plot([x_intercept,x_intercept], [0,2], color=\"black\")\n",
" # plt.plot([0,2],[y_intercept,2*x_weight+y_intercept])\n",
" plt.legend()\n",
" plt.xlim(0,3)\n",
" plt.ylim(-0.1, 1.6)\n",
" plt.show()\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Interactive experiment -- oversampling\n",
"\n",
"As the slider below is moved, the minority instances are randomly duplicated. \n",
"\n",
"This mostly has the effect of increasing the penalties for false positives (false classifications of the minority instances)."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false,
"run_control": {
"frozen": false,
"read_only": false
}
},
"outputs": [
{
"data": {
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BvDwYOBC2bIEbb3Rje+qGcULGQ4fc2eGNG13P9D//Gd79+4GS4wRVVAQ33OAS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IAAAL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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11379cc88>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"v = interact(plot_samples_oversampling, \n",
" n_minority_exs=(len(minority_all), len(majority_all)))\n",
"display(v)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Class Weights\n"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": true,
"run_control": {
"frozen": false,
"read_only": false
}
},
"outputs": [],
"source": [
"def plot_samples_class_weights(minority_weight=1.0):\n",
" plt.clf()\n",
" plt.plot(linspace1, 1/(sigma1 * np.sqrt(2 * np.pi)) *\n",
" np.exp( - (linspace1 - mu1)**2 / (2 * sigma1**2) ),\n",
" linewidth=2, color='b', label=\"Class 1 (minority)\")\n",
" plt.plot(linspace2, 1/(sigma1 * np.sqrt(2 * np.pi)) *\n",
" np.exp( - (linspace2 - mu2)**2 / (2 * sigma1**2) ),\n",
" linewidth=2, color='r', label=\"Class 2 (majority)\")\n",
" X = np.append(minority_all, majority_all)\n",
" y = np.append([0] * len(minority_all), [1] * len(majority_all))\n",
" lr = LogisticRegression(fit_intercept=True, intercept_scaling=1, solver=\"sag\", \n",
" class_weight = { 0: minority_weight})\n",
" lr.fit(X.reshape(-1,1), y)\n",
" plt.plot(minority_all, np.zeros(len(minority_all)), marker=\"o\", markersize=7, color=\"b\")\n",
" plt.plot(majority_all, np.zeros(len(majority_all)), marker=\"o\", markersize=7, color=\"r\")\n",
" x_weight = lr.coef_[0][0]\n",
" y_intercept = lr.intercept_[0]\n",
" x_intercept = -y_intercept / x_weight\n",
" plt.title(\"Minority weight %0.1f\" % (minority_weight,))\n",
" plt.plot([x_intercept,x_intercept], [0,2], color=\"black\")\n",
" # plt.plot([0,2],[y_intercept,2*x_weight+y_intercept])\n",
" plt.legend()\n",
" plt.xlim(0,3)\n",
" plt.ylim(-0.1, 1.6)\n",
" plt.show()\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Interactive experiment -- altering class_weights\n",
"\n",
"Finally, here's the same problem addressed by varying the minority class's weight passed to the logistic regression algorithm. The slider directly determines the `class_weight` parameter value.\n",
"\n",
"You may notice as you increase `class_weight` of the minority class, the separating line does not move smoothly through the region --- it sometimes jumps around unpredictably."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false,
"run_control": {
"frozen": false,
"read_only": false
}
},
"outputs": [
{
"data": {
"image/png": 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P54knnqBVq1Z07NiRZ555psJBelOmTKFjx460b9+eXr16nZfM/e1vfyM3N5fmzZvzxz/+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8AAAL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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11386a780>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"v = interact(plot_samples_class_weights, \n",
" minority_weight=(1.0, 100.0))\n",
"display(v)"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"# End"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true,
"run_control": {
"frozen": false,
"read_only": false
}
},
"source": [
"<center><h2>© <a href=\"http://www.svds.com\">2016 Silicon Valley Data Science LLC</a></h2></center>"
]
}
],
"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": "2.7.12"
}
},
"nbformat": 4,
"nbformat_minor": 0
}