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Last active August 29, 2015 14:13
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linear_problems
{
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"signature": "sha256:f2df6bbd409a5263ed5975f62791ba9a5f6c84469fdd4212a03e04b0f3bf051d"
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"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Solving Non-Linear Problems with Linear Models\n",
"\n",
"> Author: Vincent D. Warmerdam @ http://koaning.github.io \n",
"\n",
"In this notebook I will illustrate that how a logistic regression can hold up against a support vector machine in a situation where you would expect a support vector machine to perform better. Typically logistic regression fails due to the XOR phenomenon that can occur in data, but there is a trick around it. \n",
"\n",
"The goal of this notebook is to convince you that you may need to worry more about the features that go into a model, less about which model to pick and how to tune it. "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import numpy as np \n",
"import pandas as pd\n",
"import patsy \n",
"from ggplot import * \n",
"%pylab inline"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
},
{
"output_type": "stream",
"stream": "stderr",
"text": [
"WARNING: pylab import has clobbered these variables: ['xlim', 'ylim']\n",
"`%matplotlib` prevents importing * from pylab and numpy\n"
]
}
],
"prompt_number": 117
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# generate a dataset and plot it\n",
"da = np.random.multivariate_normal([1,1], [[1, 0.7],[0.7, 1]], 300)\n",
"dfa = pd.DataFrame({'x1':da[:,0], 'x2': da[:,1], 'type' : 1})\n",
"db1 = np.random.multivariate_normal([3,0], [[0.2, 0],[0, 0.2]], 150)\n",
"dfb1 = pd.DataFrame({'x1':db1[:,0], 'x2': db1[:,1], 'type' : 0})\n",
"db2 = np.random.multivariate_normal([0,3], [[0.2, 0],[0, 0.2]], 150)\n",
"dfb2 = pd.DataFrame({'x1':db2[:,0], 'x2': db2[:,1], 'type' : 0})\n",
"df = pd.concat([dfa, dfb1, dfb2])\n",
"ggplot(aes(x='x1', y='x2', color=\"type\"), data=df) + geom_point() + ggtitle(\"sampled data\")"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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04OiRjzIbDDAqhTFyTP1DwwhGCk4Cc/hIIt/9MbqiAtWjR5OspEdo1wXTbNPo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\nERERuY6Bg4iIiFzHwEFERESu+/9WIvCYrDz9ZwAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x11173fed0>"
]
},
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 118,
"text": [
"<ggplot: (286565097)>"
]
}
],
"prompt_number": 118
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We've generated a classification problem that is impossible to split linearly. Typically we would expect the (linear) logistic regression to perform poorly here and we would expect a (non-linear) support vector machine to perform well.\n",
"\n",
"### Typical Outcome "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from sklearn.linear_model import LogisticRegression\n",
"from sklearn.svm import SVC\n",
"from sklearn.metrics import confusion_matrix\n",
"y,X = patsy.dmatrices(\"type ~ x1 + x2\", df)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 119
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##### Logistic Regression "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"pred = LogisticRegression().fit(X,ravel(y)).predict(X)\n",
"confusion_matrix(y,pred)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 120,
"text": [
"array([[223, 77],\n",
" [118, 182]])"
]
}
],
"prompt_number": 120
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##### Support Vector Machine"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"pred = SVC().fit(X,ravel(y)).predict(X)\n",
"confusion_matrix(y, pred)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 121,
"text": [
"array([[294, 6],\n",
" [ 2, 298]])"
]
}
],
"prompt_number": 121
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## A dirty trick\n",
"\n",
"There is no need for a test set, the random forest obviously outperforms the logistic regression. Still, let's see if we can help the logistic regression out a bit. "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"df['x1x2'] = df['x1'] * df['x2']\n",
"y,X = patsy.dmatrices(\"type ~ x1 + x2 + x1x2\", df)\n",
"pred = LogisticRegression().fit(X,ravel(y)).predict(X)\n",
"confusion_matrix(y,pred)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 122,
"text": [
"array([[290, 10],\n",
" [ 3, 297]])"
]
}
],
"prompt_number": 122
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"I am cheating a little bit because technically I am feeding different data to the logistic regression, but by combining $x_1$ and $x_2$ we have suddenly been able to get a non-linear classification out of a linear model. I am still using the same dataset however, which goes to show that being creative with your data features can have more of an effect than you might expect.\n",
"\n",
"Notice that the support vector machine doesn't show considerable improvement when applying the same trick. "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"pred = SVC().fit(X,ravel(y)).predict(X)\n",
"confusion_matrix(y, pred)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 123,
"text": [
"array([[294, 6],\n",
" [ 2, 298]])"
]
}
],
"prompt_number": 123
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Also for Linear SVM\n",
"\n",
"> Thanks to Stijn Tonk for pointing this out. \n",
"\n",
"Note that we can apply this trick to a linear SVM and we would get similar results. Again we see that the model input seems to matter more than the model chosen."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"y,X = patsy.dmatrices(\"type ~ x1 + x2\", df)\n",
"pred = SVC(kernel='linear').fit(X,ravel(y)).predict(X)\n",
"confusion_matrix(y, pred)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 129,
"text": [
"array([[273, 27],\n",
" [150, 150]])"
]
}
],
"prompt_number": 129
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"y,X = patsy.dmatrices(\"type ~ x1 + x2 + x1x2\", df)\n",
"pred = SVC(kernel='linear').fit(X,ravel(y)).predict(X)\n",
"confusion_matrix(y, pred)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 128,
"text": [
"array([[293, 7],\n",
" [ 3, 297]])"
]
}
],
"prompt_number": 128
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Conclusion \n",
"Why is this trick so useful?\n",
"\n",
"You can apply a little bit more statistical theory to the regression model which is something a lot of clients (especially those who believe in econometrics) find very comforting. It is less a black box and feels more like a simple regression. Notice that factorization machines are powerfull because they use a very similar approach.\n",
"\n",
"The main lesson here is, before you judge a method useless, it might be better to worry about not putting useless data in it."
]
}
],
"metadata": {}
}
]
}
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