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@RMDK
Last active August 29, 2015 14:01
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Learn how to do some basic curve fitting with python!
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{
"worksheets": [
{
"cells": [
{
"metadata": {},
"cell_type": "heading",
"source": "Machine Learning: Curve Fitting Basics - Featuring ggplot",
"level": 1
},
{
"metadata": {},
"cell_type": "markdown",
"source": "This is a series of notebooks (in progress) to document my learning, and hopefully to help others learn machine learning. I would love suggestions / corrections / feedback for these notebooks.\n\n<a target=\"_parent\" href=\"http://rmdk.ca\">Visit my webpage for more</a>. \n\nEmail me: <a href=\"mailto:email.ryan.kelly@gmail.com?Subject=Hey\" target=\"_top\">email.ryan.kelly@gmail.com</a>\n\nI'd love for you to share if you liked this post."
},
{
"metadata": {},
"cell_type": "code",
"input": "social()",
"prompt_number": 51,
"outputs": [
{
"output_type": "pyout",
"html": "\n <a style='float:left; margin-right:5px;' href=\"https://twitter.com/share\" class=\"twitter-share-button\" data-text=\"Check this out\" data-via=\"Ryanmdk\">Tweet</a>\n<script>!function(d,s,id){var js,fjs=d.getElementsByTagName(s)[0],p=/^http:/.test(d.location)?'http':'https';if(!d.getElementById(id)){js=d.createElement(s);js.id=id;js.src=p+'://platform.twitter.com/widgets.js';fjs.parentNode.insertBefore(js,fjs);}}(document, 'script', 'twitter-wjs');</script>\n <a style='float:left; margin-right:5px;' href=\"https://twitter.com/Ryanmdk\" class=\"twitter-follow-button\" data-show-count=\"false\">Follow @Ryanmdk</a>\n<script>!function(d,s,id){var js,fjs=d.getElementsByTagName(s)[0],p=/^http:/.test(d.location)?'http':'https';if(!d.getElementById(id)){js=d.createElement(s);js.id=id;js.src=p+'://platform.twitter.com/widgets.js';fjs.parentNode.insertBefore(js,fjs);}}(document, 'script', 'twitter-wjs');</script>\n <a style='float:left; margin-right:5px;'target='_parent' href=\"http://www.reddit.com/submit\" onclick=\"window.location = 'http://www.reddit.com/submit?url=' + encodeURIComponent(window.location); return false\"> <img src=\"http://www.reddit.com/static/spreddit7.gif\" alt=\"submit to reddit\" border=\"0\" /> </a>\n<script src=\"//platform.linkedin.com/in.js\" type=\"text/javascript\">\n lang: en_US\n</script>\n<script type=\"IN/Share\"></script>\n",
"metadata": {},
"prompt_number": 51,
"text": "<IPython.core.display.HTML at 0x10264fa50>"
}
],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "heading",
"source": "This notebook covers or includes: ",
"level": 2
},
{
"metadata": {},
"cell_type": "markdown",
"source": "\n- Test data creation \n- ggplot plotting \n- Polynomial curve fitting and prediction\n- Complex curve fitting with scipy"
},
{
"metadata": {},
"cell_type": "heading",
"source": "Data Sources:",
"level": 2
},
{
"metadata": {},
"cell_type": "markdown",
"source": "- <a target=\"_parent\" href=\"http://nbviewer.ipython.org/gist/keflavich/4042018\">Adam Ginsburg</a>\n- <a target=\"_parent\" href=\"http://docs.scipy.org/doc/\">SciPy Docs</a>"
},
{
"metadata": {},
"cell_type": "heading",
"source": "TO DO:\n",
"level": 6
},
{
"metadata": {},
"cell_type": "markdown",
"source": "- Goodness of fit tests\n- Other suggestions? Email me: <u>ryan@rmdk.ca</u>"
},
{
"metadata": {},
"cell_type": "heading",
"source": "Getting Started:",
"level": 1
},
{
"metadata": {},
"cell_type": "markdown",
"source": "The goal of any curve fitting is to determine the underlying trend in the data in the presence of variance. This tutorial gets us going with the basics."
},
{
"metadata": {},
"cell_type": "code",
"input": "import scipy as sp\nimport numpy as np\nimport pandas as pd\n\nfrom ggplot import *\n# Enable inline plotting\n%matplotlib inline",
"prompt_number": 3,
"outputs": [],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Create some fake data"
},
{
"metadata": {},
"cell_type": "code",
"input": "x = sp.linspace(-5, 5,100) # 1000 values from 0 - 10\n# Quadratic function\ny = 2*x**2 + 5*x + 0",
"prompt_number": 4,
"outputs": [],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Load data into pandas data frame"
},
{
"metadata": {},
"cell_type": "code",
"input": "df = pd.DataFrame(zip(x,y), columns = ['x','y'])",
"prompt_number": 693,
"outputs": [],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Lets plot it quick to take a look\n\n\n<a href=\"http://blog.yhathq.com/posts/ggplot-for-python.html\">What is this amazing ggplot library you are using?</a>"
},
{
"metadata": {},
"cell_type": "code",
"input": "ggplot(df, aes(\"x\", \"y\"))+geom_line()+geom_point()",
"prompt_number": 694,
"outputs": [
{
"output_type": "display_data",
"metadata": {},
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ffvtt1CV1sUQv8ckSQ+jmzZu1Zs0arVu3TqFQSDU1NVq4cKF8Pp8CgYBSUlIU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\niIjbqQkVEREREbf7f0LDubsY1vaSAAAAAElFTkSuQmCC\n",
"text": "<matplotlib.figure.Figure at 0x10d88e410>"
},
{
"output_type": "pyout",
"prompt_number": 694,
"metadata": {},
"text": "<ggplot: (279439225)>"
}
],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Next we will add some error (noise) to make the data more \"life-like\", and then plot it without the line."
},
{
"metadata": {},
"cell_type": "code",
"input": "noisy_y = y + np.random.randn(y.size) # Random normal noise",
"prompt_number": 668,
"outputs": [],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "code",
"input": "ggplot(df, aes(\"x\", noisy_y))+geom_point()",
"prompt_number": 696,
"outputs": [
{
"output_type": "pyout",
"prompt_number": 696,
"metadata": {},
"text": "<repr(<ggplot.ggplot.ggplot at 0x10a8b3250>) failed: ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()>"
},
{
"output_type": "display_data",
"metadata": {},
"png": 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AFJmzZ89qx44dSk1N/ctjqlevLrP5/ypKpUqVFB0dXRTx4ABuWwMAgCKxevVqTZgwQefO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\nAMYojwAAADD2Hw8+Oizu2DbrAAAAAElFTkSuQmCC\n",
"text": "<matplotlib.figure.Figure at 0x10a8b3710>"
}
],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "heading",
"source": "Fitting the data",
"level": 1
},
{
"metadata": {},
"cell_type": "markdown",
"source": "To do this we can utilize SciPy's **polyfit ( )** function. We will then fit several polynomial shapes (starting with a straight line) and aim to find the order of the polynomial that minimizes the error function defined above.\n<hr>"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "First we will define an error function, which will guide us in choosing the correct model. The error is simply the squared distance of the model's prediction to the observed data above."
},
{
"metadata": {},
"cell_type": "code",
"input": "def error(f,x,y):\n return sp.sum((f(x)-y)**2)",
"prompt_number": 697,
"outputs": [],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Where f will be our fitted model and x / y contain our original data."
},
{
"metadata": {},
"cell_type": "heading",
"source": "First Order Polynomial",
"level": 2
},
{
"metadata": {},
"cell_type": "markdown",
"source": "The most basic model fit would be a straight line. This is actually \"linear regression\" but it is also a special case of a more general function: a first-order polynomial. **First-Order** means that the highest exponent of **x** in the equation is 1."
},
{
"metadata": {},
"cell_type": "code",
"input": "pf1, residuals, rank, sv, rcond = sp.polyfit(x, noisy_y, 1, full =True)",
"prompt_number": 698,
"outputs": [],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "markdown",
"source": "By setting the **full** parameter to **True** we get additional output coefficients from the fitting process, but we only really care about the residuals, which is the error of the estimation."
},
{
"metadata": {},
"cell_type": "code",
"input": "print (\"Model parameters: %s\" % pf1)\n\nprint \"\\n\", residuals\nprint pf1",
"prompt_number": 700,
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "Model parameters: [ 4.88882894 16.42093795]\n\n[ 28290.55679858]\n[ 4.88882894 16.42093795]\n"
}
],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Therefore the minimized straight line fits the following function:"
},
{
"metadata": {},
"cell_type": "code",
"input": "print \"f(x) = {} * x^2 + {}\".format(pf1[0], pf1[1])",
"prompt_number": 701,
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "f(x) = 4.88882893728 * x^2 + 16.4209379538\n"
}
],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Now we use **poly1d ( )** to create a model function object from the model parameters derived above."
},
{
"metadata": {},
"cell_type": "code",
"input": "f1 = sp.poly1d(pf1)\nprint(error(f1, x, noisy_y))",
"prompt_number": 702,
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "28290.5567986\n"
}
],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Lets take a look at what we've fit."
},
{
"metadata": {},
"cell_type": "code",
"input": "ggplot(df, aes(\"x\", noisy_y))+geom_point() + \\\ngeom_line(aes(x, y = f1(x)), color = \"red\")",
"prompt_number": 704,
"outputs": [
{
"output_type": "pyout",
"prompt_number": 704,
"metadata": {},
"text": "<repr(<ggplot.ggplot.ggplot at 0x10a8d6650>) failed: ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()>"
},
{
"output_type": "display_data",
"metadata": {},
"png": 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IiIjIaiyPRERERGQ1lkciIiIishrLIxERERFZjeWRiIiIiKzG8khERESiotVq8eabb6Jz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\nRwAAALiN8ggAAAC3UR4BAADgtv8HrFBWyeaWCngAAAAASUVORK5CYII=\n",
"text": "<matplotlib.figure.Figure at 0x10af88890>"
}
],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "markdown",
"source": "This clearly is not the best we can do."
},
{
"metadata": {},
"cell_type": "markdown",
"source": "<hr>"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Lets do the same thing, but increase the variance."
},
{
"metadata": {},
"cell_type": "code",
"input": "noisy_y = y + np.random.randn(y.size)*10\n\npf1 = sp.polyfit(x, noisy_y, 1)\n\nf1 = sp.poly1d(pf1)",
"prompt_number": 705,
"outputs": [],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "code",
"input": "ggplot(df, aes(x, noisy_y))+geom_point() + \\\ngeom_line(aes(x, y = f1(x)), color = \"red\") + \\\ngeom_line(aes(x, 2*x**2 + 5*x + 0), color = \"blue\", size = 2)",
"prompt_number": 707,
"outputs": [
{
"output_type": "pyout",
"prompt_number": 707,
"metadata": {},
"text": "<repr(<ggplot.ggplot.ggplot at 0x10a44a690>) failed: ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()>"
},
{
"output_type": "display_data",
"metadata": {},
"png": 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IDIbIgNRSoX7ZuhU++wwWLoQdO+Dmm2HwYOjUCUtkJBYgyu+Vyh/5FB7379/P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\n2dk4HA5fSwkqTz31FFu2bGHPnj1YLBb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kQlQQkjxWQCoV/Otf+dx1VwHPPVeJo0d96Nu3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\nuyDr1Oeg9wAAAABJRU5ErkJggg==\n",
"text": "<matplotlib.figure.Figure at 0x10a44aa90>"
}
],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "markdown",
"source": "- There are some small bugs with the ggplot python module, which cuts off the legends.\n\n- The dotted **blue** line is the *actual* data behind the noise\n- The **red** line is our current estimation."
},
{
"metadata": {},
"cell_type": "heading",
"source": "Second Order Polynomial",
"level": 2
},
{
"metadata": {},
"cell_type": "markdown",
"source": "We can see that we have are capturing some of the trend with the red line, but not all of it. Lets try higher-order polynomials."
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Recall the error term from our first order polynomial model:"
},
{
"metadata": {},
"cell_type": "code",
"input": "print error(f1, x, noisy_y)",
"prompt_number": 708,
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "29972.3791058\n"
}
],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Alone this error means nothing, but by comparing competing models, we can use the reported error to judge the most appropriate model."
},
{
"metadata": {},
"cell_type": "code",
"input": "# Second order Polynomial\npf2 = sp.polyfit(x, noisy_y, 2)\nf2 = sp.poly1d(pf2)\nprint f2",
"prompt_number": 711,
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": " 2\n1.909 x + 5.027 x + 1.714\n"
}
],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "code",
"input": "print error(f2, x, noisy_y)",
"prompt_number": 713,
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "8901.42029545\n"
}
],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "code",
"input": "print \"The error was reduced from {} to {}, a difference of {}\".format(\nerror(f1, x, noisy_y), error(f2, x, noisy_y), error(f1, x, noisy_y)-error(f2, x, noisy_y))",
"prompt_number": 714,
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "The error was reduced from 29972.3791058 to 8901.42029545, a difference of 21070.9588103\n"
}
],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "code",
"input": "ggplot(df, aes(\"x\", noisy_y))+geom_point(size = 4) + \\\ngeom_line(aes(x, y = f1(x)), color = \"red\") + \\\ngeom_line(aes(x, 2*x**2 + 5*x + 0), color = \"blue\", linetype = \"dashed\") + \\\ngeom_line(aes(x, y = f2(x)), color = \"green\", size=2) ",
"prompt_number": 715,
"outputs": [
{
"output_type": "pyout",
"prompt_number": 715,
"metadata": {},
"text": "<repr(<ggplot.ggplot.ggplot at 0x10af98c50>) failed: ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()>"
},
{
"output_type": "display_data",
"metadata": {},
"png": 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rCQIi4p6aN2+OyWTiwQcfdO7ANhs++/bln2GMicHr8mUsnTqRPmYM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\nsP8HXVTY28TLWt4AAAAASUVORK5CYII=\n",
"text": "<matplotlib.figure.Figure at 0x10af98110>"
}
],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Here we go, we can clearly see that the **green line** (second-order polynomial) is almost exactly the actually underlying trend."
},
{
"metadata": {},
"cell_type": "markdown",
"source": "How about we test a few polynomial errors at once to be a bit more efficient."
},
{
"metadata": {},
"cell_type": "code",
"input": "def poly_test(range, x, y):\n func_l = []\n error_l = []\n i = 1\n for order in range:\n \n pf = sp.polyfit(x, y, order)\n func = sp.poly1d(pf)\n err = error(func, x, y)\n print \"Order: {}, Error = {}\".format(i, err)\n \n func_l.append(func)\n error_l.append([i, err])\n \n i += 1\n \n error_l = pd.DataFrame((error_l), columns = [\"Order\", \"Error\"])\n return error_l, func_l",
"prompt_number": 910,
"outputs": [],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "code",
"input": "error_tests, poly_tests = poly_test(xrange(1,20), x, noisy_y)",
"prompt_number": 717,
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "Order: 1, Error = 29972.3791058\nOrder: 2, Error = 8901.42029545\nOrder: 3, Error = 8889.43020048\nOrder: 4, Error = 8827.05812909\nOrder: 5, Error = 8785.33129955\nOrder: 6, Error = 8733.05890881\nOrder: 7, Error = 8498.3744727\nOrder: 8, Error = 8407.08751693\nOrder: 9, Error = 8384.44871846\nOrder: 10, Error = 8074.70017756\nOrder: 11, Error = 8035.84966396\nOrder: 12, Error = 7942.28166492\nOrder: 13, Error = 7698.98413081\nOrder: 14, Error = 7612.94832123\nOrder: 15, Error = 7602.49546217\nOrder: 16, Error = 7567.91985168\nOrder: 17, Error = 7368.93508242\nOrder: 18, Error = 7089.18637868\nOrder: 19, Error = 6979.14519774\n"
}
],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Plot the best fit"
},
{
"metadata": {},
"cell_type": "code",
"input": "ggplot(df, aes(\"x\", noisy_y))+geom_point(size = 4) + \\\ngeom_line(aes(x, 2*x**2 + 5*x + 0), color = \"blue\", linetype = \"dashed\") + \\\ngeom_line(aes(x, y = poly_tests[18](x)), color = \"green\")",
"prompt_number": 734,
"outputs": [
{
"output_type": "pyout",
"prompt_number": 734,
"metadata": {},
"text": "<repr(<ggplot.ggplot.ggplot at 0x10b7f9750>) failed: ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()>"
},
{
"output_type": "display_data",
"metadata": {},
"png": 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svhAmIsYdbeLfJhERERmdDLcMSF2lGOI1RN+lGB3etiYiIiKjkpqXis/OfoZNPTfB1MRU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\nxvBIRERERIL9P695WymlQdoVAAAAAElFTkSuQmCC\n",
"text": "<matplotlib.figure.Figure at 0x10a466dd0>"
}
],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Woah! Hang on... Are we actually capturing the underlying process in this data? By using this higher order polynomial (9), we are actually capturing the underlying process **and** the noise. This is called **overfitting**\n\nA simplistic way to tell if we are overfitting is to examine the error improvement decay with increasing polynomial levels. In these data, we can see that there isnt really much error reduction after polynomial 2, therefore this would be our chosen model fit. There are more sophisticated ways of doing this, which will be discussed later."
},
{
"metadata": {},
"cell_type": "code",
"input": "breaks = xrange(0,21)\nggplot(error_tests, aes(x='Order', y='Error'))+geom_line() + \\\nscale_x_continuous(breaks = breaks, labels = breaks)",
"prompt_number": 733,
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"png": 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3oQAAAOQkCmwOYhkBAADAzCiwOYhbaQEAAMyMApuDOAMLAAAwMwpsDgqFQhRYAACAGVBg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\nAGyFAAsAAABb+QtpJ7NJfWBdFgAAAABJRU5ErkJggg==\n",
"text": "<matplotlib.figure.Figure at 0x102f89150>"
},
{
"output_type": "pyout",
"prompt_number": 733,
"metadata": {},
"text": "<ggplot: (280480369)>"
}
],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "heading",
"source": "Prediction:",
"level": 2
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Ok, so say we have chosen a second-order polynomial to fit our model. Lets utilize our ability to estimate the underlying trend and predict future data. Generally more sophisticated statistics would be used here to analyze the variance when predicting farther and farther into the future or unknown.\n\n\nTo find the desired unknown **y** value, we subtract **y** at *desired position i* from the polynomial. We then use **fsolve** from SciPy's **optimize** module to simply solve the polynomial function we created. Say we want to know what **x** will be when **y** = 150."
},
{
"metadata": {},
"cell_type": "code",
"input": "print f2\n\nfrom scipy.optimize import fsolve\n\nconverged = fsolve(f2 - 150, 0)\nprint (\"y = 150 is expected when x = {}\". format(converged[0]))",
"prompt_number": 746,
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": " 2\n1.909 x + 5.027 x + 1.714\ny = 150 is expected when x = 7.59426937669\n"
}
],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "heading",
"source": "Power Law Functions ",
"level": 1
},
{
"metadata": {},
"cell_type": "markdown",
"source": "We can take advantage of the fact that a power law is linear in log-space.\n\nLets make some new data."
},
{
"metadata": {},
"cell_type": "code",
"input": "t = sp.linspace(0.1,5, 1000)\n# Power function\na = 1.5\nb = 2\nz = a * t**b\n\nnoisy_y = z + sp.random.randn(z.size)**1/2\n\ndf = pd.DataFrame(zip(t,noisy_y), columns = [\"x\", \"y\"])\n\n# Plot data points and actual data as a line\nggplot(df, aes(\"x\", \"y\"))+geom_point(size = 4)+ \\\ngeom_line(df,aes(x=\"x\", y=z), color = \"blue\")",
"prompt_number": 930,
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"png": 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3Gh1Z5DephIqIiASRVq1a0apVKzweDwUFBcTGNmDy5PaUl/+dZs2+xOFoRnFx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\nKE6EAgBQnAgFAKC437xVNIOG72IVAAAAAElFTkSuQmCC\n",
"text": "<matplotlib.figure.Figure at 0x10a46a190>"
},
{
"output_type": "pyout",
"prompt_number": 930,
"metadata": {},
"text": "<ggplot: (279250721)>"
}
],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "markdown",
"source": "First we need to compute the error for a polynomial fit on untransformed data"
},
{
"metadata": {},
"cell_type": "code",
"input": "error_tests, poly_tests = poly_test(xrange(1,10), t, noisy_y)",
"prompt_number": 960,
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "Order: 1, Error = 7582.21726058\nOrder: 2, Error = 239.360725199\nOrder: 3, Error = 239.229365939\nOrder: 4, Error = 238.469422373\nOrder: 5, Error = 238.424914846\nOrder: 6, Error = 238.396983769\nOrder: 7, Error = 238.3955276\nOrder: 8, Error = 237.987503728\nOrder: 9, Error = 237.975969779\n"
}
],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Again, a second-order polynomial is most appropriate.\n\nNext lets try linearizing the data with a natural log"
},
{
"metadata": {},
"cell_type": "code",
"input": "\n# Change the variables using a natural log\nx = np.log(t)\ny = np.log(noisy_y) # Add error\n\ndf = pd.DataFrame(zip(x, y), columns = [\"x\", \"y\"])\n\nggplot(df, aes(\"x\", \"y\"))+geom_point(size = 4)+ \\\ngeom_line(aes(x=\"x\", y=np.log(a * t**b)), color = \"blue\")",
"prompt_number": 939,
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"png": 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ahIenDySqVq0aBoMBg8FA8+bNKViwIBaLhd9++40lS5YQFxfnoCsUeTIogIqI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\n",
"text": "<matplotlib.figure.Figure at 0x10a4fea90>"
},
{
"output_type": "pyout",
"prompt_number": 939,
"metadata": {},
"text": "<ggplot: (279196401)>"
}
],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "markdown",
"source": "The **blue** line is actually our observed trend, without noise. We can see that power laws are very sensitive to variation and noise. Some data points are not even plotted here because they became NaN after we logged them. We could either:\n\n- Transform the data to positive numbers before we log.\n- Just remove the NaN\n\nTo make this simpler, we will just remove these values"
},
{
"metadata": {},
"cell_type": "code",
"input": "# First make sure we didnt create any NaN values by logging a negative number\nprint \"# of missing values in y: {}\".format(len(y[pd.isnull(y)]))",
"prompt_number": 980,
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "# of missing values in y: 39\n"
}
],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "markdown",
"source": "To remove these values, we will just subset the data which are not NaN. We do this by applying a boolean mask. There are several ways to do this, but an easy one is to use pandas **isnull ( )**, which will check for all different types of NaN values, such as NA, NAN, NULL, NaN."
},
{
"metadata": {},
"cell_type": "code",
"input": "bad = pd.isnull(y)\nbad[0:5]",
"prompt_number": 949,
"outputs": [
{
"output_type": "pyout",
"prompt_number": 949,
"metadata": {},
"text": "array([False, True, False, False, False], dtype=bool)"
}
],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Once we have all the index's where **noisy_y** = NaN, we pass it to the array as an index array. We use **-** before the mask because we want everything that **is not** bad."
},
{
"metadata": {},
"cell_type": "code",
"input": "clean_y = y[-bad]\nclean_x = x[-bad]",
"prompt_number": 950,
"outputs": [],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Now finally we can fit our first-order polynomial."
},
{
"metadata": {},
"cell_type": "code",
"input": "power_law_fit = sp.polyfit(clean_x, clean_y, 1)\npower_law_func = sp.poly1d(power_law_fit)\n\n#report error\nprint \"Error improvement is {}\".format(error_tests[1:2]['Error'].values - \\\n (error(power_law_func, clean_x, clean_y)))\n\nfitted_y = sp.polyval(power_law_fit, clean_x)",
"prompt_number": 984,
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "Error improvement is [ 38.86933803]\n"
}
],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "code",
"input": "df = pd.DataFrame(zip(clean_x, clean_y), columns = [\"x\", \"y\"])\nexpected_y = np.log(a* t**b)\n# Red line is new fit\n# Blue line is actual data\nggplot(df, aes(\"x\", \"y\"))+geom_point(size = 4)+ \\\ngeom_line(aes(x=\"x\", y=fitted_y, color = \"red\")) + \\\ngeom_line(aes(x=np.log(t), y = np.log(z), color = \"blue\"))",
"prompt_number": 989,
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"png": 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gHTbbfgoXbkCZMnN48cVW2R+pG41GSpYsSWZmJlarleTkZC5evOjBoxS5M+kM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\nrkJggg==\n",
"text": "<matplotlib.figure.Figure at 0x10a404ed0>"
},
{
"output_type": "pyout",
"prompt_number": 989,
"metadata": {},
"text": "<ggplot: (279260945)>"
}
],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "markdown",
"source": "By combining the results of the error and the plot we can see that this new fit (**red line**) is slightly more accurate compared to our regular second-order polynomial fitting.\n\nHowever, to achieve this result, I had to reduce the error quite significantly."
},
{
"metadata": {},
"cell_type": "heading",
"source": "What about more complex curves?",
"level": 1
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Let's create some new fake data."
},
{
"metadata": {},
"cell_type": "code",
"input": "x = np.linspace(0,2*np.pi, 50)\n\ndef sinfun(x,a,b):\n return a*np.sin(x-b)\n\ny = sinfun(x,1,0)\n\ndf = pd.DataFrame(zip(x,y), columns = ['x','y'])\n\nggplot(df, aes(x,y))+geom_line(color=\"blue\")+geom_point()",
"prompt_number": 1034,
"outputs": [
{
"output_type": "pyout",
"prompt_number": 1034,
"metadata": {},
"text": "<repr(<ggplot.ggplot.ggplot at 0x10b7f9f90>) failed: ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()>"
},
{
"output_type": "display_data",
"metadata": {},
"png": 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5GjZsGE2bNiUmZjuhoYepV28a1113nelYIiJeSVfByVmlpVmYMyead989ZTqK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\nRK5CYII=\n",
"text": "<matplotlib.figure.Figure at 0x10e17d790>"
}
],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Lets add some error, just like before."
},
{
"metadata": {},
"cell_type": "code",
"input": "noisy_y = y + np.random.randn(y.size)\n\nggplot(df, aes(\"x\", noisy_y))+geom_point()+geom_line(aes(\"x\", \"y\", color = \"blue\"))",
"prompt_number": 1035,
"outputs": [
{
"output_type": "pyout",
"prompt_number": 1035,
"metadata": {},
"text": "<repr(<ggplot.ggplot.ggplot at 0x10a4de350>) failed: ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()>"
},
{
"output_type": "display_data",
"metadata": {},
"png": 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5UahRo4bKlSt30WOVKlUq0nN6O0JiGfTuu8EaNixS06ena+rUC6XinrfAlQoI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\n",
"text": "<matplotlib.figure.Figure at 0x10a4de150>"
}
],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Sometimes it's best to let SciPy handle more complex curves using the **curve_fit ( )** function from **scipy.optimize**. The function returns the optimized fitted parameters and a covariance matrix.\n\nThe diagonals of a covariance matrix are the variances and we take the root of them to get the standard deviation."
},
{
"metadata": {},
"cell_type": "code",
"input": "from scipy.optimize import curve_fit\n\nfitpars, covm = curve_fit(sinfun, x, noisy_y)\n\nvariance = np.sqrt(covm.diagonal())\nprint fitpars, variance",
"prompt_number": 1039,
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "[ 1.49563761 -0.01659767] [ 0.18290973 0.11987486]\n"
}
],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "code",
"input": "ggplot(df, aes(\"x\", noisy_y))+geom_point()+ \\\ngeom_line(aes(\"x\", \"y\", color=\"blue\")) + \\\ngeom_line(aes(\"x\", sinfun(x, *fitpars), color = 'red'))",
"prompt_number": 1046,
"outputs": [
{
"output_type": "pyout",
"prompt_number": 1046,
"metadata": {},
"text": "<repr(<ggplot.ggplot.ggplot at 0x10a404c10>) failed: ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()>"
},
{
"output_type": "display_data",
"metadata": {},
"png": 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GDBhAp06dmDRpEna7/d9fJCJSCikkFlP/vFQXFBREeHh4gZzLeOECEd27c7Jv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\n5ZRafn4we3YivXun0qFDJJ9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/fjBDh5qYPz+B4cNTLttB6HXsGPTrR9KqVTiuu67wCy3B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\nCAAAAANKIgAAAAwoiQAAADD4fwyhLS9x5PLCAAAAAElFTkSuQmCC\n",
"text": "<matplotlib.figure.Figure at 0x10a50e990>"
}
],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "markdown",
"source": "This is a decent fit, but you can see that it is catching quite a bit of the noise still. Granted, there is a lot of error present in this graph."
},
{
"metadata": {},
"cell_type": "markdown",
"source": "<a href=\"http://rmdk.ca\">Visit my webpage for more</a>. Email me: <u>ryan@rmdk.ca</u>"
},
{
"metadata": {},
"cell_type": "code",
"input": "from IPython.core.display import HTML\n\n\ndef css_styling():\n styles = open(\"/users/ryankelly/desktop/custom_notebook.css\", \"r\").read()\n\n return HTML(styles)\ncss_styling()\n",
"prompt_number": 1,
"outputs": [
{
"output_type": "pyout",
"html": "\n<style>\nbody {\n font-family: Century Gothic, sans;\n\n}\n\n\ndiv.text_cell_render h1 { /* Main titles bigger, centered */\nfont-size: 2.2em;\nline-height:1.4em;\ntext-align:center;\n}\n\n/*Input and output cells formatting*/\ndiv.prompt.input_prompt, div.prompt.output_prompt {\n visibility: hidden;\n /*font-family: Consolas;*/\n color: #575748;\n /*background-color: #CCCCCC;*/\n border: 0px;\n width: 6.5em;\n float:left;\n}\n\n\ndiv.output_subarea.output_text.output_stream.output_stdout,div.output_subarea.output_text {\n margin-left: 1.5em;\n padding-top: 1em;\n padding-bottom: 0.5em;\n margin-top: 8px; /*This is for getting the box-shadow property of the parent to display properly;*/\n}\n\ndiv.cell { /* Tunes the space between cells */\nmargin-top:1em;\nmargin-bottom:1em;\nwidth:100%;\nmargin-right:auto;\noverflow-x:hidden;\n}\n\ndiv.text_cell_render{\n overflow-x:hidden;\n \n}\n\n\ndiv.input{\nmargin-right:1%;\n}\n\n</style>\n \n\n\n\n",
"metadata": {},
"prompt_number": 1,
"text": "<IPython.core.display.HTML at 0x10264f3d0>"
}
],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "code",
"input": "def social():\n code = \"\"\"\n <a style='float:left; margin-right:5px;' href=\"https://twitter.com/share\" class=\"twitter-share-button\" data-text=\"Check this out\" data-via=\"Ryanmdk\">Tweet</a>\n<script>!function(d,s,id){var js,fjs=d.getElementsByTagName(s)[0],p=/^http:/.test(d.location)?'http':'https';if(!d.getElementById(id)){js=d.createElement(s);js.id=id;js.src=p+'://platform.twitter.com/widgets.js';fjs.parentNode.insertBefore(js,fjs);}}(document, 'script', 'twitter-wjs');</script>\n <a style='float:left; margin-right:5px;' href=\"https://twitter.com/Ryanmdk\" class=\"twitter-follow-button\" data-show-count=\"false\">Follow @Ryanmdk</a>\n<script>!function(d,s,id){var js,fjs=d.getElementsByTagName(s)[0],p=/^http:/.test(d.location)?'http':'https';if(!d.getElementById(id)){js=d.createElement(s);js.id=id;js.src=p+'://platform.twitter.com/widgets.js';fjs.parentNode.insertBefore(js,fjs);}}(document, 'script', 'twitter-wjs');</script>\n <a style='float:left; margin-right:5px;'target='_parent' href=\"http://www.reddit.com/submit\" onclick=\"window.location = 'http://www.reddit.com/submit?url=' + encodeURIComponent(window.location); return false\"> <img src=\"http://www.reddit.com/static/spreddit7.gif\" alt=\"submit to reddit\" border=\"0\" /> </a>\n<script src=\"//platform.linkedin.com/in.js\" type=\"text/javascript\">\n lang: en_US\n</script>\n<script type=\"IN/Share\"></script>\n\"\"\"\n return HTML(code)",
"prompt_number": 50,
"outputs": [],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "code",
"input": "",
"outputs": [],
"language": "python",
"trusted": true,
"collapsed": false
}
],
"metadata": {}
}
],
"metadata": {
"gist_id": "b50aef5cb1edda02caf7",
"name": "",
"signature": "sha256:7eac4b17675d4073f873c2d0e105433dda5a80b9464586bee6d7376784d86578"
},
"nbformat": 3
}
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