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@rawlik
Created March 10, 2014 20:19
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{
"metadata": {
"name": "correlations_in_fit"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": "%pylab inline\nfrom scipy.optimize import curve_fit",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "Populating the interactive namespace from numpy and matplotlib\n"
}
],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": "Let's take a very simple model with two parameters - a line and generate some data."
},
{
"cell_type": "code",
"collapsed": false,
"input": "def model(x, a, b):\n return a*x + b\n\na, b = 1, 3\nnoise = 0.1\n\nX = linspace(0, 2)\nD = model(X, a, b) + randn(X.size) * noise\n\nfigure(figsize=(10,6))\nerrorbar(X, D, yerr=noise, fmt='k.', label='data')\nplot(X, model(X, a, b), 'b--', label='real model')\nlegend(loc='best')",
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 2,
"text": "<matplotlib.legend.Legend at 0x7f4c019cad10>"
},
{
"metadata": {},
"output_type": "display_data",
"png": 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Rd0+cdC1z0liAgcb2cgs1NTVatWpVl12BHZPX6+rqtHTpUpLXAfTIbLK21xtY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\n",
"text": "<matplotlib.figure.Figure at 0x7f4c021042d0>"
}
],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": "Now let's fit model to data:"
},
{
"cell_type": "code",
"collapsed": false,
"input": "popt, pcov = curve_fit(model, X, D)\n\n# model with fitted parameters\nfit = lambda x: model(x, *popt)\n\nfigure(figsize=(10,6))\nerrorbar(X, D, yerr=noise, fmt='k.', label='data')\nplot(X, model(X, a, b), 'b--', label='real model')\nplot(X, fit(X), 'r--', label='fit: {:.4g}*x + {:.4g}f'.format(*popt))\nlegend(loc='best')",
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 3,
"text": "<matplotlib.legend.Legend at 0x7f4c01944a90>"
},
{
"metadata": {},
"output_type": "display_data",
"png": 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//x3mzTPXAuPjYfBgc9++Ejxd48lXKLBSYCUiIj7AF7+TrFb44ANzEmrrVvO/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\nRK5CYII=\n",
"text": "<matplotlib.figure.Figure at 0x7f4c01982110>"
}
],
"prompt_number": 3
},
{
"cell_type": "markdown",
"metadata": {},
"source": "Fitting procedures usually return also a covariance matrix. Most of the times people are only interested in what lies on it's diagonal: estimates of parameters' variances."
},
{
"cell_type": "code",
"collapsed": false,
"input": "print('Fitted parameters: ', popt)\nprint('Standard deviation estimates:', sqrt(pcov.diagonal()))",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "Fitted parameters: [ 0.99589529 2.98602926]\nStandard deviation estimates: [ 0.02644494 0.03069138]\n"
}
],
"prompt_number": 4
},
{
"cell_type": "markdown",
"metadata": {},
"source": "However, covariance matrix also has non-diagonal elements which carry a very important information - correlations between parameters. Correlations are more clearly visible if we calculate [Pearson correlation matrix](http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient):"
},
{
"cell_type": "code",
"collapsed": false,
"input": "print('Covariance matrix estimate returned by fitting procedure:')\nprint(pcov)\nprint()\nprint('Pearson correlation matrix estimate:')\nSigma = sqrt(pcov.diagonal())\nprint((pcov / Sigma).T / Sigma)",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "Covariance matrix estimate returned by fitting procedure:\n[[ 0.00069933 -0.00069933]\n [-0.00069933 0.00094196]]\n\nPearson correlation matrix estimate:\n[[ 1. -0.86164044]\n [-0.86164044 1. ]]\n"
}
],
"prompt_number": 5
},
{
"cell_type": "markdown",
"metadata": {},
"source": "Elements of this matrix are Pearson correlation coefficients between parameters. Pearson correlation coefficient is 1 when variables are in ideal linear correlation, -1 when in an anticorrelation and 0 when they are not linearly correlated. Obviously parameters are perfectly correlated with themselves, hence ones on the diagonal, but from the non-diagonal elements we see that our parameters are also strongly anticorrelated with each other. What does it mean and why should anybody care?\n\nTo explain it it's good to realise what fitting actually is, and it's nothing else than [minimisation of a function in parameters space](http://en.wikipedia.org/wiki/Least_squares). Inverse of the correlation matrix defines a [quadratic form](http://en.wikipedia.org/wiki/Quadratic_form) that describes *shape* of this minimum. It's good to remember that every sensible local minimum in it's neighbourhood can be described in general as a quadratic form (which follows directly from Taylor expansion - in extremum first derivative vanishes so the first non-trivial term is quadratic one).\n\nIn order to look at our fit's minimum let's first define a funciton to visualise any two dimensional quadratic form:"
},
{
"cell_type": "code",
"collapsed": false,
"input": "def plot_quadratic_form(A, b):\n \"\"\"Plot 2D quadratic form given by matrix A centered in vector b.\"\"\"\n N = 100\n # reasonable boundaries\n X = linspace(b[0] - 1/sqrt(A[0,0]), b[0] + 1/sqrt(A[0,0]), num=N)\n Y = linspace(b[1] - 1/sqrt(A[1,1]), b[1] + 1/sqrt(A[1,1]), num=N)\n \n Z = zeros((N, N))\n \n for j, x in enumerate(X):\n for i, y in enumerate(Y):\n v = array([x,y])\n Z[i,j] = 0.5 * (v - b).dot(A.dot((v - b)))\n \n contourf(X, Y, Z, 100)\n contour(X, Y, Z, 10)\n \nA = array([[2, 0],\n [0, 1]])\nbb = array([10,20])\nplot_quadratic_form(A,bb)",
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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sHFyjWi0xPXNAcfaYeKI32T5sdK4Cc7uo/BipVb2HAL2PwKaIRJpGwSSzVCDu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\nFSS6bdWmvNVb10k5gqxpena6zvq6W7ZAZ23dzLEmBcbEWLPIME7l7Wx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cc/zRH/2RY30d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wwkvbQQT91NelF17fapRV7q8nfsf1t0sP8sAuQlZvMOg3/dvYSEfal4d+t+/Gvve2zTJkeJeiB5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\nc7GYAAAAAElFTkSuQmCC\n",
"text": "<matplotlib.figure.Figure at 0x7f4c020ff950>"
}
],
"prompt_number": 6
},
{
"cell_type": "markdown",
"metadata": {},
"source": "Let's see how does our fit's minimum look:"
},
{
"cell_type": "code",
"collapsed": false,
"input": "plot_quadratic_form(inv(pcov), popt)",
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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BBBU00k8jAwlzpCvN8ObeMd7eOxRv8/B9Q86jdKamprj22mu5+uqrufPOO82a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\nn0ZcPYPI7lvG5cipGM4G8afSVr6iQAl/JEKi1UZyzRO1P+PzMTSviml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"text": "<matplotlib.figure.Figure at 0x7f4c01763dd0>"
}
],
"prompt_number": 7
},
{
"cell_type": "markdown",
"metadata": {},
"source": "We see that the minimum is centered in fitted parameters' optimal values and it's size roughly corresponds to their standard deviation estimates. But the minimum is also tilted and that tilt is caused exactly by the fact that in our fit $a$ and $b$ parameters are correlated. We can find base where parameters are not correlated by diagonalising the covariance matrix:"
},
{
"cell_type": "code",
"collapsed": false,
"input": "eigvalues, eigvectors = eig(pcov)\nprint('Eigenvectors:')\nprint(eigvectors)",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "Eigenvectors:\n[[-0.76515255 0.64384903]\n [-0.64384903 -0.76515255]]\n"
}
],
"prompt_number": 8
},
{
"cell_type": "markdown",
"metadata": {},
"source": "So these two parameters are uncorrelated:\n$$c \\approx -0.77a - 0.64b$$\n$$d \\approx 0.64a - 0.77b$$\n\nThe minimum in base defined by above parameters isn't tilted, so if we make a model with these and perform a fit we should get diagonal covariance and Pearson's coefficients matrices."
},
{
"cell_type": "code",
"collapsed": false,
"input": "def eigmodel(x, c, d):\n p = array([c,d])\n return eigvectors[0].dot(p) * x + eigvectors[1].dot(p)\n\neigpopt, eigpcov = curve_fit(eigmodel, X, D)\n\nprint('Covariance matrix estimate returned by fitting procedure:')\nprint(eigpcov)\nprint()\nprint('Pearson correlation matrix estimate:')\nSigma = sqrt(eigpcov.diagonal())\nprint((eigpcov / Sigma).T / Sigma)\n\nplot_quadratic_form(inv(eigpcov), eigpopt)",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "Covariance matrix estimate returned by fitting procedure:\n[[ 1.10869094e-04 1.80700122e-15]\n [ 1.80700122e-15 1.53042669e-03]]\n\nPearson correlation matrix estimate:\n[[ 1.00000000e+00 4.38679086e-12]\n [ 4.38679086e-12 1.00000000e+00]]\n"
},
{
"metadata": {},
"output_type": "display_data",
"png": 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/KvNCFlbfSxtxgGoIge4jz8ec9prXXn4JYUwycJKHygdT5POzpNJFVucukXDJ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\n",
"text": "<matplotlib.figure.Figure at 0x7f4c015a6a50>"
}
],
"prompt_number": 9
},
{
"cell_type": "markdown",
"metadata": {},
"source": "What do these $c$ and $d$ parameters do? We can visualise that:"
},
{
"cell_type": "code",
"collapsed": false,
"input": "figure(figsize=(10,6))\n\nfor c in linspace(0.9, 1.1) * eigpopt[0]:\n plot(X, eigmodel(X, c, eigpopt[1]), 'r-', alpha=0.5)\n \nfor d in linspace(0.9, 1.1) * eigpopt[1]:\n plot(X, eigmodel(X, eigpopt[0], d), 'g-', alpha=0.5)\n \nerrorbar(X, D, yerr=noise, fmt='k.', label='data')\nplot(X, model(X, a, b), 'b--', label='real')\n\nlegend(loc='best')",
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 10,
"text": "<matplotlib.legend.Legend at 0x7f4c014bc590>"
},
{
"metadata": {},
"output_type": "display_data",
"png": 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HrY+M0Hp3N4mxmhoSa2bfVGoq5vPzkfLRj2Kmvx+JQ0P0XnWd9ldXUwuws5PW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\nUuPvRHZqO4xUBVxtP0HwnEvhqN+TWw24WuxwtjhgwMDSQhz+gLOAkVLTB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Jw86f4GvsWX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fj1Lwi5CvuirNlOrqkvaeIAiCIAhzzpwKq4rNsbxR5sPxCv7NiQrdle5UQCULjz/z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\nzBL/P2D8cdwtzWgOAAAAAElFTkSuQmCC\n",
"text": "<matplotlib.figure.Figure at 0x7f4c015a6d90>"
}
],
"prompt_number": 10
},
{
"cell_type": "markdown",
"metadata": {},
"source": "So why are these correlations important? Firstly they help to understand the fit and secondly because they are important in [propagation of uncertainty](http://en.wikipedia.org/wiki/Propagation_of_uncertainty).\n\nSay that we want to calculate two simple values from fit parameters: $f := a + b$ and $g := a - b$:"
},
{
"cell_type": "code",
"collapsed": false,
"input": "print('f = a + b = %.2g' % (popt[0] + popt[1]))\nprint('g = a - b = %.2g' % (popt[0] - popt[1]))",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "f = a + b = 4\ng = a - b = -2\n"
}
],
"prompt_number": 11
},
{
"cell_type": "markdown",
"metadata": {},
"source": "If we would naively calculate uncertainties accorting to these equations:\n$$\\sigma(f) = \\sqrt{ \\left(\\frac{\\partial f}{\\partial a}\\right)^2 \\sigma(a)^2 + \\left(\\frac{\\partial f}{\\partial b}\\right)^2 \\sigma(b)^2 } = \\sqrt{ 1^2 \\sigma(a)^2 + 1^2 \\sigma(b)^2 } = \\sqrt{ \\sigma(a)^2 + \\sigma(b)^2 }$$\n$$\\sigma(g) = \\sqrt{ \\left(\\frac{\\partial g}{\\partial a}\\right)^2 \\sigma(a)^2 + \\left(\\frac{\\partial g}{\\partial b}\\right)^2 \\sigma(b)^2 } = \\sqrt{ 1^2 \\sigma(a)^2 + (-1)^2 \\sigma(b)^2 } = \\sqrt{ \\sigma(a)^2 + \\sigma(b)^2 } = \\sigma(f)$$\nwe would get following **wrong** uncertainties:"
},
{
"cell_type": "code",
"collapsed": false,
"input": "print('s(f) = %.2g' % sqrt(sum(pcov.diagonal())) )\nprint('s(g) = %.2g' % sqrt(sum(pcov.diagonal())) )",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "s(f) = 0.041\ns(g) = 0.041\n"
}
],
"prompt_number": 12
},
{
"cell_type": "markdown",
"metadata": {},
"source": "To get them right we have to use [the full equations](http://en.wikipedia.org/wiki/Propagation_of_uncertainty#Example):\n$$\\sigma(f) = \\sqrt{ \\left(\\frac{\\partial f}{\\partial a}\\right)^2 \\sigma(a)^2 + \\left(\\frac{\\partial f}{\\partial b}\\right)^2 \\sigma(b)^2 + 2 \\frac{\\partial f}{\\partial a} \\frac{\\partial f}{\\partial b} \\mathrm{cov}(a,b) } = \\sqrt{ \\sigma(a)^2 + \\sigma(b)^2 + 2\\ \\mathrm{cov}(a,b) }$$\n$$\\sigma(g) = \\sqrt{ \\left(\\frac{\\partial g}{\\partial a}\\right)^2 \\sigma(a)^2 + \\left(\\frac{\\partial g}{\\partial b}\\right)^2 \\sigma(b)^2 + 2 \\frac{\\partial g}{\\partial a} \\frac{\\partial g}{\\partial b} \\mathrm{cov}(a,b) } = \\sqrt{ \\sigma(a)^2 + \\sigma(b)^2 - 2\\ \\mathrm{cov}(a,b) }$$\n\nIt most convenient to use vector form with vector of derivatives, call it $D^f$ for function $f$ of several parameters $x_i$:\n$$D_{i}^f := \\frac{\\partial f}{\\partial x_i} $$\nThen\n$$\\sigma(f) = \\sqrt{D^T \\cdot C \\cdot D}$$\nwhere $C$ is the covariance matrix.\n\nNow we can correctly calculate uncertainties:"
},
{
"cell_type": "code",
"collapsed": false,
"input": "D = array([1., 1.])\nprint('s(f) = %.2g' % sqrt(D.dot(pcov).dot(D)))\nD = array([1., -1.])\nprint('s(g) = %.2g' % sqrt(D.dot(pcov).dot(D)))",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "s(f) = 0.016\ns(g) = 0.055\n"
}
],
"prompt_number": 13
},
{
"cell_type": "markdown",
"metadata": {},
"source": "So uncertainty of $f = a+b$ is in fact smaller then we might have thought without taking correlations into account. Worse than that we would overestimate the uncertainty of $g = a-b$.\n\nWhy? Well, it's clear when we visualise $f$ and $g$ in the parameter space:"
},
{
"cell_type": "code",
"collapsed": false,
"input": "plot_quadratic_form(inv(pcov), popt)\nA = linspace(*gca().get_xlim())\nplot(A, (A - popt[0]) + popt[1], ls='--', lw=5, color='black', label='f = a+b')\nplot(A, -(A - popt[0]) + popt[1], ls=':', lw=5, color='black', label='g = a-b')\nlegend(loc='best')",
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 14,
"text": "<matplotlib.legend.Legend at 0x7f4c018e7d50>"
},
{
"metadata": {},
"output_type": "display_data",
"png": 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v9r5d1r7bnYFLyaS8o41st9Nn6StDDipJR0WySd+JpOqfitzie4BFiCV4infM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\nGtPU1MQFF1zAlClTmD59Ops2bfK9dvvttzNhwgQ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mvBv4taZvPBOxQexG3VTq91Ww9yIq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\nk0SygJ+VrGQlKyeJ/H/2sYA0ubgfAwAAAABJRU5ErkJggg==\n",
"text": "<matplotlib.figure.Figure at 0x7f4c018f7a90>"
}
],
"prompt_number": 14
},
{
"cell_type": "markdown",
"metadata": {},
"source": "Uncertainty of $f$ is small since it 'sees' a relatively narrow minimum. $g$ on the other hand lies very close to the long axis of the minimum."
}
],
"metadata": {}
}
]
}
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