{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Curve fitting\n",
"\n",
"> Marcos Duarte \n",
"> [Laboratory of Biomechanics and Motor Control](https://bmclab.pesquisa.ufabc.edu.br/) \n",
"> Federal University of ABC, Brazil"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Curve fitting is the process of fitting a model, expressed in terms of a mathematical function, that depends on adjustable parameters to a series of data points and once adjusted, that curve has the best fit to the data points. \n",
"\n",
"The model can be an arbitrary class of functions such as polynomials and the fit would determine the polynomial coefficients to simplily summarize the data or the model parameters can represent a underlying theory that the data are supposed to satisfy such as fitting an exponential function to data of a decay process to determine its decay rate or a parabola to the position data of an object falling to determine the gravity acceleration.\n",
"\n",
"The general approach to the fitting procedure involves the definition of a merit function that measures the agreement between data and model. The model parameters are then adjusted to yield the best-fit parameters as a problem of minimization. A fitting procedure should provide (i) parameters, (ii) error estimates on the parameters, and (iii) a statistical measure of goodness-of-fit. When the third item suggests that the model is an unlikely match to the data, then items (i) and (ii) are probably worthless. \n",
"(Numerical Recipes 2007, Bevington and Robinson 2002)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Least squares\n",
"\n",
"Consider $ n $ data points $(x_i, y_i),\\: i=1, \\dots , n$, where $x_i$ is the independent variable (or predictor) and $y_i$ is the dependent variable (or response) to be fitted by a model function $y$ with $m$ adjustable parameters $\\beta_i,\\: i=1, \\dots , m$. The problem is to find the parameter values for the model which best fits the data. A classical solution is to find the best fit by minimizing the sum of the squared differences between data points and the model function (the sum of squared residuals as the merit function), which is known as the least-squares fit:\n",
"\n",
"$$ \\sum_{i=1}^{n} \\left[ y_i - y(x | \\beta_1 \\dots \\beta_{m}) \\right]^2 \\;\\;\\;\\;\\;\\; \\mathrm{minimize\\; over:} \\;\\;\\; \\beta_1 \\dots \\beta_{m} $$ \n",
"\n",
"**Chi-Square** \n",
"If we consider that each response $y_i$ has a measurement error or uncertainty described by a standard deviation, $ \\sigma_i $, the problem now is to minimize the following function:\n",
"\n",
"$$ \\sum_{i=1}^{n} \\left[ \\frac{ y_i - y(x | \\beta_1 \\dots \\beta_{m}) }{\\sigma_i} \\right]^2 = \\chi^2 $$\n",
"\n",
"Considering that the residuals are normally distributed, the sum of squared residuals divided by their variance, $\\sigma_i^2$, by definition will have a [chi-squared distribution](http://en.wikipedia.org/wiki/Chi-squared_distribution), $ \\chi^2 $. Once the best-fit parameters are found, the terms in the sum above are not all statistically independent and the probability distribution of $\\chi^2$ will be the chi-squared distribution for $n-m$ degrees of freedom.\n",
"\n",
"The uncertainty $\\sigma_i$ can be seen as the inverse of the weights in a weighted sum (because less certainty we have about this measure). Larger $\\sigma_i$, smaller the weight of $y_i$ in the sum. If $y_i$ has no uncertainty, $\\sigma_i$ should be equal to one. \n",
"\n",
"A rough estimate of the goodness of fit is the reduced chi-square statistic, $\\chi^2_{red}$: the $\\chi^2$ value divided by the number of degrees of freedom ($n-m$). \n",
"A good fitting should have $\\chi^2_{red}$ equals to one."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Linear fit\n",
"\n",
"Let's derive the analytical expression for the least-square fit when the model function is a straight line (a.k.a. linear regression) and the dependent variable $y_i$ has uncertainty:\n",
"\n",
"$$ y(x) = y(x | a,b) = a + bx $$ \n",
"\n",
"We want to find $a, b$ such that minimizes the $\\chi^2$ function defined above (a.k.a. $\\chi^2$ fitting):\n",
"\n",
"$$ \\chi^2(a,b) = \\sum_{i=1}^{n} \\left[ \\frac{ y_i - (a + bx_i) }{\\sigma_i} \\right]^2 $$\n",
"\n",
"Using the property that at the minimum of $\\chi^2$ its derivative is zero:\n",
"\n",
"$$ \\frac{\\partial \\chi^2}{\\partial a} = -2 \\sum_{i=1}^{n} \\frac{ y_i - a - bx_i }{\\sigma_i^2} = 0 $$\n",
"\n",
"$$ \\frac{\\partial \\chi^2}{\\partial b} = -2 \\sum_{i=1}^{n} \\frac{ x_i(y_i - a - bx_i) }{\\sigma_i^2} = 0 $$\n",
"\n",
"To solve these two equations, let's define the sums as:\n",
"\n",
"$$ S = \\sum_{i=1}^{n} \\frac{1}{\\sigma_i^2} \\;\\;\\; S_x = \\sum_{i=1}^{n} \\frac{x_i}{\\sigma_i^2} \\;\\;\\; S_y = \\sum_{i=1}^{n} \\frac{y_i}{\\sigma_i^2} \\;\\;\\; S_{xx} = \\sum_{i=1}^{n} \\frac{x_i^2}{\\sigma_i^2} \\;\\;\\; S_{xy} = \\sum_{i=1}^{n} \\frac{x_i y_i}{\\sigma_i^2} $$\n",
"\n",
"Using these definitions, the former two equations become:\n",
"\n",
"$$ S_y \\:\\: = aS + bS_x $$\n",
"\n",
"$$ S_{xy} = aS_x + bS_{xx} $$\n",
"\n",
"And solving these two equations for the two unknowns:\n",
"\n",
"$$ a = \\frac{S_{xx}S_y - S_x S_{xy}}{\\Delta} $$\n",
"\n",
"$$ b = \\frac{S S_{xy} - S_x S_y}{\\Delta} $$ \n",
"\n",
"Where:\n",
"\n",
"$$ \\Delta = S S_{xx} - S_x^2 $$\n",
"\n",
"With the parameters above, the straight line will be the best fit in the sense that the sum of the squared residuals are minimum. \n",
"\n",
"**Estimating the uncertainty of the parameters**\n",
"\n",
"The uncertainty of each parameter is given by:\n",
"\n",
"$$ \\sigma_a^2 = \\frac{Sxx}{\\Delta} $$\n",
"\n",
"$$ \\sigma_b^2 = \\frac{S}{\\Delta} $$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Correlation coefficient\n",
"\n",
"The Pearson product-moment correlation coefficient, or simply the correlation coefficient, is a measure of the linear correlation between two variables $x$ and $y$, with values varying from +1 to −1, where 1 is total positive correlation, 0 is no correlation, and −1 is total negative correlation. \n",
"The correlation coefficient between populations of two random variables is the covariance of the two variables divided by the product of their standard deviations:\n",
"\n",
"$$ \\rho_{x, y} = \\frac{cov(x, y)}{\\sigma_x\\sigma_y} = \\frac{E[(x-\\mu_x)(y-\\mu_y)]}{\\sqrt{E[(x-\\mu_x)^2]}\\sqrt{E[(y-\\mu_y)^2]}} $$ \n",
"\n",
"Where $ E[\\cdot] $ is the expectation operator.\n",
"\n",
"For samples of two random variables, the covariance and standard deviation are given by:\n",
"\n",
"$$ cov(x, y) = \\frac{1}{n-1}\\sum_{i=1}^{n}(x_i-\\bar{x})(y_i-\\bar{y}) $$\n",
"\n",
"$$ \\sigma_x = \\sqrt{\\frac{1}{n-1}\\sum_{i=1}^{n}(x_i-\\bar{x})^2} $$\n",
"\n",
"So, the correlation coefficient for the samples is:\n",
"\n",
"$$ r_{x, y} = \\frac{\\sum_{i=1}^{n}(x_i-\\bar{x})(y_i-\\bar{y})}{\\sqrt{\\sum_{i=1}^{n}(x_i-\\bar{x})^2}\\sqrt{\\sum_{i=1}^{n}(y_i-\\bar{y})^2}} $$\n",
"\n",
"The square of the sample correlation coefficient, denoted $r^2$ or $R^2$, is called the coefficient of determination and it can be shown it is related to the linear fit formalism by:\n",
"\n",
"$$ R^2(y, \\widehat{y}) = \\frac{\\sum_{i=1}^{n}(\\widehat{y}_i-\\bar{y})^2}{\\sum_{i=1}^{n}(y_i-\\bar{y})^2}$$\n",
"\n",
"Where $\\widehat{y}_i$ are the fitted values from the linear fit.\n",
"\n",
"Examining the division above, it consists of the variance of the fitted values around the mean value of $y$ divided by the variance of $y_i$. Because of that, it is said that the coefficient of determination is the proportion of variance in $y$ explained by a linear function of $x$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Computing the curve fitting\n",
"\n",
"Python and its ecosystem for scientific computing have plenty of functions ready available for curve fitting. Instead of writting our own code to implement the formula above, let's use the functions available which will cover many more cases (general polynomials, nonlinear functions, etc.).\n",
"\n",
"First, if we only want to fit polynomials, we can use the Numpy polyfit function: \n",
"\n",
" polyfit(x, y, deg, rcond=None, full=False, w=None, cov=False) \n",
" Least squares polynomial fit. \n",
" \n",
" Fit a polynomial ``p(x) = p[0] * x**deg + ... + p[deg]`` of degree `deg` \n",
" to points `(x, y)`. Returns a vector of coefficients `p` that minimises \n",
" the squared error. \n",
" \n",
"Let's demonstrate how polyfit works:"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"# Import the necessary libraries\n",
"import numpy as np\n",
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"import scipy.stats as stats"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Generate some data:"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"n = 50\n",
"x = np.arange(1, n+1)\n",
"y = x + 10*np.random.randn(n) + 10\n",
"yerr = np.abs(10*np.random.randn(n)) + 5"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First, let's plot the data and perform the curve fitting without considering the uncertainty:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"p, cov = np.polyfit(x, y, 1, cov=True) # coefficients and covariance matrix\n",
"yfit = np.polyval(p, x) # evaluate the polynomial at x\n",
"\n",
"perr = np.sqrt(np.diag(cov)) # standard-deviation estimates for each coefficient\n",
"R2 = np.corrcoef(x, y)[0, 1]**2 # coefficient of determination between x and y\n",
"resid = y - yfit\n",
"chi2red = np.sum((resid/yerr)**2)/(y.size - 2)\n",
"\n",
"plt.figure(figsize=(10, 5))\n",
"plt.plot(x, y, 'bo')\n",
"plt.plot(x, yfit, linewidth=3, color=[1, 0, 0, .5])\n",
"plt.xlabel('x', fontsize=16)\n",
"plt.ylabel('y', fontsize=16)\n",
"plt.title('$y = %.2f \\pm %.2f + (%.2f \\pm %.2f)x \\; [R^2=%.2f,\\, \\chi^2_{red}=%.1f]$'\n",
" %(p[1], perr[1], p[0], perr[0], R2, chi2red), fontsize=20, color=[0, 0, 0])\n",
"plt.xlim((0, n+1))\n",
"plt.ylim((-50, 100))\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The curve fitting by a line considering the uncertainty:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"p, cov = np.polyfit(x, y, 1, w=1/yerr, cov=True) # coefficients and covariance matrix\n",
"yfit = np.polyval(p, x) # evaluate the polynomial at x\n",
"\n",
"perr = np.sqrt(np.diag(cov)) # standard-deviation estimates for each coefficient\n",
"R2 = np.corrcoef(x, y)[0, 1]**2 # coefficient of determination between x and y\n",
"resid = y - yfit\n",
"chi2red = np.sum((resid/yerr)**2)/(y.size - 2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And the plot:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(10, 5))\n",
"plt.errorbar(x, y, yerr=yerr, fmt = 'bo', ecolor='b', capsize=0)\n",
"plt.plot(x, yfit, linewidth=3, color=[1, 0, 0, .5])\n",
"plt.xlabel('x', fontsize=16)\n",
"plt.ylabel('y', fontsize=16)\n",
"plt.title('$y = %.2f \\pm %.2f + (%.2f \\pm %.2f)x \\; [R^2=%.2f,\\, \\chi^2_{red}=%.1f]$'\n",
" %(p[1], perr[1], p[0], perr[0], R2, chi2red), fontsize=20, color=[0, 0, 0])\n",
"plt.xlim((0, n+1))\n",
"plt.ylim((-50, 100))\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"According to our assumptions, the residuals should be normally distributed. Let's create a function to plot the residuals and a probability plot that will be useful to check if the residuals are normally distributed:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"def plot_resid(x, resid):\n",
" \"\"\" plot residuals and probability plot of residuals for a normal distribution.\"\"\"\n",
"\n",
" import matplotlib.pyplot as plt\n",
" import scipy.stats as stats\n",
" fig, ax = plt.subplots(1, 2, figsize=(13, 5))\n",
" ax[0].plot(x, resid, 'ro')\n",
" ax[0].plot([0, x[-1]], [0, 0], 'k')\n",
" ax[0].set_xlabel('x', fontsize=12)\n",
" ax[0].set_ylabel('Residuals', fontsize=12)\n",
" stats.probplot(resid, dist=\"norm\", plot=plt)\n",
" ax[1].set_xlabel('Quantiles', fontsize=12)\n",
" ax[1].set_ylabel('Ordered values', fontsize=12)\n",
" ax[1].set_title('Probability Plot of the residuals')\n",
"\n",
" plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_resid(x, resid)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We could apply a statistical test to verify if the data above is normallly distributed, but for now, by visual inspection, the residuals indeed seem to be normallly distributed."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### The effect of uncertainty on the curve fitting\n",
"\n",
"To demonstrate the effect of uncertainty on the curve fitting, let's plot the same (x, y) values but with different errors:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"# data\n",
"x = np.array([1, 2, 3, 4, 5])\n",
"y = np.array([1, 2, 3, 6, 4])\n",
"yerr = np.array([[0, 0, 0, 0, 0],\n",
" [1, 1, 1, 1, 1],\n",
" [1, 1, 1, .5, 2],\n",
" [1, 1, 1, 2, .5]])"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"# function for the linear fit to automate the process\n",
"def linearfit(x, y, yerr=None):\n",
" w = None if (yerr is None or np.sum(yerr)==0) else 1/yerr\n",
" p, cov = np.polyfit(x, y, 1, w=w, cov=True) # coefficients and covariance matrix\n",
" yfit = np.polyval(p, x) # evaluate the polynomial at x\n",
"\n",
" perr = np.sqrt(np.diag(cov)) # standard-deviation estimates for each coefficient\n",
" R2 = np.corrcoef(x, y)[0, 1]**2 # coefficient of determination between x and y\n",
" resid = y - yfit\n",
" chi2red = np.sum((resid/yerr)**2)/(y.size - 2) if w is not None else np.nan\n",
"\n",
" return yfit, p, R2, chi2red, perr, resid"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# plot\n",
"fig, ax = plt.subplots(2, 2, figsize=(10, 6), sharex=True, sharey=True)\n",
"axs = ax.flatten()\n",
"for i, ax in enumerate(axs):\n",
" yf, p, R2, chi2red, perr, resid = linearfit(x, y, yerr=yerr[i, :])\n",
" ax.errorbar(x, y, yerr=yerr[i, :], fmt = 'bo', ecolor='b', capsize=0, elinewidth=2)\n",
" ax.plot(x, yf, linewidth=3, color=[1, 0, 0, .5])\n",
" ax.set_title('$y = %.2f + %.2f x \\, [R^2=%.2f,\\chi^2_{red}=%.1f]$'\n",
" %(p[1], p[0], R2, chi2red), fontsize=18)\n",
" ax.grid()\n",
"\n",
"ax.set_xlim(0.5, 5.5)\n",
"fig.subplots_adjust(bottom=0.1, left=.05, right=.95, hspace=.2, wspace=.05)\n",
"plt.suptitle('The effect of uncertainty on the curve fitting (same data, different errors)',\n",
" fontsize=16, y=1.02)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"From figure above, if the errors (weights) are all equal, the fitting is the same as if we don't input any error (first line). \n",
"When the errors are different across data, the uncertainty has a strong impact on the curve fitting (second line)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Curve fitting as a model\n",
"\n",
"We have to be carefull in interpreting the results of a curve fitting to determine whether the fitted model truely captures the relation between the independent variable (predictor) and the dependent variable (response).\n",
"\n",
"An illustrative example to demonstrate that the result of a curve fitting is not necessarily an indicator of the phenomenon being modelled is the [Anscombe's quartet](http://en.wikipedia.org/wiki/Anscombe%27s_quartet) data. These four sets of data have very similar basic statistical properties and linear fitting parameters, but are very different when visualized. Let's work with these data:"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The Anscombe's quartet data ha)ve the same basic statistical properties:\n",
"Mean of x : [7.50090909 7.50090909 7.5 7.50090909]\n",
"Variance of x: [3.75206281 3.75239008 3.74783636 3.74840826]\n",
"Mean of y : [7.50090909 7.50090909 7.5 7.50090909]\n",
"Variance of y: [3.75206281 3.75239008 3.74783636 3.74840826]\n"
]
}
],
"source": [
"# Anscombe's quartet data\n",
"x = np.array([[10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5],\n",
" [10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5],\n",
" [10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5],\n",
" [8, 8, 8, 8, 8, 8, 8, 19, 8, 8, 8]])\n",
"y = np.array([[8.04, 6.95, 7.58, 8.81, 8.33, 9.96, 7.24, 4.26, 10.84, 4.82, 5.68],\n",
" [9.14, 8.14, 8.74, 8.77, 9.26, 8.10, 6.13, 3.10, 9.13, 7.26, 4.74],\n",
" [7.46, 6.77, 12.74, 7.11, 7.81, 8.84, 6.08, 5.39, 8.15, 6.42, 5.73],\n",
" [6.58, 5.76, 7.71, 8.84, 8.47, 7.04, 5.25, 12.50, 5.56, 7.91, 6.89]])\n",
"# basic descriptive statistics\n",
"print(\"The Anscombe's quartet data ha)ve the same basic statistical properties:\")\n",
"print('Mean of x :', np.mean(y, axis=1))\n",
"print('Variance of x:', np.var(y, axis=1))\n",
"print('Mean of y :', np.mean(y, axis=1))\n",
"print('Variance of y:', np.var(y, axis=1))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Or we can use Pandas to describe the data:"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"