{ "metadata": { "name": "optimization" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "In this tutorial, we will learn how to use non-linear optimization routines in scipy.optimize to model data and examine a practical example, using some data from psychophysical experiments that I did in collaboration with [Ayelet Landau](http://www.esi-frankfurt.de/research/fries-lab/dr-ayelet-landau/). The code and data for generating this entire page are available in [this github repo](http://github.com/arokem/teach_optimization)\n", "\n", "This tutorial assumes that you know some python. Specifically, I am going to assume that you know how to define a function in python and that you have some acquaintance with the basics of numpy, scipy and matplotlib and that you know what to do with an ipython notebook. To get all of these installed on your own computer, your best bet is to head over to the [Enthought Python Distribution](http://www.enthought.com/products/epd_free.php). I will assume that you have started the ipython notebook session with the --pylab=inline flag, so that some of the needed modules are already imported and we are ready to display images inline as we go along. I will also assume that you know a little bit of statistics and that terms such *dependent* and *independent variable* are not completeley foreign to you. \n", "\n", "## Goals of this tutorial\n", "\n", "- Define modeling and understand why models are useful. \n", "- Learn about different strategies for fitting models.\n", "- Learn how to fit a simple model to empirical data using an iterative least-squares routine. \n", "- Learn about model selection and learn how to use cross-validation for model selection.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Why model? \n", "\n", "Let's consider a data-set taken from an experiment in visual neuroscience. In this experiment, participants viewed a stimulus that contained a grating. In each trial two gratings were displayed. To show these stimuli, let's import some stuff from IPython: " ] }, { "cell_type": "code", "collapsed": false, "input": [ "from IPython.display import display, Image" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The first grating that was shown was surrounded by another grating: " ] }, { "cell_type": "code", "collapsed": false, "input": [ "display(Image(filename='images/surrounded.png'))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The second grating was not surrounded: \n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "display(Image(filename='images/comparison.png'))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Participants had to say which interval had higher *contrast*. That is, in which interval the amplitude of the modulation between the dark stripes and the light stripes in the grating was larger. This is a way for us to measure the effects of the presencee of a surround on contrast perception. For example, it is well known that the relative orientation of the surround affects the degree to which the surround reduces the perceived contrast of the central patch (e.g., see [recent work from Kosovicheva et al.](http://www.frontiersin.org/Behavioral_Neuroscience/10.3389/fnbeh.2012.00061/abstract) using a similar experimental paradigm). \n", "\n", "Let's look at some experimental data. We have two files from one subject in csv files, ortho.csv and para.csv. As their names suggest they come from two different runs of the experiment: one in which the surrounding stimulus was oriented in the parallel orientation relative to the center stimulus (also sometimes called 'co-linear') and one in which the surrounding stimulus was orthogonal to the center stimulus. The files contain three columns: contrast1 is the contrast in the first interval, contrast2 is the contrast in the second interval and answer is what the participant thought had higher contrast. We will use the function mlab.csv2rec to read the data into a numpy recarray: " ] }, { "cell_type": "code", "collapsed": false, "input": [ "ortho = mlab.csv2rec('data/ortho.csv') \n", "para = mlab.csv2rec('data/para.csv')" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "If you take a look at the data you will see that the contrast in the second interval was always 0.3 (30% contrast), so we can safely ignore that column altogether and only look at the contrast in the first interval. Let's take a look at the data. First, we are just going to plot the raw data as it is. We will consider the contrasts as our independent variable, and the responses as the dependent variables." ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig, ax = plt.subplots(1)\n", "# We apply a small vertical jitter to each point, just to show that there are multiple points at each location:\n", "ax.plot(ortho['contrast1'], ortho['answer'] + np.random.randn(len(ortho)) * 0.02 , '*')\n", "ax.plot(para['contrast1'], para['answer'] + np.random.randn(len(para)) * 0.02 , '+')\n", "ax.set_ylim([0.9, 2.1])\n", "ax.set_xlabel('Contrast 1')\n", "ax.set_ylabel('Which stimulus had higher contrast? (1 or 2)')\n", "\n", "fig.set_size_inches([8,8])" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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qKk6dOgVHR0csXLjQnLUSERHRYxidfk9KSsLRo0dx8+ZNAEDr1q0xcOBAtGrV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\nGA69Xg/YFUCv12PixJGSfr/Lrp/fvv0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"text": [ "" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "There seems to be a trend in the data: the larger the contrast in the first interval, the more likely the subject was to press the '1' button. That's a reasonable thing to do, but it's hard to see and hard to quantify in this form. Instead, we will transform this data into a plot in which the independent variable is the contrast in interval 1 and the dependent variable is the proportion of trials for which the subject pressed the '1' key for each contrast. Let's define a function that will do that for us: " ] }, { "cell_type": "code", "collapsed": false, "input": [ "def transform_data(data): \n", " \"\"\" \n", " Function that takes experimental data and gives us the dependent/independent variables for analysis\n", "\n", " Parameters\n", " ----------\n", "\n", " data : rec array \n", " The data with records: contrast1, contrast2 and answer\n", "\n", " Returns\n", " -------\n", " x : The unique contrast differences. \n", " y : The proportion of '2' answers in each contrast difference\n", " n : The number of trials in each x,y condition \n", " \"\"\"\n", " contrast1 = data['contrast1']\n", " answers = data['answer']\n", " \n", " x = np.unique(contrast1)\n", " y = []\n", " n = []\n", "\n", " for c in x:\n", " idx = np.where(contrast1 == c)\n", " n.append(float(len(idx[0])))\n", " answer1 = len(np.where(answers[idx] == 1)[0])\n", " y.append(answer1 / n[-1])\n", "\n", " return x,y,n\n", " " ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 6 }, { "cell_type": "code", "collapsed": false, "input": [ "x_ortho, y_ortho, n_ortho = transform_data(ortho)\n", "x_para, y_para, n_para = transform_data(para) " ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 7 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, ax = plt.subplots(1)\n", "# To plot each point with size proportional to the number of trials in that condition:\n", "for x,y,n in zip(x_ortho, y_ortho, n_ortho):\n", " ax.plot(x, y, 'bo', markersize=n)\n", "\n", "for x,y,n in zip(x_para, y_para, n_para):\n", " ax.plot(x, y, 'go', markersize=n)\n", "\n", "ax.set_xlabel('Contrast in interval 1')\n", "ax.set_ylabel('Proportion answers 1')\n", "ax.set_ylim([-0.1, 1.1])\n", "ax.set_xlim([-0.1, 1.1])\n", "ax.grid('on')\n", "fig.set_size_inches([8,8])" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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5ubkYPnw4Lly4gOLiYkybNg0xMTEVi2TzJqrVMjMzMXfuVzh7tgCFhQpcXU1o06YBXntt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\nYrHVZyuOeBzBVp+tiL0Wi86TOqP38N7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"text": [ "" ] } ], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Obviously there is a systematic relationship between the contrast and the chances that this subject thought that the first interval had the higher contrast. For example, when the contrast was much higher in interval 1 (e.g. 0.9), this person never said that the second interval had higher contrast. Likewise, when the contrast was very low, this person almost never said that the contrast in interval 1 had been higher. In the middle, there seems to be a monotonic relationship between the variables. Also, notive that the two sets of data (orthogonal and parallel) seem to be slightly different. \n", "\n", "Can we say something more precise? For example, we might be interested in the contrast in which 50% of the answers would have been '1' and 50% of the answers would have been '2'. This is known as the point of subjective equality (or PSE) and we can use it to compare different conditions in this experiment and in other experiments, between different subjects, etc. \n", "\n", "In order to derive this quantity, we will have to fit a model to the data. \n", "\n", "*Note: If were doing this in earnest, we would take into account the number of trials that was performed at each contrast (especially given that there are more trials in some conditions). For the purpose of this tutorial, we will ignore that.*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Models and why we like them\n", "\n", "Models derived from data are useful for several reasons: \n", "\n", "- **They allow you to explain the data you have**: summary statistics of the data, such as the mean of some variable, or the variance of this variable, are often not the best explanation of the data you have observed, in terms of the theory. For example, in the data we have observed in our experiment, a useful quantity is the PSE, which telss us what the *perceived contrast* of the surrounding grating was. This quantity is not readily present in summary statistics of the data. A *functional form* of a model is a mathematical formula that relates systematic changes in measured dependent variables, based on experimental manipulations of the independent variables. The functional form of the model varies with changes in *model parameters*. In the typical case, parameters are variables specificied in the model, that are neither your dependent variables nor your independent variables. If the model parameters correspond to theoretically meaningful quantities (such as the PSE), that can make the model useful in explaining the data and help test hypotheses about the theory behind the experiment.\n", "\n", "- **They allow you to predict data you haven't collected**: In many cases, assuming that the parameters don't change with changes in the independent variables, models allow us to interpolate and predict what the dependent variables would have been like in other values of the independent variables. Even extrapolate to conditions that have not measured. For example, because measuring in these conditions is difficult for practical reasons. \n", "\n", "- **They allow us to build theories**: By applying a modeling approach to data, we can hope to build an incremental knowledge abouth the domain we are studying. For example, [Newton's law of gravitation](http://en.wikipedia.org/wiki/Newton's_law_of_universal_gravitation) provides us with a quantitative prediction on the behavior of any two bodies. The observation that this model does not perform well in all conditions, led to [Einstein's theory of general relativity](http://en.wikipedia.org/wiki/General_relativity), which provides a generalization of this law (model).\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Different kinds of models\n", "\n", "## Linear models\n", "The main distinction we will make here is between *linear* models and *non-linear* models. Linear models are models that can be described by the following functional form: \n", "\n", "$\\bf{y} = \\beta_0 + \\beta_1 \\bf{x}_1 + \\beta_2 \\bf{x}_2 + ... + \\beta_n \\bf{x}_n + \\epsilon$, \n", "\n", "where $\\bf{y}$ denotes the dependent variable or variables (that's why it's bold-faced: it could be a vector!) in your experiment. $\\bf{x}_i$ are sets of dependent variables (also, possibly vectors) and $\\beta_i$ are parameters. Finally, $\\epsilon$ is the noise in the experiment. You can also think about $\\epsilon$ as all the things that your model doesn't know about. For example, in the visual experiment described, changes in participants wakefulness might affect performance in a systematic way, but unless we explicitely measure wakefulness and add it as an independent variable to our analysis (as another $\\bf{x}$), we don't know it's value on each trial and it goes into the noise. \n", "\n", "Linear models are easy to fit. Under some fairly generic assumptions (for example that $\\epsilon$ has a zero-mean normal distribution), there is actually an analytic solution to this problem. That is, you can plug it into a formula and get the exact solution: the set of $\\beta$ that give you the smallest sum-of-squared-errors (SSE) between the data you collected and the function defined by the parameters (we will assume that this is your objective, though variataions on this do exist). This is the reason that if you can transform your data somehow to get it into a linear form, you should definitely do that. \n", "\n", "Let's fit a linear model to our data. In our case, a linear model would simply be a straight line: \n", "\n", "$y = \\beta_0 + \\beta_1 x$\n", "\n", "These kind of equations (*polynomials*) can be solved using np.polyfit:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Note that the coefficients go in the other direction than my equation above (the constant comes last):\n", "beta1_ortho, beta0_ortho = np.polyfit(x_ortho, y_ortho, 1)\n", "beta1_para, beta0_para = np.polyfit(x_para, y_para, 1)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 9 }, { "cell_type": "code", "collapsed": false, "input": [ "# Let's show the data and the model fit, \n", "# polyval evaluates the model at an arbitrary set of x values:\n", "x = np.linspace(np.min([x_ortho, x_para]), np.max([x_ortho, x_para]), 100)\n", "fig, ax = plt.subplots(1)\n", "ax.plot(x, np.polyval([beta1_ortho, beta0_ortho], x))\n", "ax.plot(x_ortho, y_ortho, 'bo')\n", "ax.plot(x, np.polyval([beta1_para, beta0_para], x))\n", "ax.plot(x_para, y_para, 'go')\n", "ax.set_xlabel('Contrast 1')\n", "ax.set_ylabel('Proportion responses 1')\n", "ax.set_ylim([-0.1, 1.1])\n", "ax.set_xlim([-0.1, 1.1])\n", "ax.grid('on')\n", "fig.set_size_inches([8,8])" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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XKWNxcBL72H9mP32W92FZj2U8WvFR1XFEMXLHmXdqaiqenp6OzHNLMvMWwpxu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\nCBwdHeHi4oJjx46ZuySTit8ZD68RXvAM9ITXCC/E74w3yXK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"text": [ "" ] } ], "prompt_number": 10 }, { "cell_type": "code", "collapsed": false, "input": [ "#Let's quantify the fit by calculating the sum of squared errors relative to the actual data: \n", "SSE_ortho = np.sum((y_ortho - np.polyval([beta1_ortho, beta0_ortho], x_ortho))**2)\n", "SSE_para = np.sum((y_para - np.polyval([beta1_para, beta0_para], x_para))**2)\n", "print(SSE_ortho + SSE_para)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "0.435568123024\n" ] } ], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this case, to derive the PSE, we need to do a little bit of algebra. We set y=0.5 (that's the definition of the PSE) and solve for x:\n", "\n", "$0.5 = \\beta_0 + \\beta_1 x$\n", "\n", "$\\Rightarrow 0.5 - \\beta_0 = \\beta_1 x$ \n", "\n", "$\\Rightarrow x = \\frac{0.5- \\beta_0}{\\beta1}$\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "print('PSE for the orthogonal condition is:%s'%((0.5 - beta0_ortho)/beta1_ortho))\n", "print('PSE for the parallel condition is:%s'%((0.5 - beta0_para)/beta1_para))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "PSE for the orthogonal condition is:0.42841372023\n", "PSE for the parallel condition is:0.559650372242\n" ] } ], "prompt_number": 12 }, { "cell_type": "markdown", "metadata": {}, "source": [ "OK - this model seems to capture some aspects of the data rather well. For one, it is monotonically increasing. And the SSE doesn't seem too bad (though that's hard to assess just by looking at this number). This model tells us that the PSE is at approximately 0.43 for orthogonal condition and approximately 0.56 for the parallel condition. That is, the contrast in the first interval has to be higher than the contrast in the second interval to appear exactly the same. By how much? For the orthogonal condition it's about 13% and for the parallel condition it's about 26% (considering that the comparison contrast is always 30%). This makes sense: more suppression for the parallel relative to the orthogonal condition. But there are a few problems with this model: It seems to miss a lot of the points. That could be because the data is very noisy, but we can see that the model systematically overshoot the fit for high values of x and systematically undershoots for low values of x. This indicates that another model might be better for this data. Another problem is that it seems to produce non-sensical values for some conditions. For example, it sometimes predicts values larger than 1.0 for large contrasts and values smaller than 0.0 for small contrasts. These values are meaningless, because proportion of responses can never be outside the range 0-1. We need to find a different model. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Non-linear models:\n", "\n", "Unfortunately, linear models don't always fit our data. As shown above, they might produce large and systematic fit error, or they might produce values that don't make sense. In these cases, we might need to fit a non-linear model to our data. Non-linear models cannot be described as above and are generally described by the following functional form: \n", "\n", "$\\bf{y} = f(\\bf{x}_1, \\bf{x}_2, ... \\bf{x}_n, \\bf{\\beta}) + \\epsilon$, \n", "\n", "Where $f()$ can be almost any function you can think of that takes $x$'s and $\\beta$'s as input. The problem is that there is no formula that you can just plug your function into and derive the values of the parameters. One way to find the value of the parameters for a given functional form is to use optimization. In this process, the computer systematically tries out different values of $\\beta$ and finds a set of these values that minimizes the SSE relative to the data. There are many different optimization algorithms and we will use one, a variant of the Levenberg-Marquardt algorithm, implemented in scipy.optimize as leastsq.\n", "\n", "## Step 1 : define the function\n", "To perform optimization, we need to define the functional form of our model. For this kind of data, a common model to use (e.g in [work by Yu and Levi](http://ww.journalofvision.org/content/2/3/4.full)) is a cumulative Gaussian function. The Gaussian distribution is parameterized by 2 numbers, the mean and the variance, so as in the linear model shown above, this model has 2 parameters: \n", "\n", "$y(x) = \\frac{1}{2}[1 + erf(\\frac{x-\\mu}{\\sigma \\sqrt{2} })]$, \n", "\n", "where $erf$ is the so-called 'error function', implemented in scipy.special\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from scipy.special import erf\n", "def cumgauss(x, mu, sigma):\n", " \"\"\"\n", " The cumulative Gaussian at x, for the distribution with mean mu and\n", " standard deviation sigma. \n", "\n", " Parameters\n", " ----------\n", " x : float or array\n", " The values of x over which to evaluate the cumulative Gaussian function\n", "\n", " mu : float \n", " The mean parameter. Determines the x value at which the y value is 0.5\n", " \n", " sigma : float \n", " The variance parameter. Determines the slope of the curve at the point of \n", " Deflection\n", " \n", " Returns\n", " -------\n", "\n", " Notes\n", " -----\n", " Based on:\n", " http://en.wikipedia.org/wiki/Normal_distribution#Cumulative_distribution_function\n", "\n", " \"\"\"\n", " return 0.5 * (1 + erf((x-mu)/(np.sqrt(2)*sigma)))\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The doc-string specifies one reason that we might want to use this function for this kind of data: one of the parameters of the function (mu) is simply the definition of the PSE. So, if we find this parameter, we already have the PSE in hand, without having to do any extra algebra. \n", "\n", "Let's plot a few exemplars of this function, just to get a feel for them:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig, ax = plt.subplots(1)\n", "ax.plot(x, cumgauss(x, 0.5, 0.25), label=r'$\\mu=0, \\sigma=0.25$')\n", "ax.plot(x, cumgauss(x, 0.5, 0.5), label=r'$\\mu=0, \\sigma=0.5$')\n", "ax.plot(x, cumgauss(x, 0.5, 0.75), label=r'$\\mu=0, \\sigma=0.75$')\n", "ax.plot(x, cumgauss(x, 0.3, 0.25), label=r'$\\mu=0.3, \\sigma=0.25$')\n", "ax.plot(x, cumgauss(x, 0.7, 0.25), label=r'$\\mu=0.3, \\sigma=0.25$')\n", "ax.set_ylim([-0.1, 1.1])\n", "ax.set_xlim([-0.1, 1.1])\n", "ax.grid('on')\n", "fig.set_size_inches([8,8])\n", "plt.legend(loc='lower right')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 14, "text": [ "" ] }, { "output_type": "display_data", "png": 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kvOd5W/S4wrKk5yuERjKMRjoEBjKpfn1eq11b63Ds2qxZsG0b7NkDpXQ6QfJG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"text": [ "" ] } ], "prompt_number": 14 }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, these are monotonically increasing functions. For different values of $\\mu$, the function moves left or right. As it is derived from the Gaussian function, it asymptotes at 0 and 1 at $-\\infty$ and $+\\infty$ respectively, and the rate at which it approaches these asymptotes on either side is determined by $\\sigma$. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Step 2 : define an error function\n", "\n", "The next step in the optimization procedure is to define an error-function, which can take this function, a particular set of data and a particular set of parameters and calculates the errors in fitting the function, relative to the data, given a particular set of parameters. These errors are also sometimes referred to as the *marginals* of the fitting proedure. In our optimization procedure, we will aim to minimize the sum of the squares of these marginals. If you want to optimize another cost-function (for example, sometimes you might want to minimize the *sum of the absolute error*, instead of the SSE), this is where you would implement this variation" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def err_func(params, x, y, func):\n", " \"\"\"\n", " Error function for fitting a function\n", " \n", " Parameters\n", " ----------\n", " params : tuple\n", " A tuple with the parameters of func according to their order of input\n", "\n", " x : float array \n", " An independent variable. \n", " \n", " y : float array\n", " The dependent variable. \n", " \n", " func : function\n", " A function with inputs: (x, *params)\n", " \n", " Returns\n", " -------\n", " The marginals of the fit to x/y given the params\n", " \"\"\"\n", " return y - func(x, *params)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 15 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that we are passing a function as an input to this function. This might be a pattern that you have never seen before, but when you think about it, there's nothing special about a function that doesn't allow us to pass it around as an object (well, that's not entirely true, functions are special, but bear with me). Note also that we have implemented this function to take *any* function as input and the params can be any tuple of parameters with any length. This will allow us to reuse this function later on for other models with a different number of parameters. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Step 3 : optimize!\n", "\n", "We import the scipy.optimize module and deploy leastsq: " ] }, { "cell_type": "code", "collapsed": false, "input": [ "import scipy.optimize as opt\n", "# Let's guess the inital conditions: \n", "initial = 0,0.5\n", "# We get the params, and throw away the second output of leastsq:\n", "params_ortho, _ = opt.leastsq(err_func, initial, args=(x_ortho, y_ortho, cumgauss))\n", "params_para, _ = opt.leastsq(err_func, initial, args=(x_para, y_para, cumgauss))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 16 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Step 4 : evaluate\n", "\n", "Let's compare this to the data: " ] }, { "cell_type": "code", "collapsed": false, "input": [ "plot(x, cumgauss(x, params_ortho[0], params_ortho[1]))\n", "plot(x, cumgauss(x, params_para[0], params_para[1]))\n", "plot(x_ortho, y_ortho, 'bo')\n", "plot(x_para, y_para, 'go')\n", "ax.set_ylim([-0.1, 1.1])\n", "ax.set_xlim([-0.1, 1.1])\n", "ax.grid('on')\n", "fig.set_size_inches([8,8])" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 17 }, { "cell_type": "code", "collapsed": false, "input": [ "SSE_ortho = np.sum((y_ortho - cumgauss(x_ortho, *params_ortho))**2)\n", "SSE_para = np.sum((y_para - cumgauss(x_para, *params_para))**2)\n", "print(SSE_ortho + SSE_para)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "0.101687231561\n" ] } ], "prompt_number": 18 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Step 5 : interpert\n", "\n", "In this case, one of the parameters is simply the PSE:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "print('PSE for the orthogonal condition is:%s'%params_ortho[0])\n", "print('PSE for the parallel condition is:%s'%params_para[0])" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "PSE for the orthogonal condition is:0.464386434318\n", "PSE for the parallel condition is:0.574567347471\n" ] } ], "prompt_number": 19 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that we have managed to reduce the sum-of-squared error substantially relative to the linear model presented above, but it's still not perfect. How about trying a more complicated model, with more parameters. Another function that is often used to fit psychometric data is the Weibull cumulative distribution function, named after the great Swedish mathematician and engineer [Waloddi Weibull](http://en.wikipedia.org/wiki/Waloddi_Weibull)" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def weibull(x,threshx,slope,guess,flake):\n", " \"\"\" \n", " The Weibull cumulative distribution function\n", "\n", " Parameters \n", " ---------- \n", " x : float or array\n", " The values of x over which to evaluate the cumulative Weibull function\n", " \n", " threshx : float\n", " The value of x at the deflection point of the function. For a guess set to 0.5, this is at approximately 0.81 \n", "\n", " slope : float\n", " The slope of the function at the deflection point. \n", "\n", " guess : float\n", " The guess rate. Between 0 and 1. For example, for a two-alternative forced-choice experiment, this would be 0.5\n", " \n", " flake : float \n", " The upper asymptote of the function. Often thought of as indicative of lapses in performance ('flake rate')\n", " \"\"\"\n", " threshy = 1 - (1 - guess) * np.exp(-1)\n", " flake = 1 - flake \n", " k = (-np.log((1 - threshy) / (1 - guess))) ** (1 / slope)\n", " return (flake - (flake - guess) * np.exp(-(k * x / threshx) ** slope))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 20 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, ax = plt.subplots(1)\n", "ax.plot(x, weibull(x, 0.5, 3.5, 0.5, 0.05), label='threshx=0.5, slope=3.5, guess=0.5, flake=0.05')\n", "ax.plot(x, weibull(x, 0.5, 3.5, 0, 0.05), label='threshx=0.5, slope=3.5, guess=0, flake=0.05')\n", "ax.plot(x, weibull(x, 0.5, 3.5, 0, 0.15), label='threshx=0.5, slope=3.5, guess=0, flake=0.15')\n", "ax.plot(x, weibull(x, 0.25, 3.5, 0.5, 0.05), label='threshx=0.25, slope=3.5, guess=0.5, flake=0.05')\n", "ax.plot(x, weibull(x, 0.75, 3.5, 0, 0.15), label='threshx=0.75, slope=3.5, guess=0, flake=0.15')\n", "ax.set_ylim([-0.1, 1.1])\n", "ax.set_xlim([-0.1, 1.1])\n", "ax.grid('on')\n", "fig.set_size_inches([8,8])\n", "plt.legend(loc='lower right')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 36, "text": [ "" ] }, { "output_type": "display_data", "png": 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VqsDixdpdQSZEGUjPV2jCZLUy/+xZNnfooHUoLuuFF9Sf06drGwfAgZQDbInd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\noX/2MHOGCgAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 36 }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, this function has more parameters, so it can probably account for more different shapes of data." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# We guess the inital conditions again: \n", "initial = 0.5,3.5,0,0\n", "# fit again with leastsq, this time passing weibull as the input:\n", "params_ortho, _ = opt.leastsq(err_func, initial, args=(x_ortho, y_ortho, weibull))\n", "params_para, _ = opt.leastsq(err_func, initial, args=(x_para, y_para, weibull))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 22 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, ax = plt.subplots(1)\n", "ax.plot(x, weibull(x, *params_ortho))\n", "ax.plot(x, weibull(x, *params_para))\n", "ax.plot(x_ortho, y_ortho, 'bo')\n", "ax.plot(x_para, y_para, 'go')\n", "ax.set_ylim([-0.1, 1.1])\n", "ax.set_xlim([-0.1, 1.1])\n", "ax.grid('on')\n", "fig.set_size_inches([8,8])" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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iz9Uira9TtqLFnHTbfIkot+3bgaefBurWfbTM1TUz39e6uZltVJVs8dHFGNps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\nEhERaYzNl4iISGP/BUlqxwjRNULwAAAAAElFTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 23 }, { "cell_type": "code", "collapsed": false, "input": [ "SSE_ortho = np.sum((y_ortho - weibull(x_ortho, *params_ortho))**2)\n", "SSE_para = np.sum((y_para - weibull(x_para, *params_para))**2)\n", "print(SSE_ortho + SSE_para)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "0.0864875981874\n" ] } ], "prompt_number": 24 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Wow! This looks great - we've managed to reduce the SSE even more! But maybe this is too good to be true? One thing to worry about is that this model has more parameters. That is, as we noted above, it has more freedom to fit a variety of different sets of data more closely.\n", "\n", "To understand this problem, let's consider an extreme case: consider fitting a model which is a polynomial of degree 7 to this data:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "beta_ortho = np.polyfit(x_ortho, y_ortho, 7)\n", "beta_para = np.polyfit(x_para, y_para, 7)\n", "\n", "fig, ax = plt.subplots(1)\n", "ax.plot(x, np.polyval(beta_ortho, x))\n", "ax.plot(x_ortho, y_ortho, 'bo')\n", "ax.plot(x, np.polyval(beta_para, x))\n", "ax.plot(x_para, y_para, 'go')\n", "ax.set_ylim([-0.1, 1.5])\n", "ax.set_xlim([-0.1, 1.1])\n", "ax.grid('on')\n", "fig.set_size_inches([8,8])\n", "\n", "SSE_ortho = np.sum((y_ortho - np.polyval(beta_ortho, x_ortho))**2)\n", "SSE_para = np.sum((y_para - np.polyval(beta_para, x_para))**2)\n", "print(SSE_ortho + SSE_para)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "0.0393895514125\n" ] }, { "output_type": "display_data", "png": 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qVc6+rly5MitXrszymW7dunHrrbdSsWJFjhw5wocffpjtsjp27EhERAQAZcqU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\nqJ3oLusw7YdpaDA2YOukrXCzdRO7JNmpuFqBBakL8NOZn7B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"text": [ "" ] } ], "prompt_number": 25 }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, the SSE is even lower, but the parameters are adjusted to fit not only the underlying trends in the data, but also the idiosyncratic characteristics of the noise in this sample, to the point where you might reach some absurd conclusions fitting this data (for example, note the deflections of the model around a contrast of 0.8) \n", "\n", "This model has almost as many parameters as we have data points in our data. The result is *overfitting*. How can we be sure that we were not overfitting when we fit the Weibull function to our data? \n", "\n", "## Model selection\n", "\n", "Model selection refers to a process through which different models are compared to each other and one is selected over others. \n", "\n", "There are two general ways of doing this: \n", "\n", "- **Formal/parametric model comparison**: An F-test can be used to compare models that are *nested*. That is, a model in which an additional set of (one or more) parameters is added to an existing model. In addition, a few metrics have been developed to compare different models (also models that are not nested) based on the SSE and the number of parameters. [These](http://en.wikipedia.org/wiki/Bayesian_information_criterion) [metrics](http://en.wikipedia.org/wiki/Akaike_information_criterion) generally penalize a model for having many parameters and reward it for getting small SSE. However, these methods generally have some underlying assumptions and are not that transparent to understand. For a nice exposition on how to use these methods see [this paper]() (excuse the paywall...). Also, if you are interested in more on this topic, [The stats stack exchange website](http://stats.stackexchange.com/questions/20729/best-approach-for-model-selection-bayesian-or-cross-validation) is an excellent resource.\n", "\n", "\n", "- **Cross-validation**: The method we will focus on here is cross-validation. In this method, the accuracy of a model in fitting the data is assessed by fitting the parameters on part of the data (also referred to as the *training set*) and then testing it on another, held out data set (the *testing set*). In this case, overfitting is no longer a problem, because just looking at the training set, you can't possibly fit to the idiosyncratic noise present in the testing set. Let's see how that works for the comparison of the cumulative Gaussian and the Weibull functions. \n", "\n", "\n", "\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Split the data into testing and training sets:\n", "x_ortho_1 = x_ortho[1::2]\n", "y_ortho_1 = y_ortho[1::2]\n", "x_ortho_2 = x_ortho[::2]\n", "y_ortho_2 = y_ortho[::2]\n", "\n", "x_para_1 = x_para[1::2]\n", "y_para_1 = y_para[1::2]\n", "x_para_2 = x_para[::2]\n", "y_para_2 = y_para[::2]\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 26 }, { "cell_type": "code", "collapsed": false, "input": [ "initial = 0,0.5\n", "# Fit to the training data\n", "params_ortho_1, _ = opt.leastsq(err_func, initial, args=(x_ortho_1, y_ortho_1, cumgauss))\n", "params_para_1, _ = opt.leastsq(err_func, initial, args=(x_para_1, y_para_1, cumgauss))\n", "# Check SSE on the testing data:\n", "SSE_cumgauss = (np.sum((y_ortho_2 - cumgauss(x_ortho_2, *params_ortho_1))**2) + \n", " np.sum((y_para_2 - cumgauss(x_para_2, *params_para_1))**2))\n", "\n", "\n", "# Do this again, reversing training and testing data sets: \n", "params_ortho_2, _ = opt.leastsq(err_func, initial, args=(x_ortho_2, y_ortho_2, cumgauss))\n", "params_para_2, _ = opt.leastsq(err_func, initial, args=(x_para_2, y_para_2, cumgauss))\n", "# Check SSE on the testing data:\n", "SSE_cumgauss += (np.sum((y_ortho_1 - cumgauss(x_ortho_1, *params_ortho_2))**2) + \n", " np.sum((y_para_1 - cumgauss(x_para_1, *params_para_2))**2))\n", "\n", "print(\"For the cumulative Gaussian SSE=%s\"%SSE_cumgauss)\n", "\n", "# Let's do the same for the Weibull:\n", "initial = 0.5,3.5,0,0\n", "params_ortho_1, _ = opt.leastsq(err_func, initial, args=(x_ortho_1, y_ortho_1, weibull))\n", "params_para_1, _ = opt.leastsq(err_func, initial, args=(x_para_1, y_para_1, weibull))\n", "SSE_weibull = (np.sum((y_ortho_2 - weibull(x_ortho_2, *params_ortho_1))**2) + \n", " np.sum((y_para_2 - weibull(x_para_2, *params_para_1))**2))\n", "\n", "params_ortho_2, _ = opt.leastsq(err_func, initial, args=(x_ortho_2, y_ortho_2, weibull))\n", "params_para_2, _ = opt.leastsq(err_func, initial, args=(x_para_2, y_para_2, weibull))\n", "SSE_weibull += (np.sum((y_ortho_1 - weibull(x_ortho_1, *params_ortho_2))**2) + \n", " np.sum((y_para_1 - weibull(x_para_1, *params_para_2))**2))\n", "\n", "\n", "print(\"For the Weibull SSE=%s\"%SSE_weibull)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "For the cumulative Gaussian SSE=0.255651125042\n", "For the Weibull SSE=0.288565594471\n" ] } ], "prompt_number": 32 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that the SSE we calculated are evaluated each time on a completely separate, non-overlapping set of data. This means that over-fitting could no longer occur, no matter how many parameters you fit. Therefore, this approach does not require counting of the number of parameters. In this case, the cumulative Gaussian seems to perform marginally better than the Weibull function, even though the Weibull has more parameters." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Summary\n", "\n", "This tutorial focused on fitting models to data. We examined an example of data from a psychophysical data and used the scipy.optimize function leastsq to perform an iterative fit of a non-linear model to this data. Finally, we used cross-validation to select among different models. \n", "\n", "This approach is, of course, not limited to psychophysical data and can be easily applied to other kinds of data. \n", "\n", "# Get the code\n", "\n", "If you want to try this out for yourself, the code is in [this github repo](https://github.com/arokem/teach_optimization). Comments, feedback and pull requests most welcome. " ] }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }