{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Example of using the Reversible-Jump Markov Chain Monte Carlo algorithm on some noisy data\n", "\n", "The Data Science Research theme members of the Research School of Earth Sciences, The Australian National University.\n", "\n", "9 November 2017\n", "\n", "Please see the publication:\n", "\n", "1.Sambridge, M., Gallagher, K., Jackson, A. & Rickwood, P. Trans-dimensional inverse problems, model comparison and the evidence. Geophysical Journal International 167, 528–542 (2006).\n", "\n", "for details about trans-dimentional fitting and the use of the RJ-MCMC. See the iEarth website (http://www.iearth.org.au/) to get access to RJ-MCMC.\n", "\n", "Jupyter Notebook written from the examples and documentation of RJ-MCMC.\n", "\n", "For questions/errors, contact: [Charles Le Losq](mailto:charles.lelosq@anu.edu.au)\n", "\n", "## The libraries that we need\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# need to be in first position\n", "%matplotlib inline \n", "\n", "# matplotlib library and stuff needed for plots\n", "import matplotlib\n", "from matplotlib import pyplot as plt\n", "from mpl_toolkits.mplot3d import Axes3D\n", "from matplotlib import animation, rc\n", "\n", "\n", "# For calculations\n", "import rjmcmc \n", "import numpy as np # not really necessary as rjmcmc does not handle numpy arrays\n", "import random\n", "import math" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Data Generation\n", "\n", "We create some fake data that we can play with, using an interesting mathematical function that will require\n", "some higher order polynomial to fit." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "Text(0.5,1,u'Figure 1: our noisy observation...')" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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vhuuu8zaeVBhjplhry1O5roY+JW9kat5crhZKaEGGiEj2FerWUXFK1CRvZGre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\n9VXXNgY0Au0PStRERKRDjIF77klMOn/nHXjwQW9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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# The function givin us the truth!\n", "def realfunction(x):\n", " return math.exp(x/3.0) * math.sin(2.0*x/3.0)\n", "\n", "#\n", "# Set the parameters (x range etc)\n", "#\n", "xmin = 0.0\n", "xmax = 10.0\n", "npoints = 100\n", "nsigma = 3.5\n", "\n", "# creating a randomly spaced x axis\n", "dx = (xmax - xmin)/float(2*npoints)\n", "x = [dx + 2.0*dx*float(a) + random.uniform(-dx, dx) for a in range(npoints)]\n", "\n", "#\n", "# Create a higher sampled x vector for the smooth real curve\n", "#\n", "nsmoothpoints = 100\n", "xs = map(lambda x: float(x)/float(nsmoothpoints - 1) * (xmax - xmin) + xmin, range(nsmoothpoints))\n", "\n", "#\n", "# Determine the real values at those x-coordinates\n", "#\n", "y = map(realfunction, x)\n", "ys = map(realfunction, xs)\n", "\n", "#\n", "# Add some noise\n", "#\n", "yn = map(lambda y: y + random.normalvariate(0.0, nsigma), y)\n", "\n", "#\n", "# Plotting the truth and what we observed with a dummy instrument (se ehow bad it is!)\n", "#\n", "\n", "fig = plt.figure(figsize=(10,10))\n", "plt.plot(x, y, 'b-', label = 'Truth',linewidth=3.0)\n", "plt.plot(x, yn, 'ko', label='Observations')\n", "plt.legend()\n", "plt.xlabel('X')\n", "plt.ylabel('Y')\n", "plt.title('Figure 1: our noisy observation...')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Analyse\n", "\n", "### Estimate our error standard deviation\n", "\n", "An important part of the analysis is estimating the error in the data.\n", "This is specified as a error value per data point and can be thought of a weighting\n", "as to how well the fit will attempt to fit an individual point. If the value\n", "is low, then the fit will be tight and conversely if the value is high then the \n", "fit will be loose. We now set a value of 4.0 for all data points.\n", "Use this value for now, but try other values greater than 0.0 to see the effect." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "sigma = 4.0\n", "n = len(x)*[sigma]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Create the rjmcmc dataset\n", "\n", "We construct the dataset1d object from the x, y and n lists we created.\n", "These lists must be the same length. This is an rjmcmc.dataset1d\n", "object which wraps the x and y vectors you load from the file and includes individual\n", "point noise values. This is the only parameter which doesn't have a default value." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "data = rjmcmc.dataset1d(x, y, n)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Run the default analysis\n", "\n", "We run the analysis with this dataset1d object. The regression_single1d\n", "function returns a resultset1d object which contains various results and diagnostics\n", "about the analysis. \n", "\n", "- Defaults parameters are:\n", "\n", "[burnin = 10000] The number of initial samples to throw away. We assumed the MCMC did not converged to a viable solution yet for those samples.\n", "\n", "[total = 50000] The total number of samples to use for the analysis.\n", "\n", "[max_order = 2] The maximum order of polynomial to use to fit the data.\n", "\n", "[ysamples = 100] The number of points to sample along the y directory for the statistics such\n", "as mode, median and confidence intervals. This is the number of bins for the histograms in the \n", "y direction.\n", "\n", "[confidence_interval = 0.95] The confidence interval to use for minimum and maximum confidence\n", "intervals. This should be a value between 0 and 1.\n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "results = rjmcmc.regression_single1d(data)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Retrieve the mean curve for plotting\n", "\n", "For this simple analysis we simply take the x sampling coordinates\n", "and the mean of the fits." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "xc = results.x()\n", "meancurve = results.mean()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Plot the data with black crosses and the mean with a red line" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "Text(0.5,1,u'Figure 2: MCMC fit of the observations')" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Ona22lOyOpv5poBo1ERERiUUbNkBTb5LbZVY6h5oSNRERERG/XXklFBTAihU8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\n2kmgO/VapAfLP3UzWy76Mq+zHh98AL/5DXTVeEKxjVR+9RVcNLqEZ9g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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(10,10))\n", "plt.plot(x, y, 'b-', label = 'Truth',linewidth=3.0)\n", "plt.plot(x, yn, 'ko', label='Observations')\n", "plt.plot(xc, meancurve, 'r:', label = 'Model',linewidth=3.0)\n", "plt.legend()\n", "plt.xlabel('X')\n", "plt.ylabel('Y')\n", "plt.title('Figure 2: MCMC fit of the observations')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Order analysis series\n", "\n", "A question we may ask is what order best represents the underlying\n", "function. We can develop some understanding of this by constraining\n", "the maximum allowable order of the fit and observing when the order\n", "histogram converges and/or the mean of the fits converges.\n", "\n", "### Setting parameters\n", "\n", "We set parameters with lower number of total samples, and also of burnin. We increase the order limit. Then we run the MCMC analysis in a loop in which we increase the order limit of the algorithm at each iteration." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0\n", "1\n", "2\n", "3\n", "4\n", "5\n" ] } ], "source": [ "results = []\n", "burnin = 500\n", "total = 3000\n", "orderlimit = 5\n", "for maxorder in range(orderlimit + 1):\n", " print maxorder\n", " results.append(rjmcmc.regression_single1d(data, burnin, total, maxorder))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plotting the results\n", "\n", "Now we plot the data with black crosses the curves from each of the analyses with a different colour" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "Text(0.5,1,u'Figure 3: MCMC fits with different polynomial orders')" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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ZWZl5W1ZWFk5OTly5cqXR/H19fam71umtW7e4dOkSXl5egDFerqb6AjtfX19S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\n3A6qWW6uvsmP776DabdOY/O0zfR4rQeXP325p608J+xen6XEkSOmT+b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AoD5BtkgrRgrS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5eMKl57Ti7uHG79JDw7DgwL9eYYfP9Q9vn33oPffy9KawZq7Gog8BGq7FUcKnPaTGAsKjxyBPYD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\nnU5NvAT3xsKFWlwKOED7I60A8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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "colours=['red','cyan','yellow','purple','orange','magenta']\n", "\n", "fig = plt.figure(figsize=(10,10))\n", "ax = fig.add_subplot(111)\n", "\n", "ax.plot(x, y, 'b-', label = 'Truth',linewidth=3.0)\n", "ax.plot(x, yn, 'ko', label='Observations')\n", "\n", "# Now looping to plot the result of the RJ-MCMC analysis\n", "orders = []\n", "legendtitles = []\n", "for result in results:\n", "\n", " order = result.order_histogram()\n", " if order == None: # The max order = 0 case will return None so \n", " order = [total]\n", "\n", " ax.plot(result.x(), result.mean(), c =colours[len(orders)], label= 'Max. Order %d' % len(orders),linewidth=2.0)\n", "\n", " # Create the order histogram data (append zeros for orders not allowed in the analyses)\n", " orders.append(order + [0] * (orderlimit + 1 - len(order)))\n", "\n", "legend = ax.legend()\n", "plt.xlabel('X')\n", "plt.ylabel('Y')\n", "plt.ylim(-25,15)\n", "plt.title('Figure 3: MCMC fits with different polynomial orders')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Order analysis histogram\n", "\n", "Now we can plot a 3D bar chart showing the progression of the order histogram as the analysis maximum order is increased. The order histogram reports the count of polynomials\n", "of each order where the order is randomly choosen from a \n", "probability distribution determined by the data itself. \n", "\n", "Looking at the figure, it can be seen that when the maximum permitted\n", "order is 0, all the curves sampled are 0th order as expected. As this\n", "maximum order is increased, the distribution of orders changes until\n", "the step from 4 to 5 where there is little difference. It should be\n", "noted that if a tighter noise parameter is used, that this will change\n", "slightly as higher order polynomials will be more favoured to fit the\n", "data better.\n" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "Text(0.5,0.92,u'Figure4: Histogram of maximum orders')" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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cDsNqtSohvbKyctOPB1BIJ4T8CYVyQspEcu/xtQL5/Pw8BgYGsH//flRVVSm3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\nbdOIyY9ZhuM5kIYukIYn4jkTBb/3EQACwgkgjhuAoL6lh3zT3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JyMp59+WhbkAkEW5RKB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\nqwmqtT6TyQStVguVSmXpZS2VSuHh4YHCwkL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U1FQoFAqcP38eo0aNgkwmQ0hIyG0H9KYO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\nZAzlREREREQiYygnIiIiIhLZ/wMtU/7GOrCY3wAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(10,10))\n", "ax = Axes3D(fig)\n", "xs = range(orderlimit + 1)\n", "for maxorder in xs:\n", " ax.bar(xs, \n", " orders[maxorder], \n", " zs=maxorder, \n", " zdir = 'y', \n", " color=colours[maxorder])\n", "\n", "ax.set_xlabel('Order')\n", "ax.set_ylabel('Maximum Order')\n", "ax.set_zlabel('Count')\n", "ax.set_title('Figure4: Histogram of maximum orders')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Confidence Intervals\n", "\n", "So far we have only plotted the mean of the fits, however this gives\n", "us no indication of distribution of the fit (this can be thought of as\n", "the confidence of the fit). There are a number of ways in which we can\n", "look at this and one of these is to look at the curves generated\n", "during the analysis.\n", "\n", "In this script we call a slightly different function called regression_single1d_sampled which accepts a callback function. We define this function, which accepts an x and y list which is the discretization of the current \n", "fitting polynomial being used. In this function we sample every\n", "5th polynomial and store them. " ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "Text(0.5,1,u'Figure 5: Confidence interval (in grey)')" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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D2LZtGwAff/wx06dPB+C4444jNzeXzZs3s3btWn73u98Z55uXlwfAp59+yjfffMPQoUMB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\nPx5+v1/mIsTmLJrzRLms2DzVzVx4Q2osXzUQ6v1EG2+ssYn1YtS8RDA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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# This is our callback function which samples the curves generated \n", "# during the analysis\n", "#\n", "sample_x = None\n", "sample_curves = []\n", "sample_i = 0\n", "sample_rate = 5\n", "def sampler_cb(x, y):\n", " global sample_x, sample_curves, sample_i, sample_rate\n", "\n", " if sample_i == 0:\n", " sample_x = x\n", "\n", " if sample_i % sample_rate == 0:\n", " sample_curves.append(y)\n", "\n", " sample_i = sample_i + 1\n", "\n", "#\n", "# Run a series of analyses with varying maximum allowed order\n", "#\n", "results = []\n", "burnin = 100\n", "total = 1000\n", "maxorder = 5\n", "results = rjmcmc.regression_single1d_sampled(data, \n", " sampler_cb,\n", " burnin, \n", " total, \n", " maxorder)\n", " \n", "# Plot the data with black crosses, the sample curves as faint lines, and\n", "# the mean as a red line\n", "#\n", "fig = plt.figure()\n", "ax = fig.add_subplot(111)\n", "\n", "yc = 0.5\n", "yalpha = 1.0/((1.0 - yc) * float(len(sample_curves)))\n", "for sy in sample_curves:\n", "\n", " ax.plot(sample_x, sy, \n", " color = str(yc),\n", " alpha = yalpha,\n", " linestyle = '-',\n", " linewidth = 10)\n", "\n", "ax.plot(results.x(), results.mean(), 'r-',label='Mean of models')\n", "ax.plot(x, yn, 'ko',label='Noisy observations')\n", "ax.set_xlabel('X')\n", "ax.set_ylabel('Y')\n", "plt.legend()\n", "ax.set_title('Figure 5: Confidence interval (in grey)')\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The sampled fits are plotted with transparency so that where they\n", "overlap this will show increased density implying that where these\n", "sampled polynomial ensemble appears darker, we can have higher \n", "confidence that the underlying function passes through that\n", "region.\n", "\n", "### Now let's do the same but as a GIF plot, because it's cool." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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r7Jz7f6OFJJNyjkYrHBsTohgYEL9DJgMnnyz3LhiUc0wkLDkWFdlES5PYtH+/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\nfFythr4+9eufPKnxj5YWtSS6ulQgnNM7895efc97XLyocYF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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig_gif = plt.figure()\n", "axg = fig_gif.add_subplot(111)\n", "\n", "obs, = axg.plot(x, yn, 'ko')\n", "line, = axg.plot([], [], 'r.',alpha = 0.05)\n", "\n", "xdata = []\n", "ydata = []\n", "\n", "# initialization function: plot the background of each frame\n", "def init():\n", " obs.set_data([], [])\n", " line.set_data([], [])\n", " return (obs,line,)\n", "\n", "def update(i):\n", " \n", " xdata.append(sample_x)\n", " ydata.append(sample_curves[i])\n", " \n", " line.set_xdata(xdata)\n", " line.set_ydata(ydata)\n", " \n", " return line\n", "\n", "axg.set_xlabel('X')\n", "axg.set_ylabel('Y')\n", "axg.set_title('RJ-MCMC fit of noisy observations')\n", "\n", "anim2 = animation.FuncAnimation(fig_gif, update, frames=len(sample_curves), interval=100, repeat=True)\n", "anim2.save('MCMC_example.gif', dpi=80, writer='imagemagick')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Estimating data noise\n", "\n", "With the hierarchical Bayesian approach we include the standard deviation\n", "of the noise on the observations as an unknown. In the above examples\n", "the noise $\\sigma$ was set to 3 units, but the actual $\\sigma$\n", "of the data noise in Figure 1 is 3.5.\n", "Can we use the data to detect the true standard deviation of its noise?\n", "The hierarchical Bayesian sampling scheme is implemented with the following script. Inference on the noise is implemented by \n", "introducing a new parameter, $\\lambda = \\frac{\\sigma_{est}}{\\sigma_{true}}$, \n", "defined as the ratio of the estimated noise to the real noise.\n" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Lambda Acceptance Rate (%): 11.0670194004\n", "Lambda average: 0.50661568777\n" ] }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lambda_min = 0.5\n", "lambda_max = 2.0\n", "lambda_std = 0.05\n", "\n", "\n", "#\n", "# Set the lambda range\n", "#\n", "data.set_lambda_range(lambda_min, lambda_max)\n", "data.set_lambda_std(lambda_std)\n", "\n", "#\n", "# Run the default analysis\n", "#\n", "results = rjmcmc.regression_single1d(data)\n", "\n", "#\n", "# Retrieve the mean curve for plotting\n", "#\n", "xc = results.x()\n", "meancurve = results.mean()\n", "\n", "#\n", "# Retrieve the results of the hierarchical\n", "#\n", "p = results.proposed()\n", "a = results.acceptance()\n", "\n", "print 'Lambda Acceptance Rate (%):', float(a[1])/float(p[1]) * 100.0\n", "\n", "lh = results.lambda_history()\n", "\n", "#\n", "# Plot the hostory of lambda\n", "#\n", "\n", "fig = plt.figure()\n", "plt.plot(range(len(lh)), lh)\n", "plt.xlabel('Number of runs')\n", "plt.xlabel('Lambda')\n", "plt.title('Figure 6: Lambda history')\n", "\n", "fig = plt.figure()\n", "\n", "a = plt.subplot(111)\n", "lsamples = lh[10000:]\n", "\n", "n, bins, patches = a.hist(lsamples, 100, range=(lambda_min, lambda_max))\n", "a.set_title('Figure 7: Histogram of Lambda')\n", "a.set_xlabel('Lambda')\n", "a.set_ylabel('Count')\n", "\n", "print 'Lambda average:', sum(lsamples)/float(len(lsamples))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this script we set up a uniform prior on $\\lambda$ over a pre-determined range and use\n", "a Gaussian distribution to perturb the $\\lambda$ values during the Markov chain.\n", "The range of the values of $\\lambda$ as well as the standard deviation of the\n", "perturbation are parameter that must be chosen. These are set in lines\n", "37-42. \n", "\n", "We call the function regression_single1 to do the work. \n", "We plot the posterior PDF of the noise $\\sigma$ as a histogram. \n", "This plot is shown in Figure 7.\n", "\n", "The histogram shows the support of the data for a range of $\\lambda$ values. \n", "Clearly there is information in the data on the likely values of noise.\n", "Where is the peak of the histogram? How does this compare to the ratio of the estimated\n", "to true $\\sigma$? Usually the ability of the data to constrain noise parameters will trade-off \n", "with the model complexity given, in this case, by the order of the polynomial.\n", "You can edit the script by changing the estimated noise and rerun to see what happens." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.11" } }, "nbformat": 4, "nbformat_minor": 0 }