{ "cells": [ { "cell_type": "markdown", "metadata": { "hide": true }, "source": [ "# Why do we need validation?\n", "\n", "##### Keywords: empirical risk minimization, Hoeffding's inequality, hypothesis space, training error, out-of-sample error, testing set, training set, test error, validation error, complexity parameter, cross-validation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Contents\n", "{:.no_toc}\n", "* \n", "{: toc}" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false, "hide": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "//anaconda/envs/py35/lib/python3.5/site-packages/matplotlib/__init__.py:872: UserWarning: axes.color_cycle is deprecated and replaced with axes.prop_cycle; please use the latter.\n", " warnings.warn(self.msg_depr % (key, alt_key))\n" ] } ], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import scipy as sp\n", "import matplotlib as mpl\n", "import matplotlib.cm as cm\n", "import matplotlib.pyplot as plt\n", "import pandas as pd\n", "pd.set_option('display.width', 500)\n", "pd.set_option('display.max_columns', 100)\n", "pd.set_option('display.notebook_repr_html', True)\n", "import seaborn as sns\n", "sns.set_style(\"whitegrid\")\n", "sns.set_context(\"poster\")" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false, "hide": true }, "outputs": [], "source": [ "def make_simple_plot():\n", " fig, axes=plt.subplots(figsize=(12,5), nrows=1, ncols=2);\n", " axes[0].set_ylabel(\"$y$\")\n", " axes[0].set_xlabel(\"$x$\")\n", " axes[1].set_xlabel(\"$x$\")\n", " axes[1].set_yticklabels([])\n", " axes[0].set_ylim([-2,2])\n", " axes[1].set_ylim([-2,2])\n", " plt.tight_layout();\n", " return axes\n", "def make_plot():\n", " fig, axes=plt.subplots(figsize=(20,8), nrows=1, ncols=2);\n", " axes[0].set_ylabel(\"$p_R$\")\n", " axes[0].set_xlabel(\"$x$\")\n", " axes[1].set_xlabel(\"$x$\")\n", " axes[1].set_yticklabels([])\n", " axes[0].set_ylim([0,1])\n", " axes[1].set_ylim([0,1])\n", " axes[0].set_xlim([0,1])\n", " axes[1].set_xlim([0,1])\n", " plt.tight_layout();\n", " return axes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Revisiting the model\n", "\n", "Let $x$ be the fraction of religious people in a county and $y$ be the probability of voting for Romney as a function of $x$. In other words $y_i$ is data that pollsters have taken which tells us their estimate of people voting for Romney and $x_i$ is the fraction of religious people in county $i$. Because poll samples are finite, there is a margin of error on each data point or county $i$, but we will ignore that for now." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " f i x y\n", "0 0.075881 7 0.07 0.138973\n", "1 0.085865 9 0.09 0.050510\n", "2 0.096800 11 0.11 0.183821\n", "3 0.184060 23 0.23 0.057621\n", "4 0.285470 33 0.33 0.358174" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df = pd.read_csv(\"data/noisysample.csv\")\n", "df.head()" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from sklearn.cross_validation import train_test_split\n", "datasize=df.shape[0]\n", "#split dataset using the index, as we have x,f, and y that we want to split.\n", "itrain,itest = train_test_split(range(30),train_size=24, test_size=6)\n", "xtrain= df.x[itrain].values\n", "ftrain = df.f[itrain].values\n", "ytrain = df.y[itrain].values\n", "xtest= df.x[itest].values\n", "ftest = df.f[itest].values\n", "ytest = df.y[itest].values" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Validation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A separate validation set is needed because what we have done in picking a given polynomial degree $d$ as the best hypothesis is that we have used the test set as a training set. How?\n", "\n", "Our process used the training set to fit for the **parameters**(values of the coefficients) of the polynomial of given degree $d$ based on minimizing the traing set error (empirical risk minimization). We then calculated the error on the test set at that $d$. If we go further and choose the best $d$ based on minimizing the test set error, we have then \"fit for\" $d$ on the test set. We will thus call $d$ a **hyperparameter** of the model.\n", "\n", "In this case, the test-set error will underestimate the true out-of-sample error. Furthermore, we have **contaminated the test set** by fitting for $d$ on it; it is no longer a true test set.\n", "\n", "Thus, we must introduce a new **validation set** on which the complexity parameter $d$ is fit, and leave out a test set which we can use to estimate the true out-of-sample performance of our learner. The place of this set in the scheme of things is shown below:\n", "\n", "![m:caption](images/train-validate-test.png)\n", "\n", "We have split the old training set into a training set and a validation set, holding the old test aside for FINAL testing AFTER we have \"fit\" for complexity $d$. Obviously we have decreased the size of the data available for training further, but this is a price we must pay for obtaining a good estimate of the out-of-sample risk $\\cal{E_{out}}$ (also denoted as risk $R_{out}$) through the test risk $\\cal{E_{test}}$ ($R_{test}$).\n", "\n", "![m:caption](images/train-validate-test-cont.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The validation process is illustrated in these two figures. We first loop over all the hypothesis sets that we wish to consider: in our case this is a loop over the complexity parameter $d$, the degree of the polynomials we will try and fit. Then for each degree $d$, we obtain a best fit model $g^-_d$ where the \"minus\" superscript indicates that we fit our model on the new training set which is obtained by removing (\"minusing\") a validation chunk (often the same size as the test chunk) from the old training set. We then \"test\" this model on the validation chunk, obtaining the validation error for the best-fit polynomial coefficients and for degree $d$. We move on to the next degree $d$ and repeat the process, just like before. We compare all the validation set errors, just like we did with the test errors earlier, and pick the degree $d_*$ which minimizes this validation set error.\n", "\n", "![caption](images/train-validate-test3.png)\n", "\n", "Having picked the hyperparameter $d_\\*$, we retrain using the hypothesis set $\\cal{H_\\*}$ on the entire old training-set to find the parameters of the polynomial of order $d_\\*$ and the corresponding best fit hypothesis $g_\\*$. Note that we left the minus off the $g$ to indicate that it was trained on the entire old traing set. We now compute the test error on the test set as an estimate of the test risk $\\cal{E_{test}}$.\n", "\n", "Thus the **validation** set is the set on which the hyperparameter is fit. This method of splitting the data $\\cal{D}$ is called the **train-validate-test** split.\n", "\n", "### Properties of the validation set\n", "\n", "First assume that the validation set is acting like a test set. then, for the same reasons as in the case of a test set, the validation risk or error is an unbiased estimate of the out of sample risk. Secondly, the Hoeffding bound for a validation set is then for the same reason identical to that of the test set.\n", "\n", "More often though the validation set is used in a model selection process. Here we wish to choose the complexity parameter $d$, something we **wrongly** already attempted to do on our previous test set.\n", "\n", "Notice that the process of validation consists of fixing $d$ and finding the best fit $g^\\*$ on the training set. We then calculate as many risks as our parameter grid on the validation set with the different fit hypothesis, and choose the $d, g^\\*$ combination with the lowest validation set risk. Now, $R_{val}(g^{-\\*}, d^\\*)$ also has an optimistic bias, and its Hoeffding bound must now take into account the grid-size as the effecting size of the hypothesis space. This size from hyperparameters is typically a smaller size than that from parameters.\n", "\n", "We finally now retrain on the entire train+validation set using the appropriate $(g^{-\\*}, d^\\*)$ combination. This works as training a given model with more data typically reduces the risk even further. (One can show this using learning curves but thats out of our scope).\n", "\n", "### Working it out\n", "\n", "We carry out this process for one training/validation split below. Note the smaller size of the new training set. We hold the test set at the same size." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from sklearn.preprocessing import PolynomialFeatures\n", "from sklearn.linear_model import LinearRegression\n", "from sklearn.metrics import mean_squared_error" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def make_features(train_set, test_set, degrees):\n", " traintestlist=[]\n", " for d in degrees:\n", " traintestdict={}\n", " traintestdict['train'] = PolynomialFeatures(d).fit_transform(train_set.reshape(-1,1))\n", " traintestdict['test'] = PolynomialFeatures(d).fit_transform(test_set.reshape(-1,1))\n", " traintestlist.append(traintestdict)\n", " return traintestlist" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [], "source": [ "#we split the training set down further\n", "intrain,invalid = train_test_split(itrain,train_size=18, test_size=6)\n", "xntrain= df.x[intrain].values\n", "fntrain = df.f[intrain].values\n", "yntrain = df.y[intrain].values\n", "xnvalid= df.x[invalid].values\n", "fnvalid = df.f[invalid].values\n", "ynvalid = df.y[invalid].values\n", "\n", "degrees=range(21)\n", "error_train=np.empty(len(degrees))\n", "error_valid=np.empty(len(degrees))\n", "trainvalidlists=make_features(xntrain, xnvalid, degrees)\n", "\n", "#we now train on the smaller training set\n", "for d in degrees:#for increasing polynomial degrees 0,1,2...\n", " #Create polynomials from x\n", " Xntrain = trainvalidlists[d]['train']\n", " Xnvalid = trainvalidlists[d]['test']\n", " #fit a model linear in polynomial coefficients on the new smaller training set\n", " est = LinearRegression()\n", " est.fit(Xntrain, yntrain)\n", " #predict on new training and validation sets and calculate mean squared error\n", " error_train[d] = mean_squared_error(yntrain, est.predict(Xntrain))\n", " error_valid[d] = mean_squared_error(ynvalid, est.predict(Xnvalid))\n", "\n", "#calculate the degree at which validation error is minimized\n", "mindeg = np.argmin(error_valid)\n", "#need to remake polynomial features on the whole training set\n", "ttlist=make_features(xtrain, xtest, degrees)\n", "features_at_mindeg = ttlist[mindeg]['train']\n", "test_features_at_mindeg = ttlist[mindeg]['test']\n", "#fit on whole training set now. Put MSE in variable err.\n", "#your code here\n", "clf = LinearRegression()\n", "clf.fit(features_at_mindeg, ytrain) # fit\n", "#predict on the test set now and calculate error\n", "pred = clf.predict(test_features_at_mindeg)\n", "err = mean_squared_error(ytest, pred)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2\n" ] }, { "data": { "image/png": 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zTY2dT0RERKSuuXA8yA0KIYDehIiLGYbh8N8iIiIiDUl+8Un25f8IQNuAVoQG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\nwWDA0qVLkZCQgI8//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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(degrees, error_train, marker='o', label='train (in-sample)')\n", "plt.plot(degrees, error_valid, marker='o', label='validation')\n", "plt.plot([mindeg], [err], marker='s', markersize=10, label='test', alpha=0.5, color='r')\n", "plt.ylabel('mean squared error')\n", "plt.xlabel('degree')\n", "plt.legend(loc='upper left')\n", "plt.yscale(\"log\")\n", "print(mindeg)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Lets do this again, choosing a new random split between training and validation data: " ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": true }, "outputs": [], "source": [ "intrain,invalid = train_test_split(itrain,train_size=18, test_size=6)\n", "xntrain= df.x[intrain].values\n", "fntrain = df.f[intrain].values\n", "yntrain = df.y[intrain].values\n", "xnvalid= df.x[invalid].values\n", "fnvalid = df.f[invalid].values\n", "ynvalid = df.y[invalid].values\n", "\n", "degrees=range(21)\n", "error_train=np.empty(len(degrees))\n", "error_valid=np.empty(len(degrees))\n", "trainvalidlists=make_features(xntrain, xnvalid, degrees)\n", "\n", "for d in degrees:#for increasing polynomial degrees 0,1,2...\n", " #Create polynomials from x\n", " Xntrain = trainvalidlists[d]['train']\n", " Xnvalid = trainvalidlists[d]['test']\n", " #fit a model linear in polynomial coefficients on the training set\n", " est = LinearRegression()\n", " est.fit(Xntrain, yntrain)\n", " #calculate mean squared error\n", " error_train[d] = mean_squared_error(yntrain, est.predict(Xntrain))\n", " error_valid[d] = mean_squared_error(ynvalid, est.predict(Xnvalid))\n", "\n", "mindeg = np.argmin(error_valid)\n", "ttlist=make_features(xtrain, xtest, degrees)\n", "features_at_mindeg = ttlist[mindeg]['train']\n", "test_features_at_mindeg = ttlist[mindeg]['test']\n", "clf = LinearRegression()\n", "clf.fit(features_at_mindeg, ytrain) # fit\n", "pred = clf.predict(test_features_at_mindeg)\n", "err = mean_squared_error(ytest, pred)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2\n" ] }, { "data": { "image/png": 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R5ebmesfee+893X333Zo0aZJeeuklE9MBAAAA/pd/dLeqnNWSpGHXDFZ0eJTJiS5PyBSS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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(degrees, error_train, marker='o', label='train (in-sample)')\n", "plt.plot(degrees, error_valid, marker='o', label='validation')\n", "plt.plot([mindeg], [err], marker='s', markersize=10, label='test', alpha=0.5, color='r')\n", "\n", "plt.ylabel('mean squared error')\n", "plt.xlabel('degree')\n", "plt.legend(loc='lower left')\n", "plt.yscale(\"log\")\n", "print(mindeg)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This time the validation error minimizing polynomial degree might change! What happened?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Cross Validation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The problem" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "1. Since we are dealing with small data sizes here, you should worry that a given split exposes us to the peculiarity of the data set that got randomly chosen for us. This naturally leads us to want to choose multiple such random splits and somehow average over this process to find the \"best\" validation minimizing polynomial degree or complexity $d$.\n", "2. The multiple splits process also allows us to get an estimate of how consistent our prediction error is: in other words, just like in the hair example, it gives us a distribution. So far we have been channeling the hair through the bootstrap, but choosing multiple splits is another way to get different training samples..\n", "3. Furthermore the validation set that we left out has two competing demands on it. The larger the set is, the better is our estimate of the out-of-sample error. So we'd like to hold out as much as possible. But the smaller the validation set is, the more data we have to train ourmodel on. Thus we can fit a better, more expressive model. We want to balance these two desires, and additionally, not be exposed to any peculiarities that might randomly arise in any single train-validate split of the old training set." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Idea" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To deal with this we engage in a process called **cross-validation**, which is illustrated in the figure below, for a given hypothesis set $\\cal{H}_a$ with complexity parameter $d=a$ (the polynomial degree). We do the train/validate split, not once but multiple times. \n", "\n", "In the figure below we create 4-folds from the training set part of our data set $\\cal{D}$. By this we mean that we divide our set roughly into 4 equal parts. As illustrated below, this can be done in 4 different ways, or folds. In each fold we train a model on 3 of the parts. The model so trained is denoted as $g^-_{Fi}$, for example $g^-_{F3}$ . The minus sign in the superscript once again indicates that we are training on a reduced set. The $F3$ indicates that this model was trained on the third fold. Note that the model trained on each fold will be different!\n", "\n", "For each fold, after training the model, we calculate the risk or error on the remaining one validation part. We then add the validation errors together from the different folds, and divide by the number of folds to calculate an average error. Note again that this average error is an average over different models $g^-_{Fi}$. We use this error as the validation error for $d=a$ in the validation process described earlier." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![m:caption](images/train-cv2.png)\n", "\n", "Note that the number of folds is equal to the number of splits in the data. For example, if we have 5 splits, there will be 5 folds. To illustrate cross-validation consider below fits in $\\cal{H}_0$ and $\\cal{H}_1$ (means and straight lines) to a sine curve, with only 3 data points.\n", "\n", "We have described cross-validation here from the perspective of sensibly fitting for the complexity hyperparameter $d$. But we can use it just like a pure validation set as well, just making sure we arent getting strange results due to a wierdly sampled validation set. In that case, (it can also shown that) **cross-validation error is an unbiased estimate of the out of sample-error**.\n", "\n", "Notice that just like the bootstraps we do in frequentist inference, **cross-validation is a re-sampling method**. Indeed, a question might be, why not use bootstrap instead. See http://stats.stackexchange.com/questions/18348/differences-between-cross-validation-and-bootstrapping-to-estimate-the-predictio , and note that the so-called \"out-of-bag\" errors from \"bagging\" in random forests utilizes the bootstrap." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The entire description of K-fold Cross-validation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We put thogether this scheme to calculate the error for a given polynomial degree $d$ with the method we used earlier to choose a model given the validation-set risk as a function of $d$:\n", "\n", "1. create `n_folds` partitions of the training data. \n", "2. We then train on `n_folds -1` of these partitions, and test on the remaining partition. There are `n_folds` such combinations of partitions (or folds), and thus we obtain `n_fold` risks.\n", "3. We average the error or risk of all such combinations to obtain, for each value of $d$, $R_{dCV}$.\n", "4. We move on to the next value of $d$, and repeat 3\n", "5. and then find the optimal value of d that minimizes risk $d=*$.\n", "5. We finally use that value to make the final fit in $\\cal{H}_*$ on the entire old training set.\n", "\n", "![caption](images/train-cv3.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us now do 4-fold cross-validation on our Romney votes data set. We increase the complexity from degree 0 to degree 20. In each case we take the old training set, split in 4 ways into 4 folds, train on 3 folds, and calculate the validation error on the ramining one. We then average the erros over the four folds to get a cross-validation error for that $d$. Then we did what we did before: find the hypothesis space $\\cal{H_*}$ with the lowest cross-validation error, and refit it using the entire training set. We can then use the test set to estimate $E_{out}$." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from sklearn.cross_validation import KFold\n", "n_folds=4\n", "degrees=range(21)\n", "results=[]\n", "for d in degrees:\n", " hypothesisresults=[]\n", " for train, test in KFold(24, n_folds): # split data into train/test groups, 4 times\n", " tvlist=make_features(xtrain[train], xtrain[test], degrees)\n", " clf = LinearRegression()\n", " clf.fit(tvlist[d]['train'], ytrain[train]) # fit\n", " hypothesisresults.append(mean_squared_error(ytrain[test], clf.predict(tvlist[d]['test']))) # evaluate score function on held-out data\n", " results.append((np.mean(hypothesisresults), np.min(hypothesisresults), np.max(hypothesisresults), np.std(hypothesisresults))) # average" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "//anaconda/envs/py35/lib/python3.5/site-packages/matplotlib/__init__.py:892: UserWarning: axes.color_cycle is deprecated and replaced with axes.prop_cycle; please use the latter.\n", " warnings.warn(self.msg_depr % (key, alt_key))\n" ] }, { "data": { "image/png": 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J9vaYXqclAYkQQgghRBsKR3S8NaHYbksFxZ5YQzndAOvXZeTmpDF+WCZZGYkd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\nIiIiIiLKmP8P+8qRI2MpIYYAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mindeg = np.argmin([r[0] for r in results])\n", "ttlist=make_features(xtrain, xtest, degrees)\n", "#fit on whole training set now.\n", "clf = LinearRegression()\n", "clf.fit(ttlist[mindeg]['train'], ytrain) # fit\n", "pred = clf.predict(ttlist[mindeg]['test'])\n", "err = mean_squared_error(pred, ytest)\n", "errtr=mean_squared_error(ytrain, clf.predict(ttlist[mindeg]['train']))\n", "errout=0.8*errtr+0.2*err\n", "c0=sns.color_palette()[0]\n", "c1=sns.color_palette()[1]\n", "#plt.errorbar(degrees, [r[0] for r in results], yerr=[r[1] for r in results], marker='o', label='CV error', alpha=0.5)\n", "plt.plot(degrees, [r[0] for r in results], marker='o', label='CV error', alpha=0.9)\n", "plt.fill_between(degrees, [r[1] for r in results], [r[2] for r in results], color=c0, alpha=0.2)\n", "\n", "\n", "plt.plot([mindeg], [err], 'o', label='test set error')\n", "plt.plot([mindeg], [errout], 'o', label='full sample error')\n", "\n", "\n", "plt.ylabel('mean squared error')\n", "plt.xlabel('degree')\n", "plt.legend(loc='upper right')\n", "plt.yscale(\"log\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that the cross-validation error minimizes at a low degree, and then increases. Because we have so few data points the spread in fold errors increases as well.\n", "\n", "So now we have an average out of sample error, matched to the in-sample error, and error bars telling is that the entire order 1-8 polynomial region (roughly) is trustable..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### What does Cross Validation do?\n", "\n", "One can think about the validation process as one that estimates $R_{out}$ directly, on the validation set. It's critical use is in the model selection process. Once you do that you can estimate $R_{out}$ using the test set as usual, but now you have also got the benefit of a robust average and error bars.\n", "\n", "One key subtlety to remember about cross-validation is that in the risk averaging process, you are actually averaging over different $g^-$ models, with different parameters. You arrive at the least risk for the hyperparameter and then refit on the entire training set, which will likely give you slightly different parameters as well." ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python [conda env:py35]", "language": "python", "name": "conda-env-py35-py" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 0 }