examples/BART/BART_introduction.ipynb

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    "(BART_introduction)=\n",
    "# Bayesian Additive Regression Trees: Introduction\n",
    ":::{post} Dec 21, 2021\n",
    ":tags: BART, Bayesian additive regression trees, non-parametric, pymc3.BART, pymc3.HalfNormal, pymc3.Model, pymc3.Normal, pymc3.Poisson, regression\n",
    ":category: intermediate, explanation\n",
    ":author: Osvaldo Martin\n",
    ":::"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "7c087cca",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running on PyMC v4.0.0b6\n"
     ]
    }
   ],
   "source": [
    "from pathlib import Path\n",
    "\n",
    "import arviz as az\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import pymc as pm\n",
    "import pymc_experimental as pmx\n",
    "\n",
    "print(f\"Running on PyMC v{pm.__version__}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "25cf7b45",
   "metadata": {},
   "outputs": [],
   "source": [
    "RANDOM_SEED = 8457\n",
    "rng = np.random.RandomState(RANDOM_SEED)\n",
    "az.style.use(\"arviz-darkgrid\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "444df604",
   "metadata": {},
   "source": [
    "## BART overview"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "86f379df",
   "metadata": {},
   "source": [
    "Bayesian additive regression trees (BART) is a non-parametric regression approach. If we have some covariates $X$ and we want to use them to model $Y$, a BART model (omitting the priors) can be represented as:\n",
    "\n",
    "$$Y = f(X) + \\epsilon$$\n",
    "\n",
    "where we use a sum of $m$ [regression trees](https://en.wikipedia.org/wiki/Decision_tree_learning) to model $f$, and $\\epsilon$ is some noise. In the most typical examples $\\epsilon$ is normally distributed, $\\mathcal{N}(0, \\sigma)$. So we can also write:\n",
    "\n",
    "$$Y \\sim \\mathcal{N}(\\mu=BART(X), \\sigma)$$\n",
    "\n",
    "In principle nothing restricts us to use a sum of trees to model other relationship. For example we may have:\n",
    "\n",
    "$$Y \\sim \\text{Poisson}(\\mu=BART(X))$$\n",
    "\n",
    "One of the reason BART is Bayesian is the use of priors over the regression trees. The priors are defined in such a way that they favor shallow trees with leaf values close to zero. A key idea is that a single BART-tree is not very good at fitting the data but when we sum many of these trees we get a good and flexible approximation."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e239c2c0",
   "metadata": {},
   "source": [
    "## Coal mining with BART\n",
    "\n",
    "To better understand BART in practice we are going to use the oldie but goldie coal mining disaster dataset. One of the classic examples in PyMC. Instead of thinking this problem as a switch-point model with two Poisson distribution, as in the original PyMC example. We are going to think this problem as a non-parametric regression with a Poisson response (this is usually discussed in terms of [Poisson processes](https://en.wikipedia.org/wiki/Poisson_point_process) or [Cox processes](https://en.wikipedia.org/wiki/Cox_process), but we are OK without going into those technicalities). For a similar example but with Gaussian processes see [1](https://github.com/aloctavodia/BAP/blob/master/code/Chp7/07_Gaussian%20process.ipynb) or [2](https://research.cs.aalto.fi/pml/software/gpstuff/demo_lgcp.shtml). Because our data is just a single column with dates, we need to do some pre-processing. We are going to discretize the data, just as if we were building a histogram. We are going to use the centers of the bins as the variable $X$ and the counts per bin as the variable $Y$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "85bdba1b",
   "metadata": {},
   "outputs": [],
   "source": [
    "try:\n",
    "    coal = np.loadtxt(Path(\"..\", \"data\", \"coal.csv\"))\n",
    "except FileNotFoundError:\n",
    "    coal = np.loadtxt(pm.get_data(\"coal.csv\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "5d1221b3",
   "metadata": {},
   "outputs": [],
   "source": [
    "# discretize data\n",
    "years = int(coal.max() - coal.min())\n",
    "bins = years // 4\n",
    "hist, x_edges = np.histogram(coal, bins=bins)\n",
    "# compute the location of the centers of the discretized data\n",
    "x_centers = x_edges[:-1] + (x_edges[1] - x_edges[0]) / 2\n",
    "# xdata needs to be 2D for BART\n",
    "x_data = x_centers[:, None]\n",
    "# express data as the rate number of disaster per year\n",
    "y_data = hist / 4"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "98e0da5c",
   "metadata": {},
   "source": [
    "In PyMC a BART variable can be defined very similar to other random variables. One important difference is that we have to pass ours Xs and Ys to the BART variable. Here we are also making explicit that we are going to use a sum over 20 trees (`m=20`). Low number of trees like 20 could be good enough for simple models like this and could also work very good as a quick approximation for more complex models in particular during the iterative or explorative phase of modeling. In those cases once we have more certainty about the model we really like we can improve the approximation by increasing `m`, in the literature is common to find reports of good results with numbers like 50, 100 or 200."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6ac663f0",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "PGBART: [μ]\n"
     ]
    },
    {
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       "\n",
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       "      100.00% [8000/8000 00:17<00:00 Sampling 4 chains, 0 divergences]\n",
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     "text": [
      "Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 18 seconds.\n"
     ]
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   ],
   "source": [
    "with pm.Model() as model_coal:\n",
    "    μ = pmx.BART(\"μ\", X=x_data, Y=y_data, m=20)\n",
    "    y_pred = pm.Poisson(\"y_pred\", mu=pm.math.exp(μ), observed=y_data)\n",
    "    idata_coal = pm.sample(random_seed=RANDOM_SEED)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e967bf5",
   "metadata": {},
   "source": [
    "The white line in the following plot shows the median rate of accidents. The darker orange band represent the HDI 50% and the lighter one the 94%. We can see a rapid decrease of coal accidents between 1880 and 1900. Feel free to compare these results with those in the original {ref}`pymc:pymc_overview` example."
   ]
  },
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   "cell_type": "code",
   "execution_count": 6,
   "id": "1c715dbe",
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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_, ax = plt.subplots(figsize=(10, 6))\n",
    "\n",
    "rates = np.exp(idata_coal.posterior[\"μ\"])\n",
    "rate_median = np.exp(idata_coal.posterior[\"μ\"].median(dim=[\"draw\", \"chain\"]))\n",
    "ax.plot(x_centers, rate_median, \"w\", lw=3)\n",
    "az.plot_hdi(x_centers, rates, smooth=False)\n",
    "az.plot_hdi(x_centers, rates, hdi_prob=0.5, smooth=False, plot_kwargs={\"alpha\": 0})\n",
    "ax.plot(coal, np.zeros_like(coal) - 0.5, \"k|\")\n",
    "ax.set_xlabel(\"years\")\n",
    "ax.set_ylabel(\"rate\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "81f778de",
   "metadata": {},
   "source": [
    "In the previous plot the white line is the median over 4000 posterior draws, and each one of those posterior draws is a sum over `m=20` trees. \n",
    "\n",
    "\n",
    "The following figure shows two samples from the posterior of $\\mu$. We can see that these functions are not smooth. This is fine and is a direct consequence of using regression trees. Trees can be seen as a way to represent stepwise functions, and a sum of stepwise functions is just another stepwise function. Thus, when using BART we just need to know that we are assuming that a stepwise function is a good enough approximation for our problem. In practice this is often the case because we sum over many trees, usually values like 50, 100 or 200. Additionally, we often average over the posterior distribution. All this makes the \"steps smoother\", even when we never really have an smooth function as for example with Gaussian processes (splines). A nice theoretical result, tells us that in the limit of $m \\to \\infty$ the BART prior converges to a [nowheredifferentiable](https://en.wikipedia.org/wiki/Weierstrass_function) Gaussian process."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "0c982c16",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.step(x_data, np.exp(pmx.bart.predict(idata_coal, rng, x_data, size=2).T));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8633b7b4",
   "metadata": {},
   "source": [
    "To gain further intuition the next figures show 3 of the `m` trees. As we can see these are definitely not very good approximators by themselves. inspecting individuals trees is generally not necessary. We are just showing them here to generate intuition about BART."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "252054ff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bart_trees = idata_coal.sample_stats.bart_trees\n",
    "for i in [0, 1, 2]:\n",
    "    plt.step(x_data[:, 0], [bart_trees[0, 0, i].item().predict(x) for x in x_data])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c7d04e15",
   "metadata": {},
   "source": [
    "## Biking with BART"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "abf8c799-b89e-48dc-a1c9-8366325a530a",
   "metadata": {},
   "source": [
    "To explore other features offered by BART in PyMC. We are now going to move on to a different example. In this example we have data about the  number of bikes rental in a city, and we have chosen four covariates; the hour of the day, the temperature, the humidity and whether is a workingday or a weekend. This dataset is a subset of the [bike_sharing_dataset](http://archive.ics.uci.edu/ml/datasets/Bike+Sharing+Dataset)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "099f4c0e",
   "metadata": {},
   "outputs": [],
   "source": [
    "try:\n",
    "    bikes = pd.read_csv(Path(\"..\", \"data\", \"bikes.csv\"))\n",
    "except FileNotFoundError:\n",
    "    bikes = pd.read_csv(pm.get_data(\"bikes.csv\"))\n",
    "\n",
    "X = bikes[[\"hour\", \"temperature\", \"humidity\", \"workingday\"]]\n",
    "Y = bikes[\"count\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "5f8410b2",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "CompoundStep\n",
      ">NUTS: [σ]\n",
      ">PGBART: [μ]\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       "    /* Turns off some styling */\n",
       "    progress {\n",
       "        /* gets rid of default border in Firefox and Opera. */\n",
       "        border: none;\n",
       "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
       "        background-size: auto;\n",
       "    }\n",
       "    .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
       "        background: #F44336;\n",
       "    }\n",
       "</style>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "    <div>\n",
       "      <progress value='8000' class='' max='8000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
       "      100.00% [8000/8000 00:47<00:00 Sampling 4 chains, 0 divergences]\n",
       "    </div>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 47 seconds.\n",
      "The acceptance probability does not match the target. It is 0.9019, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as model_bikes:\n",
    "    σ = pm.HalfNormal(\"σ\", Y.std())\n",
    "    μ = pmx.BART(\"μ\", X, Y, m=50)\n",
    "    y = pm.Normal(\"y\", μ, σ, observed=Y)\n",
    "    idata_bikes = pm.sample(random_seed=RANDOM_SEED)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5daefd3e",
   "metadata": {},
   "source": [
    "### Partial dependence plots"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "99fd44df",
   "metadata": {},
   "source": [
    "To help us interpret the results of our model we are going to use partial dependence plot. This is a type of plot that shows the marginal effect that one covariate has on the predicted variable. That is, what is the effect that a covariate $X_i$ has of $Y$ while we average over all the other covariates ($X_j, \\forall j \\not = i$). This type of plot are not exclusive of BART. But they are often used in the BART literature. PyMC provides an utility function to make this plot from the inference data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "9bb3955d-98d6-40b0-ab1c-10082459f72a",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/osvaldo/anaconda3/lib/python3.9/site-packages/arviz/plots/hdiplot.py:157: FutureWarning: hdi currently interprets 2d data as (draw, shape) but this will change in a future release to (chain, draw) for coherence with other functions\n",
      "  hdi_data = hdi(y, hdi_prob=hdi_prob, circular=circular, multimodal=False, **hdi_kwargs)\n",
      "/home/osvaldo/anaconda3/lib/python3.9/site-packages/arviz/plots/hdiplot.py:157: FutureWarning: hdi currently interprets 2d data as (draw, shape) but this will change in a future release to (chain, draw) for coherence with other functions\n",
      "  hdi_data = hdi(y, hdi_prob=hdi_prob, circular=circular, multimodal=False, **hdi_kwargs)\n",
      "/home/osvaldo/anaconda3/lib/python3.9/site-packages/arviz/plots/hdiplot.py:157: FutureWarning: hdi currently interprets 2d data as (draw, shape) but this will change in a future release to (chain, draw) for coherence with other functions\n",
      "  hdi_data = hdi(y, hdi_prob=hdi_prob, circular=circular, multimodal=False, **hdi_kwargs)\n",
      "/home/osvaldo/proyectos/00_BM/pymc-experimental/pymc_experimental/bart/utils.py:240: FutureWarning: hdi currently interprets 2d data as (draw, shape) but this will change in a future release to (chain, draw) for coherence with other functions\n",
      "  hdi = az.hdi(new_Y[i])\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x480 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pmx.bart.plot_dependence(idata_bikes, X=X, Y=Y, grid=(2, 2), var_discrete=[3]);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a86b72b",
   "metadata": {},
   "source": [
    "From this plot we can see the main effect of each covariate on the predicted value. This is very useful we can recover complex relationship beyond monotonic increasing or decreasing effects. For example for the `hour` covariate we can see two peaks around 8 and and 17 hs and a minimum at midnight.\n",
    "\n",
    "When interpreting partial dependence plots we should be careful about the assumptions in this plot. First we are assuming variables are independent. For example when computing the effect of `hour` we have to marginalize the effect of `temperature` and this means that to compute the partial dependence value at `hour=0` we are including all observed values of temperature, and this may include temperatures that are actually not observed at midnight, given that lower temperatures are more likely than higher ones. We are seeing only averages, so if for a covariate half the values are positively associated with predicted variable and the other half negatively associated. The partial dependence plot will be flat as their contributions will cancel each other out. This is a problem that can be solved by using instead individual conditional expectation plots `pm.bart.plot_dependence(idata_bikes, kind=\"ice\")`. Notice that all this assumptions are assumptions of the partial dependence plot, not of our model! In fact BART can easily accommodate interaction of variables Although the prior in BART regularizes high order interactions). For more on interpreting Machine Learning model you could check the \"Interpretable Machine Learning\" book {cite:p}`molnar2019`.\n",
    "\n",
    "Finally like with other regression method we should be careful that the effects we are seeing on individual variables are conditional on the inclusion of the other variables. So for example, while `humidity` seems to be mostly flat, meaning that this covariate has an small effect of the number of used bikes. This could be the case because `humidity` and `temperature` are correlated to some extend and once we include `temperature` in our model `humidity` does not provide too much information. Try for example fitting the model again but this time with `humidity` as the single covariate and then fitting the model again with `hour` as a single covariate. You should see that the result for this single-variate models will very similar to the previous figure for the `hour` covariate, but less similar for the `humidity` covariate."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54e31c66",
   "metadata": {},
   "source": [
    "### Variable importance\n",
    "\n",
    "As we saw in the previous section a partial dependence plot can visualize give us an idea of how much each covariable contributes to the predicted outcome. But BART itself leads to a simple heuristic to estimate variable importance. That is simple count how many times a variable is included in all the regression trees. The intuition is that if a variable is important they it should appears more often in the fitted trees that less important variables. While this heuristic seems to provide reasonable results in practice, there is not too much theory justifying this procedure, at least not yet.\n",
    "\n",
    "The following plot shows the relative importance in a scale from 0 to 1 (less to more importance) and the sum of the individual importance is 1. See that, at least in this case, the relative importance qualitative agrees with the partial dependence plot.\n",
    "\n",
    "Additionally, we provide a novel method to assess the variable importance. You can see an example in the bottom panel. On the x-axis we have the number of components (variables) and on the y-axis the Pearson correlation between the predictions made between the full-model (all variables included) and the restricted-models, those with only a subset of the variables in the full-model. The components are included following the relative variable importance order, as show in the top panel. Thus, in this example 1 component means `hour`, two components means `hour` and `temperature`, 3 components `hour`, `temperature`and `humidity`. Finally, four components means `hour`, `temperature`, `humidity`, `workingday`, i.e., the full model. Hence, from the next figure we can see that even a model with a single component, `hour`, is very close to the full model. Even more, the model with two components `hour`, and `temperature` is on average indistinguishable from the full model. The error bars represent the 94 \\% HDI from the posterior predictive distribution. It is important to notice that to compute these correlations we do not resample the models, instead the predictions of the restricted-models are approximated from the full-model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "2253e445",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "labels = [\"hour\", \"temperature\", \"humidity\", \"workingday\"]\n",
    "pmx.bart.utils.plot_variable_importance(idata_bikes, X.values, labels, samples=100);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "219cde48-b626-4325-afc0-2a2881fc5683",
   "metadata": {},
   "source": [
    "## Authors\n",
    "* Authored by Osvaldo Martin in Dec, 2021 ([pymc-examples#259](https://github.com/pymc-devs/pymc-examples/pull/259))\n",
    "* Updated by Osvaldo Martin in May, 2022  ([pymc-examples#323](https://github.com/pymc-devs/pymc-examples/pull/323))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3c184bc8",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    ":::{bibliography}\n",
    ":filter: docname in docnames\n",
    "\n",
    "martin2018bayesian\n",
    "martin2021bayesian\n",
    ":::"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2c557ed8",
   "metadata": {},
   "source": [
    "## Watermark"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "608086f2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Last updated: Fri May 20 2022\n",
      "\n",
      "Python implementation: CPython\n",
      "Python version       : 3.9.7\n",
      "IPython version      : 8.3.0\n",
      "\n",
      "sys              : 3.9.7 (default, Sep 16 2021, 13:09:58) \n",
      "[GCC 7.5.0]\n",
      "pandas           : 1.4.2\n",
      "pymc             : 4.0.0b6\n",
      "arviz            : 0.12.0\n",
      "pymc_experimental: 0.0.1\n",
      "numpy            : 1.21.5\n",
      "matplotlib       : 3.5.1\n",
      "\n",
      "Watermark: 2.3.0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -n -u -v -iv -w"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4b02674f-26ad-4c07-bf60-eb8edd1c520b",
   "metadata": {},
   "source": [
    ":::{include} ../page_footer.md\n",
    ":::"
   ]
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "d4ca51fc2fdee62b1a00ff5126f64ae66836e25d3ba6f45d8551026256283997"
  },
  "kernelspec": {
   "display_name": "Python 3.9.7 ('base')",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}