nb08b-model-comparison.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "05080d5f-640d-4a95-bba4-f0dadda33ce5",
   "metadata": {},
   "source": [
    "# `nb08b`: Model comparison"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e72dc22d-a680-4c48-aebe-20cd35508c77",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec084d85-4568-4c66-8688-8a08f8823560",
   "metadata": {},
   "source": [
    "# Model comparison using Bayes factors\n",
    "\n",
    "## Marginal likelihood"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e028f340-2850-438a-84f3-f281522a9dd5",
   "metadata": {},
   "source": [
    "$$p(\\theta | x, \\mathcal{M}_1) = \\frac{p(x | \\theta, \\mathcal{M}_1) p(\\theta | \\mathcal{M}_1)}{p(x | \\mathcal{M}_1)}$$\n",
    "\n",
    "$$p(x | \\mathcal{M}_1) = \\int p(x | \\theta, \\mathcal{M}_1) p(\\theta | \\mathcal{M}_1) d\\theta$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb3357a0-b777-4db9-b54b-131bfede3e18",
   "metadata": {},
   "source": [
    "We assume a study where we assess the number of successes observed in a fixed number of trials. For example, we have 80 successes out of 100 trials. \n",
    "\n",
    "A simple model of this data can be built by assuming that the data is distributed according to a binomial distribution. In a binomial distribution, $n$ independent experiments are performed and the result of each experiment is succesful with probability $\\theta$. Then, the binomial distribution is the probability distribution of the number of successes $k$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d50fef37-c596-4886-b3bb-9ae7f6b61120",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Model 1\n",
    "from scipy.stats import binom\n",
    "\n",
    "def likelihood1(theta, k, n):\n",
    "    return binom.pmf(k, n, theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8c2ddb90-9c1c-46fd-96e9-7c939b77a032",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = plt.axes()\n",
    "\n",
    "theta = 0.6\n",
    "n = 100\n",
    "\n",
    "ks = range(0, n+1)\n",
    "ax.plot(ks, likelihood1(theta, ks, n))\n",
    "ax.set(xlabel=r\"$k$\", ylabel=r\"$p(k | n={}, \\theta={})$\".format(n, theta))\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "402e038d-a425-4a92-87f5-70855f8dff0f",
   "metadata": {},
   "source": [
    "Suppose we have prior information about the probability parameter $\\theta$, encoded as a Beta distribution of parameters $a$ and $b$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "44d04c84-fcaf-4edf-ae3d-f1ba104093be",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import beta\n",
    "\n",
    "a = 4\n",
    "b = 2\n",
    "\n",
    "def prior1(theta):\n",
    "    return beta.pdf(theta, a=a, b=b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "4667df1c-db68-4d60-af33-a4d9c8ec952a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = plt.axes()\n",
    "\n",
    "thetas = np.linspace(0, 1, num=100)\n",
    "ax.plot(thetas, prior1(thetas))\n",
    "ax.plot(thetas, prior2(thetas))\n",
    "ax.set(xlabel=r\"$\\theta$\", ylabel=r\"$p(\\theta)$\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40e1e8bf-89b2-4878-a4c6-37c5f24ee054",
   "metadata": {},
   "source": [
    "Then the marginal likelihood is given by the integral of the product of the likelihood and the prior:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "2395cd7b-2c40-466e-a918-e6c217ccc5bb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.019982271038244702"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.integrate import quad\n",
    "ml1, _ = quad(lambda theta: likelihood1(theta, k=80, n=n) * prior1(theta), 0, 1)\n",
    "ml1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "a170d37b-10cb-422c-8f98-d0ddec099879",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.009900990099009892"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Model 2: wider prior\n",
    "def prior2(theta):\n",
    "    return beta.pdf(theta, a=1, b=1)\n",
    "\n",
    "ml2, _ = quad(lambda theta: likelihood1(theta, k=80, n=n) * prior2(theta), 0, 1)\n",
    "ml2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "a5d32917-e629-4e81-b644-53b84b95448a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Model 3: more complex likelihood\n",
    "from scipy.stats import betabinom, lognorm\n",
    "\n",
    "def likelihood3(alpha, beta, k, n):\n",
    "    return betabinom.pmf(k, n, alpha, beta)\n",
    "\n",
    "def prior3(alpha, beta):\n",
    "    return lognorm.pdf(alpha, 100) * lognorm.pdf(beta, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "9582cd84-df61-40a3-871c-558249d40087",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = plt.axes()\n",
    "\n",
    "vs = np.linspace(0, 100)\n",
    "ax.plot(vs, lognorm.pdf(vs, 100))\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "600c6588-4d31-4795-8f4a-1e3403864287",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/glouppe/anaconda3/envs/dats0001/lib/python3.9/site-packages/scipy/integrate/_quadpack_py.py:1233: IntegrationWarning: The integral is probably divergent, or slowly convergent.\n",
      "  quad_r = quad(f, low, high, args=args, full_output=self.full_output,\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "5.750979990594095e-06"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.integrate import dblquad\n",
    "ml3, _ = dblquad(lambda alpha, beta: likelihood3(alpha, beta, k=80, n=n) * prior3(alpha, beta), 0, np.inf, 0, np.inf)\n",
    "ml3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "53b049dc-78c5-478c-a8f4-ab548f68a331",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model 1: 0.019982271038244702\n",
      "Model 2: 0.009900990099009892\n",
      "Model 3: 5.750979990594095e-06\n"
     ]
    }
   ],
   "source": [
    "print(\"Model 1:\", ml1)\n",
    "print(\"Model 2:\", ml2)\n",
    "print(\"Model 3:\", ml3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d005ffc-8c56-4ce2-96a8-7cb615fe114f",
   "metadata": {},
   "source": [
    "## Bayes factor"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d5e8f4b-23dc-4b34-b1a4-5aea50ae74c2",
   "metadata": {},
   "source": [
    "$$\\text{BF}_{1,2} = \\frac{p(x | \\mathcal{M}_1)}{p(x | \\mathcal{M}_2)}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "68ab30c5-3e39-4a1b-9819-9e2f09472c59",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "BF(1,2): 2.0182093748627166 0.7022106701979013\n",
      "BF(1,3): 3474.585387347256 8.153230437886936\n",
      "BF(2,3): 1721.617900810517 7.451019767689035\n"
     ]
    }
   ],
   "source": [
    "print(\"BF(1,2):\", ml1 / ml2, np.log(ml1 / ml2))\n",
    "print(\"BF(1,3):\", ml1 / ml3, np.log(ml1 / ml3))\n",
    "print(\"BF(2,3):\", ml2 / ml3, np.log(ml2 / ml3))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8571a89f-a9d8-4d85-a512-1983f9ad7a16",
   "metadata": {},
   "source": [
    "If we want to know, given the data $x$, how much more probable model $\\mathcal{M}_1$ is than model $\\mathcal{M}_2$, then we need the prior odds:\n",
    "\n",
    "$$\\frac{p(\\mathcal{M}_1 | x)}{p(\\mathcal{M}_2 | x)} = \\frac{p(\\mathcal{M}_1)}{p(\\mathcal{M}_2)} \\frac{p(x | \\mathcal{M}_1)}{p(x | \\mathcal{M}_2)} = \\frac{p(\\mathcal{M}_1)}{p(\\mathcal{M}_2)} \\text{BF}_{1,2}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51d20df7-e069-4209-bf54-8fc080e08e91",
   "metadata": {},
   "source": [
    "![](figures/nb11/bf.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f97fed4c-f739-46e0-ae18-77a5c8104857",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-success\">\n",
    "    \n",
    "**Exercise**. Using the light speed experiment data from `nb10`, compare:\n",
    "- $\\mathcal{M}_1: p(x | \\mu, \\sigma) = \\mathcal{N}(x | \\mu, \\sigma), p(\\mu, \\sigma) = \\mathcal{U}$\n",
    "- $\\mathcal{M}_2: p(x | \\mu, \\sigma, a) = \\text{skewnorm}(x | \\mu, \\sigma, a), p(\\mu, \\sigma, a) = \\mathcal{U}$.\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4126d5ad-a9d0-4c2d-a05a-7dc3cb72180f",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "ff3f4fa7-c60d-4b9b-ac62-a162f396f606",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-success\">\n",
    "    \n",
    "**Exercise**. How to compute the Bayes factor for more complicated models?\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e890697c-8a53-404c-95c2-7faeb2d9a3e5",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "bfed2a7d-bc08-4fc5-aeab-4e9c48ae1b4a",
   "metadata": {},
   "source": [
    "# Cross-validation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2027fedb-3bcc-4f89-8232-fcbad320e398",
   "metadata": {},
   "source": [
    "A popular way to evaluate and compare models is on their ability to make predictions for future or unseen observations $x_\\text{pred}$, using what we learned from the observed data $\\{x\\} = \\{x_1, ..., x_n\\}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4237e60a-f71c-4889-ba3d-8d078c579977",
   "metadata": {},
   "source": [
    "## Expected log predictive density"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e26e8a8c-4099-491f-b96b-53d6f10e5931",
   "metadata": {},
   "source": [
    "Let $$u(\\mathcal{M}_1, x_\\text{pred}) = \\log p(x_\\text{pred} | \\{x\\}, \\mathcal{M}_1)$$\n",
    "\n",
    "$$\\log p(x_\\text{pred} | \\{x\\}, \\mathcal{M}_1) = \\log \\int p(x_\\text{pred} | \\theta, \\mathcal{M}_1) p(\\theta | \\{x\\}, \\mathcal{M}_1) d\\theta $$\n",
    "\n",
    "$$\\text{elpd} = u(\\mathcal{M}_1) = \\mathbb{E}_{p_\\text{true}(x_\\text{pred})} [ \\log p(x_\\text{pred} | \\{x\\}, \\mathcal{M}_1) ]$$\n",
    "\n",
    "where $p_\\text{true}$ is the true data generating distribution. \n",
    "\n",
    "The model with the highest $\\text{elpd}$ is the the model with the predictions that are the closest to the ones of the true data generating process."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eeb90917-766b-4244-8ca2-eb102facd4e8",
   "metadata": {},
   "source": [
    "But we we don't know $p_\\text{true}$! Solution: use the $n$ observations from $\\{x\\}$:\n",
    "\n",
    "$$\\widehat{\\text{elpd}} = \\frac{1}{n} \\sum_{i=1}^n \\log p(x_i | \\{x\\}, \\mathcal{M}_1)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "b348864b-0913-400d-97a1-06cf71d467ea",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Example\n",
    "theta_true = np.array([1.0, 3.0])\n",
    "p_true = beta(a=theta_true[0], b=theta_true[1])\n",
    "\n",
    "np.random.seed(42)\n",
    "n = 50\n",
    "xs = p_true.rvs(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "eae78204-705f-40f9-acbe-127d88bf1ddf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = plt.axes()\n",
    "\n",
    "vs = np.linspace(0, 1)\n",
    "ax.plot(vs, p_true.pdf(vs))\n",
    "ax.hist(xs, density=True)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "18744c51-c17c-4414-b5f3-bb2b0626e963",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Model 1\n",
    "def log_likelihood(theta, x):\n",
    "    return beta(theta[0], theta[1]).logpdf(x).sum()\n",
    "\n",
    "def log_prior(theta):\n",
    "    return lognorm.pdf(theta[0], 10) * lognorm.pdf(theta[1], 10)\n",
    "\n",
    "def log_posterior(theta, x):\n",
    "    if theta[0] <= 0 or theta[1] <= 0:\n",
    "        return -np.inf\n",
    "    else:                          \n",
    "        return log_likelihood(theta, x) + log_prior(theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "16ae458e-198a-464b-af6a-6d431d9d4cde",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████████████████████████████████| 1000/1000 [00:02<00:00, 336.05it/s]\n"
     ]
    }
   ],
   "source": [
    "# Fit the posterior\n",
    "import emcee\n",
    "pos = np.array([1.0, 1.0]) + 0.1 * np.random.randn(5, 2)\n",
    "nwalkers, ndim = pos.shape\n",
    "\n",
    "sampler = emcee.EnsembleSampler(nwalkers, ndim, log_posterior, args=(xs,))\n",
    "sampler.run_mcmc(pos, 1000, progress=True);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "2a6883bc-4f0d-4e46-bf8b-a6d9aa67ed9c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4500\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 550x550 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import corner\n",
    "thetas = sampler.get_chain(flat=True, discard=100)\n",
    "print(len(thetas))\n",
    "fig = corner.corner(thetas, labels=[\"a\", \"b\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "861476c5-aa46-4e23-a561-555da2d7c458",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5654324527537117"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# elpd\n",
    "def log_posterior_predictive(x_i, thetas):\n",
    "    return np.mean([log_likelihood(theta, x_i) for theta in thetas])\n",
    "\n",
    "def elpd(xs, thetas):\n",
    "    return np.mean([log_posterior_predictive(x_i, thetas) for x_i in xs])\n",
    "\n",
    "subset = np.random.permutation(len(thetas))[:500]\n",
    "elpd(xs, thetas[subset])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0d10b96-1397-4bc5-8030-336880937d95",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-success\">\n",
    "    \n",
    "**Exercise**. What's wrong with this procedure?\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "806bf9fc-f9f3-4f08-bd5b-2dc6a49c32e3",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "cafde425-e4cc-411b-a8f6-0833e1e11eea",
   "metadata": {},
   "source": [
    "## K-fold validation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "9b12efe9-bb13-411f-8b33-6eb61633fff8",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████████████████████████████████| 1000/1000 [00:03<00:00, 328.86it/s]\n",
      "100%|██████████████████████████████████████| 1000/1000 [00:03<00:00, 324.25it/s]\n",
      "100%|██████████████████████████████████████| 1000/1000 [00:02<00:00, 345.12it/s]\n",
      "100%|██████████████████████████████████████| 1000/1000 [00:02<00:00, 339.77it/s]\n",
      "100%|██████████████████████████████████████| 1000/1000 [00:02<00:00, 334.81it/s]\n",
      "100%|██████████████████████████████████████| 1000/1000 [00:03<00:00, 326.30it/s]\n",
      "100%|██████████████████████████████████████| 1000/1000 [00:03<00:00, 331.20it/s]\n",
      "100%|██████████████████████████████████████| 1000/1000 [00:03<00:00, 331.12it/s]\n",
      "100%|██████████████████████████████████████| 1000/1000 [00:03<00:00, 327.24it/s]\n",
      "100%|██████████████████████████████████████| 1000/1000 [00:03<00:00, 331.09it/s]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import KFold\n",
    "kf = KFold(n_splits=10, shuffle=True)\n",
    "elpd_test = []\n",
    "\n",
    "for train_idx, test_idx in kf.split(xs):\n",
    "    # posterior fit\n",
    "    pos = np.array([1.0, 1.0]) + 0.1 * np.random.randn(5, 2)\n",
    "    nwalkers, ndim = pos.shape\n",
    "    sampler = emcee.EnsembleSampler(nwalkers, ndim, log_posterior, args=(xs[train_idx],))\n",
    "    sampler.run_mcmc(pos, 1000, progress=True);\n",
    "    thetas = sampler.get_chain(flat=True, discard=100)\n",
    "    \n",
    "    # epld\n",
    "    subset = np.random.permutation(len(thetas))[:500]\n",
    "    elpd_test.append(elpd(xs[test_idx], thetas[subset]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "0a32f432-fcac-43ef-af81-7214ccfca624",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.8105294047367207,\n",
       " 0.027101230705309565,\n",
       " 0.7385731299975092,\n",
       " 0.6418294451361742,\n",
       " 0.6790205968563633,\n",
       " 0.4567709801665624,\n",
       " 0.9205155545551229,\n",
       " 0.6293925926367321,\n",
       " 0.012135612593329893,\n",
       " 0.4072099427231815]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "elpd_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "5626a279-8ca8-4327-8e02-8d7203a1dd00",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.5323078490107005, 0.2933890025426623)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(elpd_test), np.std(elpd_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2800ca6e-88b5-4806-b51e-6733c679b39b",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-success\">\n",
    "    \n",
    "**Exercise**. Evaluate the K-Fold estimate as a function of $K$. \n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "93777fd5-6c3b-4c24-b778-4207d6642543",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:dats0001]",
   "language": "python",
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