Synthetic-dataset.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6a5b101e",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from skbio.stats.composition import clr\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.ensemble import RandomForestClassifier\n",
    "from debiasm.torch_functions import rescale\n",
    "from scipy.stats import pointbiserialr\n",
    "from matplotlib.colors import LogNorm, Normalize\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set(rc={'axes.facecolor':'white', \n",
    "            'figure.facecolor':'white', \n",
    "            'axes.edgecolor':'black', \n",
    "            'grid.color': 'black'\n",
    "            }, \n",
    "       font_scale=2)\n",
    "np.random.seed(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "90c43603",
   "metadata": {},
   "source": [
    "### description of experiment\n",
    "- we generate a set of 50 positive and 50 negative samples\n",
    "- samples w/ a positive `y` have 30 features drawn from a uniform distribution, and one that is empty\n",
    "- samples w/ a negative `y` have 20 features drawn from a uniform distribution, and 11 empty features. \n",
    "- By construction, one feature is empty for all samples; question: will a clr transform introduce an association with `y` for that empty sample?\n",
    "- We give all features an added pseudocount of $10^{-6}$, before which we rescale all samples to represent a relative abundance space\n",
    "- Next, we run clr transfom using scipy.stats.composition's implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "9e750fb1",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_samples=100\n",
    "frac_pos=.5\n",
    "n_features_both = 20\n",
    "n_features_pos = 10\n",
    "n_features_empty = 1\n",
    "\n",
    "n_pos = int( n_samples*frac_pos )\n",
    "n_neg = n_samples-n_pos\n",
    "# X = np.zeros((n_samples,\n",
    "#              n_features_both + \\\n",
    "#              n_features_pos + \\\n",
    "#              n_features_empty\n",
    "#              ))\n",
    "\n",
    "X = np.hstack((\n",
    "    np.vstack( ( np.random.uniform(size=( n_pos, n_features_both + n_features_pos )), \n",
    "            \n",
    "                np.hstack(( np.random.uniform(size = ( n_neg, n_features_both )), \n",
    "                            np.zeros((n_neg, n_features_pos))\n",
    "                          ) ))), \n",
    "    np.zeros((n_samples, n_features_empty)) \n",
    "        )) \n",
    "\n",
    "\n",
    "y = np.array([1]*n_pos + [0]*n_neg)\n",
    "\n",
    "rsc_df = rescale(X)\n",
    "pseudocount = 10**np.floor(np.log10(rsc_df[rsc_df != 0].min()))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c0a78ada",
   "metadata": {},
   "source": [
    "p-value of transformed empty feature and outcome:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4334a7b0",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_clr = clr( rescale( pseudocount + rescale(X) ) ) ## the second `rescale` is different"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "9e84435f",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "plt.figure(figsize=(8,8))\n",
    "ax=sns.histplot(x = X_clr[:, -1], \n",
    "                hue = ['Negative' if not i else 'Positive' for i in y], \n",
    "                palette={'Negative':'#3b4ea2',\n",
    "                         'Positive':'#b11e23'}\n",
    "             )\n",
    "plt.title(\"Histogram of an empty feature that is associated with\\n\"+\\\n",
    "            \"phenotype outcome after centered log ratio transform\\n\"\n",
    "         )\n",
    "plt.xlabel('CLR transform of the empty feature')\n",
    "plt.savefig('plots/Fig-1.pdf', \n",
    "            dpi=900,\n",
    "            bbox_inches='tight', \n",
    "            format='pdf'\n",
    "            )\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "da0b403c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,8))\n",
    "ax=sns.histplot(x = X_clr[:, -1], \n",
    "                hue = ['Negative' if not i else 'Positive' for i in y] ,\n",
    "                palette={'Negative':'#3b4ea2',\n",
    "                         'Positive':'#b11e23'}\n",
    "                 )\n",
    "plt.title(\"Histogram of an empty feature that is associated with\\n\"+\\\n",
    "            \"phenotype outcome after centered log ratio transform\\n\"\n",
    "         )\n",
    "plt.xlabel('CLR transform of the empty feature')\n",
    "ax.get_legend().remove()\n",
    "ax.set(\n",
    "       yticklabels=[], \n",
    "       xticklabels=[])\n",
    "plt.xlabel(None)\n",
    "plt.ylabel(None)\n",
    "plt.title(None)\n",
    "plt.savefig('plots/Fig-1-no-axes.pdf', \n",
    "            dpi=900, \n",
    "            bbox_inches='tight', \n",
    "            format='pdf'\n",
    "            )\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "a9ab321a",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06,\n",
       "       1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06,\n",
       "       1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06,\n",
       "       1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06,\n",
       "       1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06,\n",
       "       1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06,\n",
       "       1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06,\n",
       "       1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06,\n",
       "       1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06,\n",
       "       1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06,\n",
       "       1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06,\n",
       "       1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06, 1.e-06,\n",
       "       1.e-06, 1.e-06, 1.e-06, 1.e-06])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rescale( pseudocount + rescale(X) )[:, -1].round(9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a16da91b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=0.0, pvalue=3.533035965194466e-18)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats import mannwhitneyu\n",
    "mannwhitneyu(X_clr[:, -1][y==0], \n",
    "             X_clr[:, -1][y==1]\n",
    "             )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "3e6a4406",
   "metadata": {},
   "outputs": [],
   "source": [
    "def geo_mean(iterable): # credit to stack overflow\n",
    "    a = np.array(iterable)\n",
    "    return a.prod()**(1.0/len(a))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "5029d3a8",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_rs = rescale( pseudocount + rescale(X) ).round(9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "efded086",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,8))\n",
    "ax = sns.heatmap(rescale(X), cmap='coolwarm')\n",
    "ax.set(\n",
    "       yticklabels=[], \n",
    "       xticklabels=[]\n",
    ")\n",
    "plt.savefig('plots/Fig-1-dataset-heatmap.pdf', \n",
    "            bbox_inches='tight', \n",
    "            dpi=900, \n",
    "            format='pdf'\n",
    "            )\n",
    "# plt.title('Relative abundance of simulated dataset')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "b20a4ef2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 180x576 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (2.5,8))\n",
    "ggm=np.array([geo_mean(a) for a in X_rs])[:, np.newaxis]\n",
    "ax = sns.heatmap(ggm,# - ggm.min()+1e-3, \n",
    "#                 norm=LogNorm(), \n",
    "                cmap='coolwarm', \n",
    "#                 vmin=1e-4, \n",
    "#                 vmax=100\n",
    "                )\n",
    "ax.set(\n",
    "       yticklabels=[], \n",
    "       xticklabels=[]\n",
    ")\n",
    "plt.savefig('plots/Fig-1-dataset-geometric-mean.pdf', \n",
    "            bbox_inches='tight', \n",
    "            dpi=900, \n",
    "            format='pdf'\n",
    "            )\n",
    "# plt.title('Geometric mean')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "3e04a95d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 172.8x576 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "plt.figure(figsize=(2.4,8))\n",
    "ax = sns.heatmap(np.array(y)[:, np.newaxis], \n",
    "                 cmap='coolwarm'\n",
    "                )\n",
    "ax.set(\n",
    "       yticklabels=[], \n",
    "       xticklabels=[]\n",
    "       )\n",
    "plt.savefig('plots/Fig-1-dataset-labels.pdf', \n",
    "            bbox_inches='tight', \n",
    "            dpi=900, \n",
    "            format='pdf'\n",
    "            )\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "f4b3e8a6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.colors import LogNorm, Normalize\n",
    "plt.figure(figsize=(8,8))\n",
    "ax = sns.heatmap(X_clr, \n",
    "                 cmap='coolwarm',\n",
    "                 )\n",
    "ax.set(\n",
    "       yticklabels=[], \n",
    "       xticklabels=[]\n",
    "       )\n",
    "plt.savefig('plots/Fig-1-dataset-clr.pdf', \n",
    "            bbox_inches='tight', \n",
    "            dpi=900, \n",
    "            format='pdf'\n",
    "            )\n",
    "# plt.title('CLR transform of simulated dataset')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "06af5a6b",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5d31b847",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8b122e7e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "5b0915a6",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-9.83818015, -9.83314304, -9.74879889, -9.76865982, -9.89496248,\n",
       "       -9.6314239 , -9.82832546, -9.81515878, -9.76436073, -9.81147667,\n",
       "       -9.71371915, -9.80059377, -9.97095572, -9.53593702, -9.87142911,\n",
       "       -9.88099316, -9.88844761, -9.70259296, -9.71296976, -9.72868033,\n",
       "       -9.88790081, -9.79456921, -9.83990636, -9.71765279, -9.68190584,\n",
       "       -9.79445686, -9.80732721, -9.65401417, -9.79803553, -9.99103799,\n",
       "       -9.7687469 , -9.82383747, -9.90295441, -9.60638951, -9.81608534,\n",
       "       -9.41133412, -9.76532728, -9.71231493, -9.74681574, -9.89264969,\n",
       "       -9.80669447, -9.72215563, -9.78157675, -9.79851016, -9.75514282,\n",
       "       -9.83015045, -9.79993993, -9.79713029, -9.9486388 , -9.66938548,\n",
       "       -6.8704822 , -6.85920341, -6.83385718, -6.74447044, -6.80023635,\n",
       "       -6.81326652, -6.64301832, -6.81714547, -6.84913589, -6.78386699,\n",
       "       -6.69786406, -6.74948955, -6.76288527, -6.83375726, -6.82567279,\n",
       "       -6.69084164, -6.87364587, -6.8525895 , -6.82341595, -6.74398937,\n",
       "       -6.87765036, -6.56777489, -6.67274756, -6.67913739, -6.86222846,\n",
       "       -6.79346437, -6.65149088, -6.53203715, -6.8571449 , -6.89494839,\n",
       "       -6.84755152, -6.79631616, -6.71770726, -6.81148051, -6.74995174,\n",
       "       -6.82714224, -6.73063638, -6.729455  , -6.8978632 , -6.81260982,\n",
       "       -6.88272323, -6.85720957, -6.64718982, -6.88735246, -6.85969697,\n",
       "       -6.64448162, -6.66915518, -6.80330099, -6.68697112, -6.81310501])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_clr[:, -1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "a316c2ed",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-9.83815016, -9.83311305, -9.74876888, -9.76862977, -9.89493249,\n",
       "       -9.63139388, -9.82829547, -9.81512878, -9.76433073, -9.81144666,\n",
       "       -9.71368917, -9.80056378, -9.97092572, -9.53590702, -9.87139911,\n",
       "       -9.88096316, -9.88841761, -9.70256298, -9.71293968, -9.72865034,\n",
       "       -9.8878708 , -9.79453921, -9.83987636, -9.71762279, -9.6818759 ,\n",
       "       -9.79442693, -9.80729721, -9.65398443, -9.79800556, -9.99100799,\n",
       "       -9.7687169 , -9.82380747, -9.90292441, -9.60635953, -9.81605534,\n",
       "       -9.41130388, -9.76529728, -9.71228497, -9.74678574, -9.8926197 ,\n",
       "       -9.80666447, -9.72212562, -9.78154675, -9.79848017, -9.75511281,\n",
       "       -9.83012044, -9.79990994, -9.79710028, -9.9486088 , -9.6693555 ,\n",
       "       -6.8704622 , -6.85918341, -6.83383718, -6.74445044, -6.80021635,\n",
       "       -6.81324652, -6.64299809, -6.81712547, -6.84911588, -6.78384699,\n",
       "       -6.69784408, -6.74946955, -6.76286527, -6.83373726, -6.82565279,\n",
       "       -6.69082164, -6.87362587, -6.85256949, -6.82339594, -6.74396937,\n",
       "       -6.87763036, -6.5677549 , -6.67272759, -6.67911738, -6.86220846,\n",
       "       -6.79344437, -6.65147082, -6.53201807, -6.85712491, -6.89492839,\n",
       "       -6.84753152, -6.79629616, -6.71768727, -6.81146053, -6.74993174,\n",
       "       -6.82712224, -6.73061637, -6.72943501, -6.8978432 , -6.81258981,\n",
       "       -6.88270323, -6.85718957, -6.64716981, -6.88733246, -6.85967697,\n",
       "       -6.64446163, -6.66913514, -6.80328099, -6.68695111, -6.813085  ])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.log(X_rs[:, -1] / np.array([geo_mean(a) for a in X_rs]) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "c538fab2",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    50.000000\n",
       "mean      0.000882\n",
       "std       0.000076\n",
       "min       0.000687\n",
       "25%       0.000829\n",
       "50%       0.000904\n",
       "75%       0.000945\n",
       "max       0.000990\n",
       "dtype: float64"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.Series( ( np.array([geo_mean(a) for a in X_rs])[y==0] ) ).describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "3ea03652",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    50.000000\n",
       "mean      0.017791\n",
       "std       0.001785\n",
       "min       0.012226\n",
       "25%       0.016710\n",
       "50%       0.017990\n",
       "75%       0.018627\n",
       "max       0.021829\n",
       "dtype: float64"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.Series( ( np.array([geo_mean(a) for a in X_rs])[y==1] ) ).describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "0c7f3947",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=0.0, pvalue=3.533035965194466e-18)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mannwhitneyu( np.array([geo_mean(a) for a in X_rs])[y==0],\n",
    "              np.array([geo_mean(a) for a in X_rs])[y==1] \n",
    "            )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "f6c0ee7c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    50.000000\n",
       "mean     -6.778587\n",
       "std       0.089123\n",
       "min      -6.897863\n",
       "25%      -6.851726\n",
       "50%      -6.807391\n",
       "75%      -6.720644\n",
       "max      -6.532037\n",
       "dtype: float64"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.Series( ( X_clr[:, -1] )[y==0] ).describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "44f55482",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    50.000000\n",
       "mean     -9.781268\n",
       "std       0.104420\n",
       "min      -9.991038\n",
       "25%      -9.832395\n",
       "50%      -9.797583\n",
       "75%      -9.723787\n",
       "max      -9.411334\n",
       "dtype: float64"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.Series( ( X_clr[:, -1] )[y==1] ).describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "edcad1a9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-7.600902459542082"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.log( np.power(10., -5) / 0.02 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "dd85b077",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-5.298317366548036"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.log( np.power(10., -5) / 0.002 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "0a68620a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.Series( rescale( pseudocount + rescale(X) )[:, -1] ).nunique()\n",
    "## rounding to 9 because this step had some rounding errors...\n",
    "## this is carried through in the clr analysis above"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "b0eb2d6f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.Series( rescale( pseudocount + rescale(X) )[:, -1].round(9) ).nunique()\n",
    "## rounding to 9 because this step had some rounding errors...\n",
    "## this is carried through in the clr analysis above\n",
    "\n",
    "## to have multiple unique values before clr would undermine our argument.."
   ]
  }
 ],
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