{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "0ad85a1e",
   "metadata": {},
   "source": [
    "# Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e84bb922-5f9f-4da0-8bc5-2b65a26021df",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/63/wxl6xn215jv9b9snrf52bxd00000gq/T/ipykernel_78013/3791004227.py:15: DeprecationWarning: `set_matplotlib_formats` is deprecated since IPython 7.23, directly use `matplotlib_inline.backend_inline.set_matplotlib_formats()`\n",
      "  set_matplotlib_formats('svg')\n"
     ]
    }
   ],
   "source": [
    "#Imports\n",
    "import warnings\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import set_matplotlib_formats\n",
    "import lightgbm as lgb\n",
    "from scipy.stats import spearmanr\n",
    "\n",
    "sns.set_style(\"white\")\n",
    "warnings.filterwarnings(\"ignore\", category=UserWarning)\n",
    "\n",
    "%matplotlib inline\n",
    "set_matplotlib_formats('svg')\n",
    "\n",
    "plt.rcParams[\"font.family\"] = \"Times New Roman\" # !!!!\n",
    "plt.rcParams.update({'font.size': 32})\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c04f1aac",
   "metadata": {},
   "source": [
    "# Loading Files"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e9cc5e4b",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>index</th>\n",
       "      <th>train_the_pile_arxiv</th>\n",
       "      <th>train_the_pile_freelaw</th>\n",
       "      <th>train_the_pile_nih_exporter</th>\n",
       "      <th>train_the_pile_pubmed_central</th>\n",
       "      <th>train_the_pile_wikipedia_en</th>\n",
       "      <th>train_the_pile_dm_mathematics</th>\n",
       "      <th>train_the_pile_github</th>\n",
       "      <th>train_the_pile_philpapers</th>\n",
       "      <th>train_the_pile_stackexchange</th>\n",
       "      <th>train_the_pile_enron_emails</th>\n",
       "      <th>train_the_pile_gutenberg_pg_19</th>\n",
       "      <th>train_the_pile_pile_cc</th>\n",
       "      <th>train_the_pile_ubuntu_irc</th>\n",
       "      <th>train_the_pile_europarl</th>\n",
       "      <th>train_the_pile_hackernews</th>\n",
       "      <th>train_the_pile_pubmed_abstracts</th>\n",
       "      <th>train_the_pile_uspto_backgrounds</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.209</td>\n",
       "      <td>0.787</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>0.025</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.05</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.047</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.304</td>\n",
       "      <td>0.009</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.103</td>\n",
       "      <td>0.299</td>\n",
       "      <td>0.024</td>\n",
       "      <td>0.040</td>\n",
       "      <td>0.090</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>0.679</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.044</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.269</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>0.008</td>\n",
       "      <td>0.025</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.007</td>\n",
       "      <td>0.015</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.315</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.216</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.109</td>\n",
       "      <td>0.006</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.009</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.054</td>\n",
       "      <td>0.237</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>0.193</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.060</td>\n",
       "      <td>0.010</td>\n",
       "      <td>0.061</td>\n",
       "      <td>0.031</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.417</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.128</td>\n",
       "      <td>0.022</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.008</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.067</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   index  train_the_pile_arxiv  train_the_pile_freelaw  \\\n",
       "0      1                 0.000                   0.000   \n",
       "1      2                 0.025                   0.002   \n",
       "2      3                 0.679                   0.000   \n",
       "3      4                 0.008                   0.025   \n",
       "4      5                 0.193                   0.003   \n",
       "\n",
       "   train_the_pile_nih_exporter  train_the_pile_pubmed_central  \\\n",
       "0                         0.00                          0.000   \n",
       "1                         0.05                          0.000   \n",
       "2                         0.00                          0.044   \n",
       "3                         0.00                          0.007   \n",
       "4                         0.00                          0.060   \n",
       "\n",
       "   train_the_pile_wikipedia_en  train_the_pile_dm_mathematics  \\\n",
       "0                        0.000                          0.000   \n",
       "1                        0.047                          0.000   \n",
       "2                        0.000                          0.001   \n",
       "3                        0.015                          0.000   \n",
       "4                        0.010                          0.061   \n",
       "\n",
       "   train_the_pile_github  train_the_pile_philpapers  \\\n",
       "0                  0.000                      0.004   \n",
       "1                  0.304                      0.009   \n",
       "2                  0.000                      0.003   \n",
       "3                  0.315                      0.000   \n",
       "4                  0.031                      0.000   \n",
       "\n",
       "   train_the_pile_stackexchange  train_the_pile_enron_emails  \\\n",
       "0                         0.000                        0.000   \n",
       "1                         0.003                        0.001   \n",
       "2                         0.000                        0.001   \n",
       "3                         0.216                        0.000   \n",
       "4                         0.417                        0.000   \n",
       "\n",
       "   train_the_pile_gutenberg_pg_19  train_the_pile_pile_cc  \\\n",
       "0                           0.209                   0.787   \n",
       "1                           0.103                   0.299   \n",
       "2                           0.000                   0.269   \n",
       "3                           0.109                   0.006   \n",
       "4                           0.128                   0.022   \n",
       "\n",
       "   train_the_pile_ubuntu_irc  train_the_pile_europarl  \\\n",
       "0                      0.000                    0.000   \n",
       "1                      0.024                    0.040   \n",
       "2                      0.000                    0.000   \n",
       "3                      0.000                    0.009   \n",
       "4                      0.000                    0.008   \n",
       "\n",
       "   train_the_pile_hackernews  train_the_pile_pubmed_abstracts  \\\n",
       "0                      0.000                            0.000   \n",
       "1                      0.090                            0.001   \n",
       "2                      0.000                            0.003   \n",
       "3                      0.000                            0.054   \n",
       "4                      0.001                            0.000   \n",
       "\n",
       "   train_the_pile_uspto_backgrounds  \n",
       "0                             0.000  \n",
       "1                             0.000  \n",
       "2                             0.000  \n",
       "3                             0.237  \n",
       "4                             0.067  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_config = pd.read_csv(\"data/train_mixture_1m.csv\")\n",
    "df_config.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "372a873e",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>index</th>\n",
       "      <th>metric/the_pile_arxiv_val_loss</th>\n",
       "      <th>metric/the_pile_freelaw_val_loss</th>\n",
       "      <th>metric/the_pile_pubmed_central_val_loss</th>\n",
       "      <th>metric/the_pile_wikipedia_en_val_loss</th>\n",
       "      <th>metric/the_pile_dm_mathematics_val_loss</th>\n",
       "      <th>metric/the_pile_github_val_loss</th>\n",
       "      <th>metric/the_pile_stackexchange_val_loss</th>\n",
       "      <th>metric/the_pile_gutenberg_pg_19_val_loss</th>\n",
       "      <th>metric/the_pile_pile_cc_val_loss</th>\n",
       "      <th>metric/the_pile_ubuntu_irc_val_loss</th>\n",
       "      <th>metric/the_pile_hackernews_val_loss</th>\n",
       "      <th>metric/the_pile_pubmed_abstracts_val_loss</th>\n",
       "      <th>metric/the_pile_uspto_backgrounds_val_loss</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>7.025587</td>\n",
       "      <td>5.360581</td>\n",
       "      <td>6.536047</td>\n",
       "      <td>5.639575</td>\n",
       "      <td>5.820675</td>\n",
       "      <td>6.632823</td>\n",
       "      <td>6.107804</td>\n",
       "      <td>4.726567</td>\n",
       "      <td>5.169478</td>\n",
       "      <td>7.224245</td>\n",
       "      <td>5.206871</td>\n",
       "      <td>5.892633</td>\n",
       "      <td>5.417375</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>4.738542</td>\n",
       "      <td>5.466145</td>\n",
       "      <td>5.808464</td>\n",
       "      <td>5.425566</td>\n",
       "      <td>4.614905</td>\n",
       "      <td>4.141744</td>\n",
       "      <td>4.922904</td>\n",
       "      <td>4.954422</td>\n",
       "      <td>5.343519</td>\n",
       "      <td>5.278083</td>\n",
       "      <td>4.801190</td>\n",
       "      <td>5.653642</td>\n",
       "      <td>5.584351</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>3.730259</td>\n",
       "      <td>5.793972</td>\n",
       "      <td>4.721465</td>\n",
       "      <td>5.933120</td>\n",
       "      <td>4.077418</td>\n",
       "      <td>6.540956</td>\n",
       "      <td>6.079324</td>\n",
       "      <td>5.561454</td>\n",
       "      <td>5.506681</td>\n",
       "      <td>7.476072</td>\n",
       "      <td>5.495143</td>\n",
       "      <td>5.626058</td>\n",
       "      <td>5.507367</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>4.887355</td>\n",
       "      <td>5.040224</td>\n",
       "      <td>5.371085</td>\n",
       "      <td>5.858129</td>\n",
       "      <td>5.298434</td>\n",
       "      <td>4.150363</td>\n",
       "      <td>4.455072</td>\n",
       "      <td>5.095428</td>\n",
       "      <td>5.828740</td>\n",
       "      <td>7.491353</td>\n",
       "      <td>5.551083</td>\n",
       "      <td>5.268948</td>\n",
       "      <td>4.475535</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>4.034541</td>\n",
       "      <td>5.597910</td>\n",
       "      <td>4.693126</td>\n",
       "      <td>5.814626</td>\n",
       "      <td>2.008140</td>\n",
       "      <td>4.485220</td>\n",
       "      <td>4.249207</td>\n",
       "      <td>5.003798</td>\n",
       "      <td>5.760408</td>\n",
       "      <td>7.100966</td>\n",
       "      <td>5.329304</td>\n",
       "      <td>5.664215</td>\n",
       "      <td>4.813331</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   index  metric/the_pile_arxiv_val_loss  metric/the_pile_freelaw_val_loss  \\\n",
       "0      1                        7.025587                          5.360581   \n",
       "1      2                        4.738542                          5.466145   \n",
       "2      3                        3.730259                          5.793972   \n",
       "3      4                        4.887355                          5.040224   \n",
       "4      5                        4.034541                          5.597910   \n",
       "\n",
       "   metric/the_pile_pubmed_central_val_loss  \\\n",
       "0                                 6.536047   \n",
       "1                                 5.808464   \n",
       "2                                 4.721465   \n",
       "3                                 5.371085   \n",
       "4                                 4.693126   \n",
       "\n",
       "   metric/the_pile_wikipedia_en_val_loss  \\\n",
       "0                               5.639575   \n",
       "1                               5.425566   \n",
       "2                               5.933120   \n",
       "3                               5.858129   \n",
       "4                               5.814626   \n",
       "\n",
       "   metric/the_pile_dm_mathematics_val_loss  metric/the_pile_github_val_loss  \\\n",
       "0                                 5.820675                         6.632823   \n",
       "1                                 4.614905                         4.141744   \n",
       "2                                 4.077418                         6.540956   \n",
       "3                                 5.298434                         4.150363   \n",
       "4                                 2.008140                         4.485220   \n",
       "\n",
       "   metric/the_pile_stackexchange_val_loss  \\\n",
       "0                                6.107804   \n",
       "1                                4.922904   \n",
       "2                                6.079324   \n",
       "3                                4.455072   \n",
       "4                                4.249207   \n",
       "\n",
       "   metric/the_pile_gutenberg_pg_19_val_loss  metric/the_pile_pile_cc_val_loss  \\\n",
       "0                                  4.726567                          5.169478   \n",
       "1                                  4.954422                          5.343519   \n",
       "2                                  5.561454                          5.506681   \n",
       "3                                  5.095428                          5.828740   \n",
       "4                                  5.003798                          5.760408   \n",
       "\n",
       "   metric/the_pile_ubuntu_irc_val_loss  metric/the_pile_hackernews_val_loss  \\\n",
       "0                             7.224245                             5.206871   \n",
       "1                             5.278083                             4.801190   \n",
       "2                             7.476072                             5.495143   \n",
       "3                             7.491353                             5.551083   \n",
       "4                             7.100966                             5.329304   \n",
       "\n",
       "   metric/the_pile_pubmed_abstracts_val_loss  \\\n",
       "0                                   5.892633   \n",
       "1                                   5.653642   \n",
       "2                                   5.626058   \n",
       "3                                   5.268948   \n",
       "4                                   5.664215   \n",
       "\n",
       "   metric/the_pile_uspto_backgrounds_val_loss  \n",
       "0                                    5.417375  \n",
       "1                                    5.584351  \n",
       "2                                    5.507367  \n",
       "3                                    4.475535  \n",
       "4                                    4.813331  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_wandb = pd.read_csv(\"data/train_pile_loss_1m.csv\")\n",
    "df_wandb.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ed442af0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(512, 17)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train = df_config[df_config.columns[1:]].values\n",
    "X_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "8b33982e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(512, 13)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train = df_wandb[df_wandb.columns[1:]].values\n",
    "y_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "0a4a6b09",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>index</th>\n",
       "      <th>train_the_pile_arxiv</th>\n",
       "      <th>train_the_pile_freelaw</th>\n",
       "      <th>train_the_pile_nih_exporter</th>\n",
       "      <th>train_the_pile_pubmed_central</th>\n",
       "      <th>train_the_pile_wikipedia_en</th>\n",
       "      <th>train_the_pile_dm_mathematics</th>\n",
       "      <th>train_the_pile_github</th>\n",
       "      <th>train_the_pile_philpapers</th>\n",
       "      <th>train_the_pile_stackexchange</th>\n",
       "      <th>train_the_pile_enron_emails</th>\n",
       "      <th>train_the_pile_gutenberg_pg_19</th>\n",
       "      <th>train_the_pile_pile_cc</th>\n",
       "      <th>train_the_pile_ubuntu_irc</th>\n",
       "      <th>train_the_pile_europarl</th>\n",
       "      <th>train_the_pile_hackernews</th>\n",
       "      <th>train_the_pile_pubmed_abstracts</th>\n",
       "      <th>train_the_pile_uspto_backgrounds</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>0.080</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.464</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.015</td>\n",
       "      <td>0.353</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.042</td>\n",
       "      <td>0.039</td>\n",
       "      <td>0.005</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>0.035</td>\n",
       "      <td>0.016</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.022</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.040</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.097</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.632</td>\n",
       "      <td>0.066</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.092</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>0.014</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.022</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.084</td>\n",
       "      <td>0.477</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.209</td>\n",
       "      <td>0.052</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.013</td>\n",
       "      <td>0.093</td>\n",
       "      <td>0.027</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>0.215</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.238</td>\n",
       "      <td>0.012</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.050</td>\n",
       "      <td>0.009</td>\n",
       "      <td>0.186</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.258</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.032</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>0.732</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.027</td>\n",
       "      <td>0.035</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.113</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.005</td>\n",
       "      <td>0.040</td>\n",
       "      <td>0.037</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.003</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   index  train_the_pile_arxiv  train_the_pile_freelaw  \\\n",
       "0      1                 0.080                   0.000   \n",
       "1      2                 0.035                   0.016   \n",
       "2      3                 0.014                   0.000   \n",
       "3      4                 0.215                   0.000   \n",
       "4      5                 0.732                   0.000   \n",
       "\n",
       "   train_the_pile_nih_exporter  train_the_pile_pubmed_central  \\\n",
       "0                        0.000                          0.464   \n",
       "1                        0.000                          0.022   \n",
       "2                        0.004                          0.022   \n",
       "3                        0.000                          0.238   \n",
       "4                        0.000                          0.000   \n",
       "\n",
       "   train_the_pile_wikipedia_en  train_the_pile_dm_mathematics  \\\n",
       "0                        0.000                          0.000   \n",
       "1                        0.000                          0.040   \n",
       "2                        0.003                          0.084   \n",
       "3                        0.012                          0.000   \n",
       "4                        0.004                          0.027   \n",
       "\n",
       "   train_the_pile_github  train_the_pile_philpapers  \\\n",
       "0                  0.000                      0.000   \n",
       "1                  0.000                      0.001   \n",
       "2                  0.477                      0.000   \n",
       "3                  0.050                      0.009   \n",
       "4                  0.035                      0.001   \n",
       "\n",
       "   train_the_pile_stackexchange  train_the_pile_enron_emails  \\\n",
       "0                         0.000                        0.000   \n",
       "1                         0.097                        0.000   \n",
       "2                         0.000                        0.000   \n",
       "3                         0.186                        0.000   \n",
       "4                         0.113                        0.004   \n",
       "\n",
       "   train_the_pile_gutenberg_pg_19  train_the_pile_pile_cc  \\\n",
       "0                           0.015                   0.353   \n",
       "1                           0.000                   0.632   \n",
       "2                           0.209                   0.052   \n",
       "3                           0.258                   0.000   \n",
       "4                           0.000                   0.005   \n",
       "\n",
       "   train_the_pile_ubuntu_irc  train_the_pile_europarl  \\\n",
       "0                      0.001                    0.000   \n",
       "1                      0.066                    0.000   \n",
       "2                      0.000                    0.002   \n",
       "3                      0.000                    0.001   \n",
       "4                      0.040                    0.037   \n",
       "\n",
       "   train_the_pile_hackernews  train_the_pile_pubmed_abstracts  \\\n",
       "0                      0.042                            0.039   \n",
       "1                      0.000                            0.000   \n",
       "2                      0.013                            0.093   \n",
       "3                      0.032                            0.000   \n",
       "4                      0.000                            0.000   \n",
       "\n",
       "   train_the_pile_uspto_backgrounds  \n",
       "0                             0.005  \n",
       "1                             0.092  \n",
       "2                             0.027  \n",
       "3                             0.000  \n",
       "4                             0.003  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_config = pd.read_csv(\"data/test_mixture_1m.csv\")\n",
    "df_config.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "70596ce2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>index</th>\n",
       "      <th>metric/the_pile_arxiv_val_loss</th>\n",
       "      <th>metric/the_pile_freelaw_val_loss</th>\n",
       "      <th>metric/the_pile_pubmed_central_val_loss</th>\n",
       "      <th>metric/the_pile_wikipedia_en_val_loss</th>\n",
       "      <th>metric/the_pile_dm_mathematics_val_loss</th>\n",
       "      <th>metric/the_pile_github_val_loss</th>\n",
       "      <th>metric/the_pile_stackexchange_val_loss</th>\n",
       "      <th>metric/the_pile_gutenberg_pg_19_val_loss</th>\n",
       "      <th>metric/the_pile_pile_cc_val_loss</th>\n",
       "      <th>metric/the_pile_ubuntu_irc_val_loss</th>\n",
       "      <th>metric/the_pile_hackernews_val_loss</th>\n",
       "      <th>metric/the_pile_pubmed_abstracts_val_loss</th>\n",
       "      <th>metric/the_pile_uspto_backgrounds_val_loss</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>4.409878</td>\n",
       "      <td>5.640963</td>\n",
       "      <td>4.020510</td>\n",
       "      <td>5.786687</td>\n",
       "      <td>5.373440</td>\n",
       "      <td>6.537395</td>\n",
       "      <td>6.013463</td>\n",
       "      <td>5.168976</td>\n",
       "      <td>5.318246</td>\n",
       "      <td>6.674062</td>\n",
       "      <td>4.873102</td>\n",
       "      <td>4.895959</td>\n",
       "      <td>5.148867</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>4.512283</td>\n",
       "      <td>4.921931</td>\n",
       "      <td>4.903955</td>\n",
       "      <td>5.703417</td>\n",
       "      <td>2.097457</td>\n",
       "      <td>5.441458</td>\n",
       "      <td>4.677061</td>\n",
       "      <td>5.263875</td>\n",
       "      <td>5.180474</td>\n",
       "      <td>5.076257</td>\n",
       "      <td>5.219115</td>\n",
       "      <td>5.637612</td>\n",
       "      <td>4.686644</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>4.887048</td>\n",
       "      <td>5.998435</td>\n",
       "      <td>4.854981</td>\n",
       "      <td>5.970596</td>\n",
       "      <td>2.001365</td>\n",
       "      <td>3.971266</td>\n",
       "      <td>4.995669</td>\n",
       "      <td>4.931247</td>\n",
       "      <td>5.765591</td>\n",
       "      <td>7.315047</td>\n",
       "      <td>5.190172</td>\n",
       "      <td>5.143716</td>\n",
       "      <td>5.084033</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>4.036879</td>\n",
       "      <td>6.015464</td>\n",
       "      <td>4.318847</td>\n",
       "      <td>5.785333</td>\n",
       "      <td>5.331811</td>\n",
       "      <td>4.567320</td>\n",
       "      <td>4.527231</td>\n",
       "      <td>4.845276</td>\n",
       "      <td>5.847572</td>\n",
       "      <td>7.271599</td>\n",
       "      <td>5.007455</td>\n",
       "      <td>5.406201</td>\n",
       "      <td>5.613669</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>3.706780</td>\n",
       "      <td>6.436367</td>\n",
       "      <td>6.248679</td>\n",
       "      <td>6.208549</td>\n",
       "      <td>2.151843</td>\n",
       "      <td>4.729089</td>\n",
       "      <td>4.668032</td>\n",
       "      <td>6.203099</td>\n",
       "      <td>6.068568</td>\n",
       "      <td>5.248656</td>\n",
       "      <td>5.765752</td>\n",
       "      <td>6.618337</td>\n",
       "      <td>5.621876</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   index  metric/the_pile_arxiv_val_loss  metric/the_pile_freelaw_val_loss  \\\n",
       "0      1                        4.409878                          5.640963   \n",
       "1      2                        4.512283                          4.921931   \n",
       "2      3                        4.887048                          5.998435   \n",
       "3      4                        4.036879                          6.015464   \n",
       "4      5                        3.706780                          6.436367   \n",
       "\n",
       "   metric/the_pile_pubmed_central_val_loss  \\\n",
       "0                                 4.020510   \n",
       "1                                 4.903955   \n",
       "2                                 4.854981   \n",
       "3                                 4.318847   \n",
       "4                                 6.248679   \n",
       "\n",
       "   metric/the_pile_wikipedia_en_val_loss  \\\n",
       "0                               5.786687   \n",
       "1                               5.703417   \n",
       "2                               5.970596   \n",
       "3                               5.785333   \n",
       "4                               6.208549   \n",
       "\n",
       "   metric/the_pile_dm_mathematics_val_loss  metric/the_pile_github_val_loss  \\\n",
       "0                                 5.373440                         6.537395   \n",
       "1                                 2.097457                         5.441458   \n",
       "2                                 2.001365                         3.971266   \n",
       "3                                 5.331811                         4.567320   \n",
       "4                                 2.151843                         4.729089   \n",
       "\n",
       "   metric/the_pile_stackexchange_val_loss  \\\n",
       "0                                6.013463   \n",
       "1                                4.677061   \n",
       "2                                4.995669   \n",
       "3                                4.527231   \n",
       "4                                4.668032   \n",
       "\n",
       "   metric/the_pile_gutenberg_pg_19_val_loss  metric/the_pile_pile_cc_val_loss  \\\n",
       "0                                  5.168976                          5.318246   \n",
       "1                                  5.263875                          5.180474   \n",
       "2                                  4.931247                          5.765591   \n",
       "3                                  4.845276                          5.847572   \n",
       "4                                  6.203099                          6.068568   \n",
       "\n",
       "   metric/the_pile_ubuntu_irc_val_loss  metric/the_pile_hackernews_val_loss  \\\n",
       "0                             6.674062                             4.873102   \n",
       "1                             5.076257                             5.219115   \n",
       "2                             7.315047                             5.190172   \n",
       "3                             7.271599                             5.007455   \n",
       "4                             5.248656                             5.765752   \n",
       "\n",
       "   metric/the_pile_pubmed_abstracts_val_loss  \\\n",
       "0                                   4.895959   \n",
       "1                                   5.637612   \n",
       "2                                   5.143716   \n",
       "3                                   5.406201   \n",
       "4                                   6.618337   \n",
       "\n",
       "   metric/the_pile_uspto_backgrounds_val_loss  \n",
       "0                                    5.148867  \n",
       "1                                    4.686644  \n",
       "2                                    5.084033  \n",
       "3                                    5.613669  \n",
       "4                                    5.621876  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_wandb = pd.read_csv(\"data/test_pile_loss_1m.csv\")\n",
    "df_wandb.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "0a52772f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(256, 17)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_test = df_config[df_config.columns[1:]].values\n",
    "X_test.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "513dbfb6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(256, 13)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_test = df_wandb[df_wandb.columns[1:]].values\n",
    "y_test.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "862ad594",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['metric/the_pile_arxiv_val_loss',\n",
       " 'metric/the_pile_freelaw_val_loss',\n",
       " 'metric/the_pile_pubmed_central_val_loss',\n",
       " 'metric/the_pile_wikipedia_en_val_loss',\n",
       " 'metric/the_pile_dm_mathematics_val_loss',\n",
       " 'metric/the_pile_github_val_loss',\n",
       " 'metric/the_pile_stackexchange_val_loss',\n",
       " 'metric/the_pile_gutenberg_pg_19_val_loss',\n",
       " 'metric/the_pile_pile_cc_val_loss',\n",
       " 'metric/the_pile_ubuntu_irc_val_loss',\n",
       " 'metric/the_pile_hackernews_val_loss',\n",
       " 'metric/the_pile_pubmed_abstracts_val_loss',\n",
       " 'metric/the_pile_uspto_backgrounds_val_loss']"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "KEY_METRICS = df_wandb.columns[1:].tolist()\n",
    "KEY_METRICS"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6bd3058a",
   "metadata": {},
   "source": [
    "# Fitting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "26922ce7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 metric/the_pile_arxiv_val_loss Correlation: 99.6\n",
      "1 metric/the_pile_freelaw_val_loss Correlation: 99.71\n",
      "2 metric/the_pile_pubmed_central_val_loss Correlation: 99.08\n",
      "3 metric/the_pile_wikipedia_en_val_loss Correlation: 99.45\n",
      "4 metric/the_pile_dm_mathematics_val_loss Correlation: 97.2\n",
      "5 metric/the_pile_github_val_loss Correlation: 99.77\n",
      "6 metric/the_pile_stackexchange_val_loss Correlation: 99.73\n",
      "7 metric/the_pile_gutenberg_pg_19_val_loss Correlation: 99.18\n",
      "8 metric/the_pile_pile_cc_val_loss Correlation: 98.92\n",
      "9 metric/the_pile_ubuntu_irc_val_loss Correlation: 96.87\n",
      "10 metric/the_pile_hackernews_val_loss Correlation: 98.51\n",
      "11 metric/the_pile_pubmed_abstracts_val_loss Correlation: 99.19\n",
      "12 metric/the_pile_uspto_backgrounds_val_loss Correlation: 99.12\n"
     ]
    }
   ],
   "source": [
    "hyper_params = {\n",
    "    'task': 'train',\n",
    "    'boosting_type': 'gbdt',\n",
    "    'objective': 'regression',\n",
    "    'metric': ['l1','l2'],\n",
    "    \"num_iterations\": 1000, \n",
    "    'seed': 42,\n",
    "    'learning_rate': 1e-2,\n",
    "    \"verbosity\": -1,\n",
    "}\n",
    "\n",
    "        \n",
    "np.random.seed(42)\n",
    "\n",
    "predictor = []\n",
    "\n",
    "for i in range(len(KEY_METRICS)):\n",
    "\n",
    "    target = y_train[:, i]\n",
    "    test_target = y_test[:, i]\n",
    "    \n",
    "    gbm = lgb.LGBMRegressor(**hyper_params)\n",
    "\n",
    "    reg = gbm.fit(X_train, target,\n",
    "        eval_set=[(X_test, test_target)],\n",
    "        eval_metric='l2', callbacks=[\n",
    "        lgb.early_stopping(stopping_rounds=3, verbose=False),\n",
    "    ])\n",
    "    r, p = spearmanr(reg.predict(X_test), test_target)\n",
    "    print(i, KEY_METRICS[i], \"Correlation: {}\".format(np.round(r*100, 2)))\n",
    "\n",
    "    predictor.append(reg)\n",
    "    # break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "65947198",
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<Figure size 1000x1000 with 1 Axes>"
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     "metadata": {},
     "output_type": "display_data"
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   ],
   "source": [
    "# Visualize the fitting on Pile-CC\n",
    "selected = 8\n",
    "\n",
    "data = {\n",
    "    'True Loss': y_test[:, selected],\n",
    "    'Pred Loss': predictor[selected].predict(X_test)\n",
    "}\n",
    "\n",
    "graph = sns.jointplot(data, x='Pred Loss', y='True Loss', kind='reg',\n",
    "                      height=10, \n",
    "                      scatter_kws={'s': 128, 'color': '#5969CB'},\n",
    "                  joint_kws={'line_kws': {\n",
    "                      'color': '#C3364A', \n",
    "                                          'linewidth': 6,\n",
    "                      'linestyle': 'dashed',\n",
    "                  }},\n",
    "                  marginal_kws={'line_kws': {\n",
    "                      'color': '#5969CB', \n",
    "                      'linewidth': 6}}\n",
    "             )\n",
    "\n",
    "r, p = spearmanr(data['Pred Loss'], data['True Loss'])\n",
    "\n",
    "phantom, = graph.ax_joint.plot([], [], linestyle=\"\", alpha=0)\n",
    "\n",
    "graph.ax_joint.legend(\n",
    "    [phantom],['Correlation: {:.2f}'.format(np.round(r, 2))],\n",
    "    edgecolor='black', \n",
    "           fancybox=False,\n",
    "           prop={'size': 32, }, \n",
    "           handlelength=-0.5\n",
    ")\n",
    "\n",
    "graph.ax_joint.set_ylabel('True Loss', fontdict={\n",
    "    'size':48\n",
    "})\n",
    "graph.ax_joint.set_xlabel('Pred Loss', fontdict={\n",
    "    'size':48\n",
    "})\n",
    "\n",
    "graph.ax_marg_x.remove()\n",
    "graph.ax_marg_y.remove()\n",
    "\n",
    "graph.ax_joint.grid(True, ls='dashed')\n",
    "graph.ax_joint.spines[['right', 'top']].set_visible(True)\n",
    "\n",
    "plt.savefig('misc/1m_pile_cc_loss.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d8267e47",
   "metadata": {},
   "source": [
    "# Simulate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "1a30cf13-5633-4e15-94a7-6b1e61f0b673",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100000, 17)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# simulate for Pile-CC\n",
    "selected = 8\n",
    "np.random.seed(42)\n",
    "\n",
    "# token distribution of each domain\n",
    "prior_dist = [0.11328527, 0.07960865, 0.00391349, 0.1853759, \n",
    "              0.05108136, 0.01596293, 0.10175077, 0.00370752, \n",
    "              0.06652935, 0.00175077, 0.02708548, 0.23686921, \n",
    "              0.01184346, 0.00792997, 0.00803296, 0.03882595, \n",
    "              0.04644696]\n",
    "\n",
    "samples = np.random.dirichlet(prior_dist * 1, 100000)\n",
    "samples.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "409601e6-8270-468e-8267-d76b52a08f7c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
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   "source": [
    "# The targe metric is set as the Pile-CC validation loss\n",
    "simulation = predictor[selected].predict(samples)\n",
    "\n",
    "plt.hist(simulation, bins=32)\n",
    "\n",
    "plt.xlabel('Pred Loss')\n",
    "plt.ylabel('Frequency')\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "fe1beed8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4.66329544e-03 3.94374644e-03 4.83724817e-07 5.81013210e-03\n",
      " 7.25528969e-03 6.89717990e-04 1.13732015e-03 1.25776313e-04\n",
      " 1.11175820e-03 2.56605336e-03 3.72214513e-03 8.90924344e-01\n",
      " 6.14285142e-02 3.44762896e-04 2.49409048e-03 1.23006293e-02\n",
      " 1.48194075e-03]\n"
     ]
    }
   ],
   "source": [
    "# take the average of top-k simulated data mixture as the optimal data mixture \n",
    "k = 128\n",
    "top_k_samples = samples[np.argsort(simulation)[0:k]]\n",
    "top_k_samples.shape\n",
    "\n",
    "# you can get the optimal data mixture by taking the average of top-k samples\n",
    "optimal_data_mixture = np.mean(top_k_samples, axis=0)\n",
    "print(optimal_data_mixture)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "2c6a0134",
   "metadata": {},
   "outputs": [
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 2193 entries, 0 to 2192\n",
      "Data columns (total 3 columns):\n",
      " #   Column    Non-Null Count  Dtype  \n",
      "---  ------    --------------  -----  \n",
      " 0   variable  2193 non-null   object \n",
      " 1   value     2193 non-null   float64\n",
      " 2   type      2193 non-null   object \n",
      "dtypes: float64(1), object(2)\n",
      "memory usage: 51.5+ KB\n"
     ]
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   ],
   "source": [
    "df = pd.DataFrame(data=np.concatenate([np.array([prior_dist]), \n",
    "                                       top_k_samples], axis=0), columns=[i.split('train_the_pile_')[-1] for i in df_config.columns[1:]])\n",
    "df = pd.melt(df)\n",
    "df['type'] = (['Human']+['RegMix']*top_k_samples.shape[0])*len(df_config.columns[1:])\n",
    "df.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "fcd709eb",
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       "       <use xlink:href=\"#Cmr10-65\" x=\"69.628906\"/>\n",
       "       <use xlink:href=\"#Cmr10-65\" x=\"114.013672\"/>\n",
       "       <use xlink:href=\"#Cmr10-6c\" x=\"158.398438\"/>\n",
       "       <use xlink:href=\"#Cmr10-61\" x=\"186.083984\"/>\n",
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       "L 1094 1141 \n",
       "L 1094 428 \n",
       "Q 1094 294 1236 259 \n",
       "Q 1378 225 1594 225 \n",
       "L 1594 0 \n",
       "L 166 0 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#Cmr10-77\"/>\n",
       "       <use xlink:href=\"#Cmr10-69\" x=\"72.216797\"/>\n",
       "       <use xlink:href=\"#Cmr10-6b\" x=\"99.902344\"/>\n",
       "       <use xlink:href=\"#Cmr10-69\" x=\"152.587891\"/>\n",
       "       <use xlink:href=\"#Cmr10-70\" x=\"180.273438\"/>\n",
       "       <use xlink:href=\"#Cmr10-65\" x=\"235.791016\"/>\n",
       "       <use xlink:href=\"#Cmr10-64\" x=\"280.175781\"/>\n",
       "       <use xlink:href=\"#Cmr10-69\" x=\"335.693359\"/>\n",
       "       <use xlink:href=\"#Cmr10-61\" x=\"363.378906\"/>\n",
       "       <use xlink:href=\"#Cmr10-5f\" x=\"413.378906\"/>\n",
       "       <use xlink:href=\"#Cmr10-65\" x=\"441.064453\"/>\n",
       "       <use xlink:href=\"#Cmr10-6e\" x=\"485.449219\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_6\">\n",
       "     <g id=\"line2d_6\">\n",
       "      <path d=\"M 349.093374 406.91452 \n",
       "L 349.093374 7.2 \n",
       "\" clip-path=\"url(#p384c17f922)\" style=\"fill: none; stroke: #cccccc; stroke-width: 0.8; stroke-linecap: round\"/>\n",
       "     </g>\n",
       "     <g id=\"text_6\">\n",
       "      <!-- dm_mathematics -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(357.093374 644.98952) rotate(-90) scale(0.32 -0.32)\">\n",
       "       <defs>\n",
       "        <path id=\"Cmr10-73\" d=\"M 213 -19 \n",
       "L 213 1025 \n",
       "Q 213 1075 269 1075 \n",
       "L 347 1075 \n",
       "Q 384 1075 397 1025 \n",
       "Q 575 97 1259 97 \n",
       "Q 1563 97 1767 234 \n",
       "Q 1972 372 1972 659 \n",
       "Q 1972 866 1812 1011 \n",
       "Q 1653 1156 1434 1209 \n",
       "L 1006 1294 \n",
       "Q 791 1341 614 1437 \n",
       "Q 438 1534 325 1695 \n",
       "Q 213 1856 213 2069 \n",
       "Q 213 2350 361 2529 \n",
       "Q 509 2709 746 2789 \n",
       "Q 984 2869 1259 2869 \n",
       "Q 1588 2869 1831 2694 \n",
       "L 2016 2853 \n",
       "Q 2016 2869 2047 2869 \n",
       "L 2094 2869 \n",
       "Q 2113 2869 2128 2851 \n",
       "Q 2144 2834 2144 2816 \n",
       "L 2144 1978 \n",
       "Q 2144 1919 2094 1919 \n",
       "L 2016 1919 \n",
       "Q 1959 1919 1959 1978 \n",
       "Q 1959 2313 1773 2516 \n",
       "Q 1588 2719 1253 2719 \n",
       "Q 966 2719 755 2612 \n",
       "Q 544 2506 544 2247 \n",
       "Q 544 2069 695 1955 \n",
       "Q 847 1841 1050 1791 \n",
       "L 1484 1709 \n",
       "Q 1703 1659 1892 1540 \n",
       "Q 2081 1422 2192 1240 \n",
       "Q 2303 1059 2303 831 \n",
       "Q 2303 600 2223 429 \n",
       "Q 2144 259 2001 146 \n",
       "Q 1859 34 1665 -19 \n",
       "Q 1472 -72 1259 -72 \n",
       "Q 859 -72 575 197 \n",
       "L 341 -56 \n",
       "Q 341 -72 306 -72 \n",
       "L 269 -72 \n",
       "Q 213 -72 213 -19 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#Cmr10-64\"/>\n",
       "       <use xlink:href=\"#Cmr10-6d\" x=\"55.517578\"/>\n",
       "       <use xlink:href=\"#Cmr10-5f\" x=\"138.818359\"/>\n",
       "       <use xlink:href=\"#Cmr10-6d\" x=\"166.503906\"/>\n",
       "       <use xlink:href=\"#Cmr10-61\" x=\"249.804688\"/>\n",
       "       <use xlink:href=\"#Cmr10-74\" x=\"299.804688\"/>\n",
       "       <use xlink:href=\"#Cmr10-68\" x=\"338.623047\"/>\n",
       "       <use xlink:href=\"#Cmr10-65\" x=\"394.140625\"/>\n",
       "       <use xlink:href=\"#Cmr10-6d\" x=\"438.525391\"/>\n",
       "       <use xlink:href=\"#Cmr10-61\" x=\"521.826172\"/>\n",
       "       <use xlink:href=\"#Cmr10-74\" x=\"571.826172\"/>\n",
       "       <use xlink:href=\"#Cmr10-69\" x=\"610.644531\"/>\n",
       "       <use xlink:href=\"#Cmr10-63\" x=\"638.330078\"/>\n",
       "       <use xlink:href=\"#Cmr10-73\" x=\"682.714844\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_7\">\n",
       "     <g id=\"line2d_7\">\n",
       "      <path d=\"M 393.972169 406.91452 \n",
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       "\" clip-path=\"url(#p384c17f922)\" style=\"fill: none; stroke: #cccccc; stroke-width: 0.8; stroke-linecap: round\"/>\n",
       "     </g>\n",
       "     <g id=\"text_7\">\n",
       "      <!-- github -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(401.777169 504.48952) rotate(-90) scale(0.32 -0.32)\">\n",
       "       <defs>\n",
       "        <path id=\"Cmr10-67\" d=\"M 178 -500 \n",
       "Q 178 -272 343 -101 \n",
       "Q 509 69 738 141 \n",
       "Q 609 238 542 384 \n",
       "Q 475 531 475 697 \n",
       "Q 475 997 666 1228 \n",
       "Q 372 1516 372 1888 \n",
       "Q 372 2088 458 2263 \n",
       "Q 544 2438 697 2566 \n",
       "Q 850 2694 1037 2761 \n",
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       "Q 1803 2828 2106 2606 \n",
       "Q 2238 2747 2417 2823 \n",
       "Q 2597 2900 2791 2900 \n",
       "Q 2928 2900 3015 2801 \n",
       "Q 3103 2703 3103 2566 \n",
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       "Q 2984 2369 2906 2369 \n",
       "Q 2825 2369 2765 2428 \n",
       "Q 2706 2488 2706 2566 \n",
       "Q 2706 2684 2784 2731 \n",
       "Q 2453 2731 2216 2503 \n",
       "Q 2331 2388 2401 2220 \n",
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       "Q 2472 1616 2322 1398 \n",
       "Q 2172 1181 1926 1061 \n",
       "Q 1681 941 1422 941 \n",
       "Q 1072 941 781 1131 \n",
       "Q 691 1006 691 850 \n",
       "Q 691 681 802 554 \n",
       "Q 913 428 1081 428 \n",
       "L 1606 428 \n",
       "Q 1988 428 2294 359 \n",
       "Q 2600 291 2808 84 \n",
       "Q 3016 -122 3016 -500 \n",
       "Q 3016 -781 2778 -967 \n",
       "Q 2541 -1153 2211 -1236 \n",
       "Q 1881 -1319 1600 -1319 \n",
       "Q 1316 -1319 984 -1236 \n",
       "Q 653 -1153 415 -967 \n",
       "Q 178 -781 178 -500 \n",
       "z\n",
       "M 538 -500 \n",
       "Q 538 -716 713 -861 \n",
       "Q 888 -1006 1134 -1076 \n",
       "Q 1381 -1147 1600 -1147 \n",
       "Q 1816 -1147 2062 -1076 \n",
       "Q 2309 -1006 2482 -861 \n",
       "Q 2656 -716 2656 -500 \n",
       "Q 2656 -166 2350 -67 \n",
       "Q 2044 31 1606 31 \n",
       "L 1081 31 \n",
       "Q 934 31 811 -39 \n",
       "Q 688 -109 613 -236 \n",
       "Q 538 -363 538 -500 \n",
       "z\n",
       "M 1422 1113 \n",
       "Q 1966 1113 1966 1888 \n",
       "Q 1966 2222 1850 2439 \n",
       "Q 1734 2656 1422 2656 \n",
       "Q 1109 2656 993 2439 \n",
       "Q 878 2222 878 1888 \n",
       "Q 878 1675 922 1503 \n",
       "Q 966 1331 1084 1222 \n",
       "Q 1203 1113 1422 1113 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#Cmr10-67\"/>\n",
       "       <use xlink:href=\"#Cmr10-69\" x=\"50\"/>\n",
       "       <use xlink:href=\"#Cmr10-74\" x=\"77.685547\"/>\n",
       "       <use xlink:href=\"#Cmr10-68\" x=\"116.503906\"/>\n",
       "       <use xlink:href=\"#Cmr10-75\" x=\"172.021484\"/>\n",
       "       <use xlink:href=\"#Cmr10-62\" x=\"227.539062\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_8\">\n",
       "     <g id=\"line2d_8\">\n",
       "      <path d=\"M 438.850965 406.91452 \n",
       "L 438.850965 7.2 \n",
       "\" clip-path=\"url(#p384c17f922)\" style=\"fill: none; stroke: #cccccc; stroke-width: 0.8; stroke-linecap: round\"/>\n",
       "     </g>\n",
       "     <g id=\"text_8\">\n",
       "      <!-- philpapers -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(446.850965 558.02452) rotate(-90) scale(0.32 -0.32)\">\n",
       "       <use xlink:href=\"#Cmr10-70\"/>\n",
       "       <use xlink:href=\"#Cmr10-68\" x=\"55.517578\"/>\n",
       "       <use xlink:href=\"#Cmr10-69\" x=\"111.035156\"/>\n",
       "       <use xlink:href=\"#Cmr10-6c\" x=\"138.720703\"/>\n",
       "       <use xlink:href=\"#Cmr10-70\" x=\"166.40625\"/>\n",
       "       <use xlink:href=\"#Cmr10-61\" x=\"221.923828\"/>\n",
       "       <use xlink:href=\"#Cmr10-70\" x=\"271.923828\"/>\n",
       "       <use xlink:href=\"#Cmr10-65\" x=\"327.441406\"/>\n",
       "       <use xlink:href=\"#Cmr10-72\" x=\"371.826172\"/>\n",
       "       <use xlink:href=\"#Cmr10-73\" x=\"410.9375\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_9\">\n",
       "     <g id=\"line2d_9\">\n",
       "      <path d=\"M 483.72976 406.91452 \n",
       "L 483.72976 7.2 \n",
       "\" clip-path=\"url(#p384c17f922)\" style=\"fill: none; stroke: #cccccc; stroke-width: 0.8; stroke-linecap: round\"/>\n",
       "     </g>\n",
       "     <g id=\"text_9\">\n",
       "      <!-- stackexchange -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(491.53476 613.01452) rotate(-90) scale(0.32 -0.32)\">\n",
       "       <use xlink:href=\"#Cmr10-73\"/>\n",
       "       <use xlink:href=\"#Cmr10-74\" x=\"39.404297\"/>\n",
       "       <use xlink:href=\"#Cmr10-61\" x=\"78.222656\"/>\n",
       "       <use xlink:href=\"#Cmr10-63\" x=\"128.222656\"/>\n",
       "       <use xlink:href=\"#Cmr10-6b\" x=\"172.607422\"/>\n",
       "       <use xlink:href=\"#Cmr10-65\" x=\"225.292969\"/>\n",
       "       <use xlink:href=\"#Cmr10-78\" x=\"269.677734\"/>\n",
       "       <use xlink:href=\"#Cmr10-63\" x=\"322.363281\"/>\n",
       "       <use xlink:href=\"#Cmr10-68\" x=\"366.748047\"/>\n",
       "       <use xlink:href=\"#Cmr10-61\" x=\"422.265625\"/>\n",
       "       <use xlink:href=\"#Cmr10-6e\" x=\"472.265625\"/>\n",
       "       <use xlink:href=\"#Cmr10-67\" x=\"527.783203\"/>\n",
       "       <use xlink:href=\"#Cmr10-65\" x=\"577.783203\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_10\">\n",
       "     <g id=\"line2d_10\">\n",
       "      <path d=\"M 528.608555 406.91452 \n",
       "L 528.608555 7.2 \n",
       "\" clip-path=\"url(#p384c17f922)\" style=\"fill: none; stroke: #cccccc; stroke-width: 0.8; stroke-linecap: round\"/>\n",
       "     </g>\n",
       "     <g id=\"text_10\">\n",
       "      <!-- enron_emails -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(536.608555 588.21452) rotate(-90) scale(0.32 -0.32)\">\n",
       "       <use xlink:href=\"#Cmr10-65\"/>\n",
       "       <use xlink:href=\"#Cmr10-6e\" x=\"44.384766\"/>\n",
       "       <use xlink:href=\"#Cmr10-72\" x=\"99.902344\"/>\n",
       "       <use xlink:href=\"#Cmr10-6f\" x=\"139.013672\"/>\n",
       "       <use xlink:href=\"#Cmr10-6e\" x=\"189.013672\"/>\n",
       "       <use xlink:href=\"#Cmr10-5f\" x=\"244.53125\"/>\n",
       "       <use xlink:href=\"#Cmr10-65\" x=\"272.216797\"/>\n",
       "       <use xlink:href=\"#Cmr10-6d\" x=\"316.601562\"/>\n",
       "       <use xlink:href=\"#Cmr10-61\" x=\"399.902344\"/>\n",
       "       <use xlink:href=\"#Cmr10-69\" x=\"449.902344\"/>\n",
       "       <use xlink:href=\"#Cmr10-6c\" x=\"477.587891\"/>\n",
       "       <use xlink:href=\"#Cmr10-73\" x=\"505.273438\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_11\">\n",
       "     <g id=\"line2d_11\">\n",
       "      <path d=\"M 573.487351 406.91452 \n",
       "L 573.487351 7.2 \n",
       "\" clip-path=\"url(#p384c17f922)\" style=\"fill: none; stroke: #cccccc; stroke-width: 0.8; stroke-linecap: round\"/>\n",
       "     </g>\n",
       "     <g id=\"text_11\">\n",
       "      <!-- gutenberg_pg_19 -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(581.292351 636.03952) rotate(-90) scale(0.32 -0.32)\">\n",
       "       <defs>\n",
       "        <path id=\"Cmr10-31\" d=\"M 594 0 \n",
       "L 594 225 \n",
       "Q 1394 225 1394 428 \n",
       "L 1394 3788 \n",
       "Q 1063 3628 556 3628 \n",
       "L 556 3853 \n",
       "Q 1341 3853 1741 4263 \n",
       "L 1831 4263 \n",
       "Q 1853 4263 1873 4245 \n",
       "Q 1894 4228 1894 4206 \n",
       "L 1894 428 \n",
       "Q 1894 225 2694 225 \n",
       "L 2694 0 \n",
       "L 594 0 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "        <path id=\"Cmr10-39\" d=\"M 722 269 \n",
       "Q 897 63 1331 63 \n",
       "Q 1575 63 1786 228 \n",
       "Q 1997 394 2113 634 \n",
       "Q 2247 906 2284 1214 \n",
       "Q 2322 1522 2322 1978 \n",
       "Q 2213 1719 2008 1553 \n",
       "Q 1803 1388 1538 1388 \n",
       "Q 1166 1388 873 1589 \n",
       "Q 581 1791 425 2120 \n",
       "Q 269 2450 269 2822 \n",
       "Q 269 3206 444 3539 \n",
       "Q 619 3872 928 4067 \n",
       "Q 1238 4263 1631 4263 \n",
       "Q 2019 4263 2280 4052 \n",
       "Q 2541 3841 2678 3508 \n",
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       "Q 2925 1575 2744 1061 \n",
       "Q 2563 547 2202 203 \n",
       "Q 1841 -141 1331 -141 \n",
       "Q 953 -141 690 37 \n",
       "Q 428 216 428 575 \n",
       "Q 428 706 517 795 \n",
       "Q 606 884 738 884 \n",
       "Q 866 884 955 795 \n",
       "Q 1044 706 1044 575 \n",
       "Q 1044 450 953 359 \n",
       "Q 863 269 738 269 \n",
       "L 722 269 \n",
       "z\n",
       "M 1563 1556 \n",
       "Q 1825 1556 1992 1732 \n",
       "Q 2159 1909 2234 2171 \n",
       "Q 2309 2434 2309 2694 \n",
       "L 2309 2816 \n",
       "L 2309 2841 \n",
       "Q 2309 3322 2168 3700 \n",
       "Q 2028 4078 1631 4078 \n",
       "Q 1378 4078 1220 3967 \n",
       "Q 1063 3856 988 3672 \n",
       "Q 913 3488 892 3278 \n",
       "Q 872 3069 872 2822 \n",
       "Q 872 2459 906 2203 \n",
       "Q 941 1947 1094 1751 \n",
       "Q 1247 1556 1563 1556 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#Cmr10-67\"/>\n",
       "       <use xlink:href=\"#Cmr10-75\" x=\"50\"/>\n",
       "       <use xlink:href=\"#Cmr10-74\" x=\"105.517578\"/>\n",
       "       <use xlink:href=\"#Cmr10-65\" x=\"144.335938\"/>\n",
       "       <use xlink:href=\"#Cmr10-6e\" x=\"188.720703\"/>\n",
       "       <use xlink:href=\"#Cmr10-62\" x=\"244.238281\"/>\n",
       "       <use xlink:href=\"#Cmr10-65\" x=\"299.755859\"/>\n",
       "       <use xlink:href=\"#Cmr10-72\" x=\"344.140625\"/>\n",
       "       <use xlink:href=\"#Cmr10-67\" x=\"383.251953\"/>\n",
       "       <use xlink:href=\"#Cmr10-5f\" x=\"433.251953\"/>\n",
       "       <use xlink:href=\"#Cmr10-70\" x=\"460.9375\"/>\n",
       "       <use xlink:href=\"#Cmr10-67\" x=\"516.455078\"/>\n",
       "       <use xlink:href=\"#Cmr10-5f\" x=\"566.455078\"/>\n",
       "       <use xlink:href=\"#Cmr10-31\" x=\"594.140625\"/>\n",
       "       <use xlink:href=\"#Cmr10-39\" x=\"644.140625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_12\">\n",
       "     <g id=\"line2d_12\">\n",
       "      <path d=\"M 618.366146 406.91452 \n",
       "L 618.366146 7.2 \n",
       "\" clip-path=\"url(#p384c17f922)\" style=\"fill: none; stroke: #cccccc; stroke-width: 0.8; stroke-linecap: round\"/>\n",
       "     </g>\n",
       "     <g id=\"text_12\">\n",
       "      <!-- pile_cc -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(626.366146 500.87452) rotate(-90) scale(0.32 -0.32)\">\n",
       "       <use xlink:href=\"#Cmr10-70\"/>\n",
       "       <use xlink:href=\"#Cmr10-69\" x=\"55.517578\"/>\n",
       "       <use xlink:href=\"#Cmr10-6c\" x=\"83.203125\"/>\n",
       "       <use xlink:href=\"#Cmr10-65\" x=\"110.888672\"/>\n",
       "       <use xlink:href=\"#Cmr10-5f\" x=\"155.273438\"/>\n",
       "       <use xlink:href=\"#Cmr10-63\" x=\"182.958984\"/>\n",
       "       <use xlink:href=\"#Cmr10-63\" x=\"227.34375\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_13\">\n",
       "     <g id=\"line2d_13\">\n",
       "      <path d=\"M 663.244941 406.91452 \n",
       "L 663.244941 7.2 \n",
       "\" clip-path=\"url(#p384c17f922)\" style=\"fill: none; stroke: #cccccc; stroke-width: 0.8; stroke-linecap: round\"/>\n",
       "     </g>\n",
       "     <g id=\"text_13\">\n",
       "      <!-- ubuntu_irc -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(671.244941 559.59952) rotate(-90) scale(0.32 -0.32)\">\n",
       "       <use xlink:href=\"#Cmr10-75\"/>\n",
       "       <use xlink:href=\"#Cmr10-62\" x=\"55.517578\"/>\n",
       "       <use xlink:href=\"#Cmr10-75\" x=\"111.035156\"/>\n",
       "       <use xlink:href=\"#Cmr10-6e\" x=\"166.552734\"/>\n",
       "       <use xlink:href=\"#Cmr10-74\" x=\"222.070312\"/>\n",
       "       <use xlink:href=\"#Cmr10-75\" x=\"260.888672\"/>\n",
       "       <use xlink:href=\"#Cmr10-5f\" x=\"316.40625\"/>\n",
       "       <use xlink:href=\"#Cmr10-69\" x=\"344.091797\"/>\n",
       "       <use xlink:href=\"#Cmr10-72\" x=\"371.777344\"/>\n",
       "       <use xlink:href=\"#Cmr10-63\" x=\"410.888672\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_14\">\n",
       "     <g id=\"line2d_14\">\n",
       "      <path d=\"M 708.123736 406.91452 \n",
       "L 708.123736 7.2 \n",
       "\" clip-path=\"url(#p384c17f922)\" style=\"fill: none; stroke: #cccccc; stroke-width: 0.8; stroke-linecap: round\"/>\n",
       "     </g>\n",
       "     <g id=\"text_14\">\n",
       "      <!-- europarl -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(716.123736 529.53952) rotate(-90) scale(0.32 -0.32)\">\n",
       "       <use xlink:href=\"#Cmr10-65\"/>\n",
       "       <use xlink:href=\"#Cmr10-75\" x=\"44.384766\"/>\n",
       "       <use xlink:href=\"#Cmr10-72\" x=\"99.902344\"/>\n",
       "       <use xlink:href=\"#Cmr10-6f\" x=\"139.013672\"/>\n",
       "       <use xlink:href=\"#Cmr10-70\" x=\"189.013672\"/>\n",
       "       <use xlink:href=\"#Cmr10-61\" x=\"244.53125\"/>\n",
       "       <use xlink:href=\"#Cmr10-72\" x=\"294.53125\"/>\n",
       "       <use xlink:href=\"#Cmr10-6c\" x=\"333.642578\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_15\">\n",
       "     <g id=\"line2d_15\">\n",
       "      <path d=\"M 753.002532 406.91452 \n",
       "L 753.002532 7.2 \n",
       "\" clip-path=\"url(#p384c17f922)\" style=\"fill: none; stroke: #cccccc; stroke-width: 0.8; stroke-linecap: round\"/>\n",
       "     </g>\n",
       "     <g id=\"text_15\">\n",
       "      <!-- hackernews -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(761.002532 573.15452) rotate(-90) scale(0.32 -0.32)\">\n",
       "       <use xlink:href=\"#Cmr10-68\"/>\n",
       "       <use xlink:href=\"#Cmr10-61\" x=\"55.517578\"/>\n",
       "       <use xlink:href=\"#Cmr10-63\" x=\"105.517578\"/>\n",
       "       <use xlink:href=\"#Cmr10-6b\" x=\"149.902344\"/>\n",
       "       <use xlink:href=\"#Cmr10-65\" x=\"202.587891\"/>\n",
       "       <use xlink:href=\"#Cmr10-72\" x=\"246.972656\"/>\n",
       "       <use xlink:href=\"#Cmr10-6e\" x=\"286.083984\"/>\n",
       "       <use xlink:href=\"#Cmr10-65\" x=\"341.601562\"/>\n",
       "       <use xlink:href=\"#Cmr10-77\" x=\"385.986328\"/>\n",
       "       <use xlink:href=\"#Cmr10-73\" x=\"458.203125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_16\">\n",
       "     <g id=\"line2d_16\">\n",
       "      <path d=\"M 797.881327 406.91452 \n",
       "L 797.881327 7.2 \n",
       "\" clip-path=\"url(#p384c17f922)\" style=\"fill: none; stroke: #cccccc; stroke-width: 0.8; stroke-linecap: round\"/>\n",
       "     </g>\n",
       "     <g id=\"text_16\">\n",
       "      <!-- pubmed_abstracts -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(805.881327 661.23952) rotate(-90) scale(0.32 -0.32)\">\n",
       "       <use xlink:href=\"#Cmr10-70\"/>\n",
       "       <use xlink:href=\"#Cmr10-75\" x=\"55.517578\"/>\n",
       "       <use xlink:href=\"#Cmr10-62\" x=\"111.035156\"/>\n",
       "       <use xlink:href=\"#Cmr10-6d\" x=\"166.552734\"/>\n",
       "       <use xlink:href=\"#Cmr10-65\" x=\"249.853516\"/>\n",
       "       <use xlink:href=\"#Cmr10-64\" x=\"294.238281\"/>\n",
       "       <use xlink:href=\"#Cmr10-5f\" x=\"349.755859\"/>\n",
       "       <use xlink:href=\"#Cmr10-61\" x=\"377.441406\"/>\n",
       "       <use xlink:href=\"#Cmr10-62\" x=\"427.441406\"/>\n",
       "       <use xlink:href=\"#Cmr10-73\" x=\"482.958984\"/>\n",
       "       <use xlink:href=\"#Cmr10-74\" x=\"522.363281\"/>\n",
       "       <use xlink:href=\"#Cmr10-72\" x=\"561.181641\"/>\n",
       "       <use xlink:href=\"#Cmr10-61\" x=\"600.292969\"/>\n",
       "       <use xlink:href=\"#Cmr10-63\" x=\"650.292969\"/>\n",
       "       <use xlink:href=\"#Cmr10-74\" x=\"694.677734\"/>\n",
       "       <use xlink:href=\"#Cmr10-73\" x=\"733.496094\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_17\">\n",
       "     <g id=\"line2d_17\">\n",
       "      <path d=\"M 842.760122 406.91452 \n",
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       "\" clip-path=\"url(#p384c17f922)\" style=\"fill: none; stroke: #cccccc; stroke-width: 0.8; stroke-linecap: round\"/>\n",
       "     </g>\n",
       "     <g id=\"text_17\">\n",
       "      <!-- uspto_backgrounds -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(850.565122 674.58452) rotate(-90) scale(0.32 -0.32)\">\n",
       "       <use xlink:href=\"#Cmr10-75\"/>\n",
       "       <use xlink:href=\"#Cmr10-73\" x=\"55.517578\"/>\n",
       "       <use xlink:href=\"#Cmr10-70\" x=\"94.921875\"/>\n",
       "       <use xlink:href=\"#Cmr10-74\" x=\"150.439453\"/>\n",
       "       <use xlink:href=\"#Cmr10-6f\" x=\"189.257812\"/>\n",
       "       <use xlink:href=\"#Cmr10-5f\" x=\"239.257812\"/>\n",
       "       <use xlink:href=\"#Cmr10-62\" x=\"266.943359\"/>\n",
       "       <use xlink:href=\"#Cmr10-61\" x=\"322.460938\"/>\n",
       "       <use xlink:href=\"#Cmr10-63\" x=\"372.460938\"/>\n",
       "       <use xlink:href=\"#Cmr10-6b\" x=\"416.845703\"/>\n",
       "       <use xlink:href=\"#Cmr10-67\" x=\"469.53125\"/>\n",
       "       <use xlink:href=\"#Cmr10-72\" x=\"519.53125\"/>\n",
       "       <use xlink:href=\"#Cmr10-6f\" x=\"558.642578\"/>\n",
       "       <use xlink:href=\"#Cmr10-75\" x=\"608.642578\"/>\n",
       "       <use xlink:href=\"#Cmr10-6e\" x=\"664.160156\"/>\n",
       "       <use xlink:href=\"#Cmr10-64\" x=\"719.677734\"/>\n",
       "       <use xlink:href=\"#Cmr10-73\" x=\"775.195312\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_18\">\n",
       "     <!-- Domain -->\n",
       "     <g style=\"fill: #262626\" transform=\"translate(401.45476 711.89202) scale(0.48 -0.48)\">\n",
       "      <defs>\n",
       "       <path id=\"Cmr10-44\" d=\"M 213 0 \n",
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       "L 213 4372 \n",
       "L 2572 4372 \n",
       "Q 3009 4372 3371 4183 \n",
       "Q 3734 3994 3990 3678 \n",
       "Q 4247 3363 4386 2963 \n",
       "Q 4525 2563 4525 2144 \n",
       "Q 4525 1738 4384 1355 \n",
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       "Q 3716 356 3355 178 \n",
       "Q 2994 0 2572 0 \n",
       "L 213 0 \n",
       "z\n",
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       "Q 1447 291 1525 258 \n",
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       "Q 2734 225 3029 367 \n",
       "Q 3325 509 3519 763 \n",
       "Q 3722 1031 3790 1364 \n",
       "Q 3859 1697 3859 2144 \n",
       "Q 3859 2609 3790 2959 \n",
       "Q 3722 3309 3519 3584 \n",
       "Q 3328 3856 3034 4001 \n",
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       "Q 1656 4147 1592 4137 \n",
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       "L 1447 428 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "      </defs>\n",
       "      <use xlink:href=\"#Cmr10-44\"/>\n",
       "      <use xlink:href=\"#Cmr10-6f\" x=\"76.318359\"/>\n",
       "      <use xlink:href=\"#Cmr10-6d\" x=\"126.318359\"/>\n",
       "      <use xlink:href=\"#Cmr10-61\" x=\"209.619141\"/>\n",
       "      <use xlink:href=\"#Cmr10-69\" x=\"259.619141\"/>\n",
       "      <use xlink:href=\"#Cmr10-6e\" x=\"287.304688\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_2\">\n",
       "    <g id=\"ytick_1\">\n",
       "     <g id=\"line2d_18\">\n",
       "      <path d=\"M 102.26 406.91452 \n",
       "L 865.19952 406.91452 \n",
       "\" clip-path=\"url(#p384c17f922)\" style=\"fill: none; stroke: #cccccc; stroke-width: 0.8; stroke-linecap: round\"/>\n",
       "     </g>\n",
       "     <g id=\"text_19\">\n",
       "      <!-- 0.0 -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(54.4 418.01702) scale(0.32 -0.32)\">\n",
       "       <defs>\n",
       "        <path id=\"Cmr10-30\" d=\"M 1600 -141 \n",
       "Q 816 -141 533 504 \n",
       "Q 250 1150 250 2041 \n",
       "Q 250 2597 351 3087 \n",
       "Q 453 3578 754 3920 \n",
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       "Q 2022 4263 2290 4056 \n",
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       "Q 2841 3197 2892 2823 \n",
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       "Q 2944 1491 2842 1011 \n",
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       "Q 2147 -141 1600 -141 \n",
       "z\n",
       "M 1600 25 \n",
       "Q 1956 25 2131 390 \n",
       "Q 2306 756 2347 1200 \n",
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       "Q 2388 2625 2347 3031 \n",
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       "Q 1959 4097 1600 4097 \n",
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       "Q 888 3434 847 3029 \n",
       "Q 806 2625 806 2144 \n",
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       "Q 1325 25 1600 25 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "        <path id=\"Cmr10-2e\" d=\"M 538 353 \n",
       "Q 538 497 644 600 \n",
       "Q 750 703 891 703 \n",
       "Q 978 703 1062 656 \n",
       "Q 1147 609 1194 525 \n",
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       "Q 538 213 538 353 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#Cmr10-30\"/>\n",
       "       <use xlink:href=\"#Cmr10-2e\" x=\"50\"/>\n",
       "       <use xlink:href=\"#Cmr10-30\" x=\"77.685547\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_2\">\n",
       "     <g id=\"line2d_19\">\n",
       "      <path d=\"M 102.26 334.239153 \n",
       "L 865.19952 334.239153 \n",
       "\" clip-path=\"url(#p384c17f922)\" style=\"fill: none; stroke: #cccccc; stroke-width: 0.8; stroke-linecap: round\"/>\n",
       "     </g>\n",
       "     <g id=\"text_20\">\n",
       "      <!-- 0.2 -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(54.4 345.341653) scale(0.32 -0.32)\">\n",
       "       <defs>\n",
       "        <path id=\"Cmr10-32\" d=\"M 319 0 \n",
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       "Q 319 188 331 206 \n",
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       "Q 1906 519 2211 526 \n",
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       "L 319 0 \n",
       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#Cmr10-30\"/>\n",
       "       <use xlink:href=\"#Cmr10-2e\" x=\"50\"/>\n",
       "       <use xlink:href=\"#Cmr10-32\" x=\"77.685547\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_3\">\n",
       "     <g id=\"line2d_20\">\n",
       "      <path d=\"M 102.26 261.563785 \n",
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       "     </g>\n",
       "     <g id=\"text_21\">\n",
       "      <!-- 0.4 -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(54.4 272.666285) scale(0.32 -0.32)\">\n",
       "       <defs>\n",
       "        <path id=\"Cmr10-34\" d=\"M 178 1056 \n",
       "L 178 1281 \n",
       "L 2156 4231 \n",
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       "L 2316 4263 \n",
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       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#Cmr10-30\"/>\n",
       "       <use xlink:href=\"#Cmr10-2e\" x=\"50\"/>\n",
       "       <use xlink:href=\"#Cmr10-34\" x=\"77.685547\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_4\">\n",
       "     <g id=\"line2d_21\">\n",
       "      <path d=\"M 102.26 188.888418 \n",
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       "     <g id=\"text_22\">\n",
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       "      <g style=\"fill: #262626\" transform=\"translate(54.4 199.990918) scale(0.32 -0.32)\">\n",
       "       <defs>\n",
       "        <path id=\"Cmr10-36\" d=\"M 1600 -141 \n",
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       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#Cmr10-30\"/>\n",
       "       <use xlink:href=\"#Cmr10-2e\" x=\"50\"/>\n",
       "       <use xlink:href=\"#Cmr10-36\" x=\"77.685547\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_5\">\n",
       "     <g id=\"line2d_22\">\n",
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       "     <g id=\"text_23\">\n",
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       "      <g style=\"fill: #262626\" transform=\"translate(54.4 127.315551) scale(0.32 -0.32)\">\n",
       "       <defs>\n",
       "        <path id=\"Cmr10-38\" d=\"M 269 972 \n",
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       "z\n",
       "\" transform=\"scale(0.015625)\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#Cmr10-30\"/>\n",
       "       <use xlink:href=\"#Cmr10-2e\" x=\"50\"/>\n",
       "       <use xlink:href=\"#Cmr10-38\" x=\"77.685547\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_6\">\n",
       "     <g id=\"line2d_23\">\n",
       "      <path d=\"M 102.26 43.537684 \n",
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       "     </g>\n",
       "     <g id=\"text_24\">\n",
       "      <!-- 1.0 -->\n",
       "      <g style=\"fill: #262626\" transform=\"translate(54.4 54.640184) scale(0.32 -0.32)\">\n",
       "       <use xlink:href=\"#Cmr10-31\"/>\n",
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      "text/plain": [
       "<Figure size 1200x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
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   ],
   "source": [
    "plt.rc('axes', unicode_minus=False)\n",
    "\n",
    "plt.rcParams.update({# Use mathtext, not LaTeX\n",
    "                            'text.usetex': False,\n",
    "                            # Use the Computer modern font\n",
    "                            'font.family': 'serif',\n",
    "                            'font.serif': 'cmr10',\n",
    "                            'mathtext.fontset': 'cm',\n",
    "                            })\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(12, 10), layout='compressed')\n",
    "\n",
    "pal = {\n",
    "    'Human':'#5969CB',\n",
    "    'RegMix': '#C3364A',\n",
    "}\n",
    "sns.barplot(data=df, \n",
    "            x='variable', \n",
    "            y='value', \n",
    "            hue='type',\n",
    "            palette=pal\n",
    "           )\n",
    "\n",
    "ax.tick_params(axis='x', labelrotation=90)\n",
    "\n",
    "ax.legend(\n",
    "    edgecolor='black', \n",
    "           fancybox=False,\n",
    "           prop={'size': 24, }, \n",
    "             handlelength=0.5, \n",
    "    ncol=2,\n",
    ")\n",
    "\n",
    "ax.grid(True)\n",
    "\n",
    "ax.set_ylim(0, 1.1)\n",
    "\n",
    "ax.set_xlabel('Domain', fontdict={\n",
    "    'size': 48,\n",
    "})\n",
    "ax.set_ylabel('Weight', fontdict={\n",
    "    'size': 48,\n",
    "})\n",
    "\n",
    "# save the regmix optimized data mixture\n",
    "plt.savefig('misc/prior_vs_regmix.pdf', bbox_inches='tight', pad_inches=0.1)"
   ]
  }
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