{
 "cells": [
  {
   "cell_type": "markdown",
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   "source": [
    "# Union evaluations\n",
    "In this notebook, we will evaluate the Jaccard similarity of the different methods. The first will be the implementation as provided from this Rust crate HyperLogLog couters, testing all of the available bits and precisions. Note that, since there are no Python bindings for the Rust crate (yet) we run the cose as one of the test in the crate test suite. \n",
    "\n",
    "The second one will be MinHash, using the implementation provided by the datasketch library. We will compare the performance of the two methods for the same amount of memory used.\n",
    "\n",
    "## What is an HyperLogLog counter?\n",
    "An HyperLogLog counter is a probabilistic data structure used to estimate the cardinality of a set. It is based on the observation that the cardinality of a set can be estimated by the maximum number of leading zeros in the binary representation of the hashes of the elements of the set. The HyperLogLog counter is a data structure that stores the maximum number of leading zeros for a set of hashes. The counter is initialized with a number of bits, which determines the maximum number of leading zeros that can be stored. The counter is then updated with the hashes of the elements of the set. The estimate of the cardinality is then given by the harmonic mean of the values stored in the counter. HyperLogLog counters can be used to compute the cardinality of the union of two sets by taking the maximum of the values stored in the two counters, and therefore we can also compute the Jaccard similarity of two sets.\n"
   ]
  },
  {
   "cell_type": "code",
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   "id": "dd95a263",
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       "      <th></th>\n",
       "      <th>precision</th>\n",
       "      <th>bits</th>\n",
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       "      <th>old</th>\n",
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       "      <td>18.064531</td>\n",
       "      <td>siphasher::sip::SipHasher13</td>\n",
       "      <td>16</td>\n",
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       "      <td>1378.304000</td>\n",
       "      <td>siphasher::sip::SipHasher13</td>\n",
       "      <td>48</td>\n",
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       "      <th>3</th>\n",
       "      <td>4</td>\n",
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       "      <td>4</td>\n",
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       "      <td>31895.666000</td>\n",
       "      <td>siphasher::sip::SipHasher13</td>\n",
       "      <td>80</td>\n",
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       "      <td>29055.014000</td>\n",
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       "      <td>29055.014000</td>\n",
       "      <td>29055.014000</td>\n",
       "      <td>siphasher::sip::SipHasher13</td>\n",
       "      <td>393216</td>\n",
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       "      <th>167997</th>\n",
       "      <td>17</td>\n",
       "      <td>4</td>\n",
       "      <td>29069</td>\n",
       "      <td>29055.014000</td>\n",
       "      <td>29055.014000</td>\n",
       "      <td>siphasher::sip::SipHasher13</td>\n",
       "      <td>524288</td>\n",
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       "      <th>167998</th>\n",
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       "      <td>29055.014000</td>\n",
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       "      <td>655360</td>\n",
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       "<p>168000 rows × 7 columns</p>\n",
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       "        precision  bits  exact           old        recent  \\\n",
       "0               4     1  44199     18.064531     18.064531   \n",
       "1               4     2  44199     86.144000     86.144000   \n",
       "2               4     3  44199   1378.304000   1378.304000   \n",
       "3               4     4  44199  31895.666000  31895.666000   \n",
       "4               4     5  44199  31895.666000  31895.666000   \n",
       "...           ...   ...    ...           ...           ...   \n",
       "167995         17     2  29069  29055.014000  29055.014000   \n",
       "167996         17     3  29069  29055.014000  29055.014000   \n",
       "167997         17     4  29069  29055.014000  29055.014000   \n",
       "167998         17     5  29069  29055.014000  29055.014000   \n",
       "167999         17     6  29069  29055.014000  29055.014000   \n",
       "\n",
       "                          hash_name  memory  \n",
       "0       siphasher::sip::SipHasher13      16  \n",
       "1       siphasher::sip::SipHasher13      32  \n",
       "2       siphasher::sip::SipHasher13      48  \n",
       "3       siphasher::sip::SipHasher13      64  \n",
       "4       siphasher::sip::SipHasher13      80  \n",
       "...                             ...     ...  \n",
       "167995  siphasher::sip::SipHasher13  262144  \n",
       "167996  siphasher::sip::SipHasher13  393216  \n",
       "167997  siphasher::sip::SipHasher13  524288  \n",
       "167998  siphasher::sip::SipHasher13  655360  \n",
       "167999  siphasher::sip::SipHasher13  786432  \n",
       "\n",
       "[168000 rows x 7 columns]"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "df = pd.read_csv(\"union_cardinality_benchmark.tsv\", sep=\"\\t\")\n",
    "df[\"memory\"] = 2**df.precision * df.bits\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "1c3eed05",
   "metadata": {},
   "outputs": [
    {
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       "version_major": 2,
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      "text/plain": [
       "  0%|          | 0/100000 [00:00<?, ?it/s]"
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       "      <th>precision</th>\n",
       "      <th>bits</th>\n",
       "      <th>exact</th>\n",
       "      <th>hll</th>\n",
       "      <th>nn</th>\n",
       "      <th>memory</th>\n",
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       "      <td>336592.90</td>\n",
       "      <td>1536</td>\n",
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       "      <td>360504.88</td>\n",
       "      <td>1536</td>\n",
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       "      <td>279168.88</td>\n",
       "      <td>1536</td>\n",
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       "      <td>367946.720</td>\n",
       "      <td>337073.16</td>\n",
       "      <td>1536</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>8</td>\n",
       "      <td>6</td>\n",
       "      <td>320244</td>\n",
       "      <td>333806.600</td>\n",
       "      <td>304779.56</td>\n",
       "      <td>1536</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>8</td>\n",
       "      <td>6</td>\n",
       "      <td>224682</td>\n",
       "      <td>245158.900</td>\n",
       "      <td>225524.06</td>\n",
       "      <td>1536</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100000 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    precision  bits   exact         hll         nn  memory\n",
       "0           8     6  397062  426806.470  391157.78    1536\n",
       "0           8     6  450075  478586.780  436966.63    1536\n",
       "0           8     6  105663  119218.484  108914.68    1536\n",
       "0           8     6  346393  366406.220  336592.90    1536\n",
       "0           8     6  265464  283791.660  259825.06    1536\n",
       "..        ...   ...     ...         ...        ...     ...\n",
       "0           8     6  370409  394773.470  360504.88    1536\n",
       "0           8     6  308056  305078.840  279168.88    1536\n",
       "0           8     6  331971  367946.720  337073.16    1536\n",
       "0           8     6  320244  333806.600  304779.56    1536\n",
       "0           8     6  224682  245158.900  225524.06    1536\n",
       "\n",
       "[100000 rows x 6 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from glob import glob\n",
    "import pandas as pd\n",
    "from tqdm.auto import tqdm\n",
    "\n",
    "df = pd.concat([\n",
    "    pd.read_csv(path, sep=\"\\t\")\n",
    "    for path in tqdm(glob(\"union_test/*.tsv.gz\"))\n",
    "])\n",
    "\n",
    "df[\"memory\"] = 2**df.precision * df.bits\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "745dfb45",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.13306"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "df[\"mse_hll\"] = (df.exact - df.hll)**2\n",
    "df[\"mse_nn\"] = (df.exact - df.nn)**2\n",
    "df[\"mse_rates\"] = np.log((df.exact - df.nn)**2 / (df.exact - df.hll)**2)\n",
    "\n",
    "(df[\"mse_rates\"] > 1.0).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "58e7ea9d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "df.mse_rates.hist(log=True, bins=1000)\n",
    "#plt.xscale(\"log\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b5e9bfe8",
   "metadata": {},
   "source": [
    "We determine the number of u64 words to use for the MinHash to execute versions of MinHash with comparable memory usage to the HyperLogLog counters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ef240523",
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "\n",
    "bits = df.bits.unique()\n",
    "precision = df.precision.unique()\n",
    "\n",
    "number_of_words = {\n",
    "    # We divide again by 2 because the number of permutations used is a u64\n",
    "    # and by two again as \n",
    "    math.ceil(b * 2**p / 32) // 2 // 2\n",
    "    for b in bits\n",
    "    for p in precision\n",
    "}\n",
    "\n",
    "# Some HyperLogLog counters require less than 64 bits, so there will be\n",
    "# values in the list that are zero. We remove them.\n",
    "number_of_words = [\n",
    "    word\n",
    "    for word in number_of_words\n",
    "    if word > 0\n",
    "]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7b8c5238",
   "metadata": {},
   "source": [
    "We parallelize the computation of the Jaccard similarity using MinHash, which is significantly slower than the HyperLogLog counters as while the former is an extensively optimized Rust implementation, the latter is more didactical Python implementation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "b8106fcc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr th {\n",
       "        text-align: left;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>precision</th>\n",
       "      <th>bits</th>\n",
       "      <th>memory</th>\n",
       "      <th colspan=\"2\" halign=\"left\">old_squared_error</th>\n",
       "      <th colspan=\"2\" halign=\"left\">recent_squared_error</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>8</td>\n",
       "      <td>6</td>\n",
       "      <td>1536</td>\n",
       "      <td>1.961102e+09</td>\n",
       "      <td>2.419204e+09</td>\n",
       "      <td>3.716497e+08</td>\n",
       "      <td>6.508915e+08</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  precision bits memory old_squared_error               recent_squared_error  \\\n",
       "                                     mean           std                 mean   \n",
       "0         8    6   1536      1.961102e+09  2.419204e+09         3.716497e+08   \n",
       "\n",
       "                 \n",
       "            std  \n",
       "0  6.508915e+08  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[\"old_squared_error\"] = (df.exact - df.hll)**2\n",
    "df[\"recent_squared_error\"] = (df.exact - df.nn)**2\n",
    "#df[\"bounded_squared_error\"] = (df.exact - df.bounded_approximation)**2\n",
    "columns = [\n",
    "    \"old_squared_error\",\n",
    "    \"recent_squared_error\",\n",
    "    #\"bounded_squared_error\"\n",
    "]\n",
    "data_hll = df.groupby([\"precision\", \"bits\", \"memory\",])[columns].agg([\"mean\", \"std\"])\n",
    "data_hll = data_hll.reset_index()\n",
    "data_hll"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "49d6a372",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    0.189511\n",
       "Name: mean, dtype: float64"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_hll.recent_squared_error[\"mean\"] / data_hll.old_squared_error[\"mean\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a53f306",
   "metadata": {},
   "source": [
    "We visualize two versions of the HyperLogLog counters, one including also **EXTREMELY SMALL** registers of 1 and 2 bits, which really push the limits of the HyperLogLog counters, and one without them, which is more representative of the performance of the HyperLogLog counters for the more common use cases. We include these tiny registers as exploring the limits of the HyperLogLog counters is one of the main goals of this project."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "9a370282",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1920x1440 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1920x1440 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "bits_to_discard = (1, 2, 3, 4, 5)\n",
    "\n",
    "hash_name_line_style = {\n",
    "    \"Hasher64_1\": \"-\",\n",
    "    \"MetroHasher\": \"-\",\n",
    "    \"SipHasher13\": \"--\",\n",
    "    \"SipHasher24\": \"-.\",\n",
    "    \"HighwayHasher\": \":\",\n",
    "}\n",
    "\n",
    "hash_name_marker_style = {\n",
    "    \"Hasher64_1\": \"o\",\n",
    "    \"MetroHasher\": \"o\",\n",
    "    \"SipHasher13\": \"^\",\n",
    "    \"SipHasher24\": \"s\",\n",
    "    \"HighwayHasher\": \"x\",\n",
    "}\n",
    "\n",
    "for yscale in (\"linear\", \"log\"):\n",
    "    fig, axes = plt.subplots(dpi=300)\n",
    "    for bits in data_hll[\"bits\"].unique():\n",
    "        if bits in bits_to_discard:\n",
    "            continue\n",
    "        for column in columns:\n",
    "            filtered = data_hll[data_hll.bits == bits]\n",
    "\n",
    "            plt.errorbar(\n",
    "                filtered.memory,\n",
    "                filtered[column][\"mean\"],\n",
    "                filtered[column][\"std\"],\n",
    "                alpha=0.5,\n",
    "                label=f\"{bits}b, {column.split('_')[0]}\"\n",
    "            )\n",
    "    plt.legend()\n",
    "    plt.xscale(\"log\")\n",
    "    plt.yscale(yscale)\n",
    "    plt.ylabel(f\"Union MSE, 100k sets ({yscale})\")\n",
    "    plt.xlabel(\"Memory required (bits)\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5085bf55",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.16"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}