Customer_lifetime_value.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from lifetimes.datasets import load_cdnow_summary\n",
    "data = load_cdnow_summary(index_col=[0])\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    frequency  recency      T\n",
      "ID                           \n",
      "1           2    30.43  38.86\n",
      "2           1     1.71  38.86\n",
      "3           0     0.00  38.86\n",
      "4           0     0.00  38.86\n",
      "5           0     0.00  38.86\n"
     ]
    }
   ],
   "source": [
    "print(data.head())\n",
    "#T表示从第一次购买到现在的持续时间\n",
    "#frequency：（重复购买次数，比如买了3次，则重复了2次，购买了5次，则重复了4次）。这里是表示重复买东西的天数\n",
    "#recency表示第一次购买与最后一次购买所持续的时间，如果只购买了一次，那么第一次购买也就是最后一次购买，因此recency=0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<lifetimes.BetaGeoFitter: fitted with 2357 subjects, a: 0.79, alpha: 4.41, b: 2.43, r: 0.24>\n"
     ]
    }
   ],
   "source": [
    "#拟合 BG/NBD 模型\n",
    "from lifetimes import BetaGeoFitter\n",
    "bgf = BetaGeoFitter(penalizer_coef=0.0)\n",
    "bgf.fit(data['frequency'], data['recency'], data['T'])\n",
    "print(bgf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1d7fa222668>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from lifetimes.plotting import plot_frequency_recency_matrix\n",
    "\n",
    "plot_frequency_recency_matrix(bgf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1d7fb2ba780>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from lifetimes.plotting import plot_probability_alive_matrix\n",
    "\n",
    "plot_probability_alive_matrix(bgf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "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 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>frequency</th>\n",
       "      <th>recency</th>\n",
       "      <th>T</th>\n",
       "      <th>predicted_purchases</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ID</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>509</th>\n",
       "      <td>18</td>\n",
       "      <td>35.14</td>\n",
       "      <td>35.86</td>\n",
       "      <td>0.424877</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>841</th>\n",
       "      <td>19</td>\n",
       "      <td>34.00</td>\n",
       "      <td>34.14</td>\n",
       "      <td>0.474738</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1981</th>\n",
       "      <td>17</td>\n",
       "      <td>28.43</td>\n",
       "      <td>28.86</td>\n",
       "      <td>0.486525</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>157</th>\n",
       "      <td>29</td>\n",
       "      <td>37.71</td>\n",
       "      <td>38.00</td>\n",
       "      <td>0.662395</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1516</th>\n",
       "      <td>26</td>\n",
       "      <td>30.86</td>\n",
       "      <td>31.00</td>\n",
       "      <td>0.710622</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      frequency  recency      T  predicted_purchases\n",
       "ID                                                  \n",
       "509          18    35.14  35.86             0.424877\n",
       "841          19    34.00  34.14             0.474738\n",
       "1981         17    28.43  28.86             0.486525\n",
       "157          29    37.71  38.00             0.662395\n",
       "1516         26    30.86  31.00             0.710622"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#预测下一期用户购买的概率\n",
    "t = 1\n",
    "data['predicted_purchases'] = bgf.conditional_expected_number_of_purchases_up_to_time(t, data['frequency'], data['recency'], data['T'])\n",
    "data.sort_values(by='predicted_purchases').tail(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1d7fb4425c0>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#验证模型\n",
    "from lifetimes.plotting import plot_period_transactions\n",
    "plot_period_transactions(bgf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                  date  id\n",
      "0  2014-03-08 00:00:00   0\n",
      "1  2014-05-21 00:00:00   1\n",
      "2  2014-03-14 00:00:00   2\n",
      "3  2014-04-09 00:00:00   2\n",
      "4  2014-05-21 00:00:00   2\n"
     ]
    }
   ],
   "source": [
    "#transactional datasets 转换成RF数据格式\n",
    "from lifetimes.datasets import load_transaction_data\n",
    "from lifetimes.utils import summary_data_from_transaction_data\n",
    "\n",
    "transaction_data = load_transaction_data()\n",
    "print(transaction_data.head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "summary = summary_data_from_transaction_data(transaction_data, 'id', 'date', observation_period_end='2014-12-31')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    frequency  recency      T\n",
      "id                           \n",
      "0         0.0      0.0  298.0\n",
      "1         0.0      0.0  224.0\n",
      "2         6.0    142.0  292.0\n",
      "3         0.0      0.0  147.0\n",
      "4         2.0      9.0  183.0\n"
     ]
    }
   ],
   "source": [
    "print(summary.head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.08001721956615553"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#单个顾客在未来一段时间的预测\n",
    "t = 10 #10期\n",
    "individual = summary.iloc[20]\n",
    "\n",
    "bgf.predict(t, individual['frequency'], individual['recency'], individual['T'])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1d7fb4e0198>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from lifetimes.plotting import plot_history_alive\n",
    "\n",
    "id = 35\n",
    "days_since_birth = 200\n",
    "sp_trans = transaction_data.loc[transaction_data['id'] == id]\n",
    "plot_history_alive(bgf, days_since_birth, sp_trans, 'date')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "             frequency  recency      T  monetary_value\n",
      "customer_id                                           \n",
      "1                    2    30.43  38.86           22.35\n",
      "2                    1     1.71  38.86           11.77\n",
      "6                    7    29.43  38.86           73.74\n",
      "7                    1     5.00  38.86           11.77\n",
      "9                    2    35.71  38.86           25.55\n"
     ]
    }
   ],
   "source": [
    "#Estimating customer lifetime value using the Gamma-Gamma model\n",
    "from lifetimes.datasets import load_cdnow_summary_data_with_monetary_value\n",
    "\n",
    "summary_with_money_value = load_cdnow_summary_data_with_monetary_value()\n",
    "summary_with_money_value.head()\n",
    "returning_customers_summary = summary_with_money_value[summary_with_money_value['frequency']>0]\n",
    "\n",
    "print(returning_customers_summary.head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "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 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>monetary_value</th>\n",
       "      <th>frequency</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>monetary_value</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.113884</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>frequency</th>\n",
       "      <td>0.113884</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                monetary_value  frequency\n",
       "monetary_value        1.000000   0.113884\n",
       "frequency             0.113884   1.000000"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "returning_customers_summary[['monetary_value', 'frequency']].corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<lifetimes.GammaGammaFitter: fitted with 946 subjects, p: 6.25, q: 3.74, v: 15.45>\n"
     ]
    }
   ],
   "source": [
    "from lifetimes import GammaGammaFitter\n",
    "\n",
    "ggf = GammaGammaFitter(penalizer_coef = 0)\n",
    "ggf.fit(returning_customers_summary['frequency'],\n",
    "        returning_customers_summary['monetary_value'])\n",
    "print(ggf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "customer_id\n",
      "1     24.658619\n",
      "2     18.911488\n",
      "3     35.171004\n",
      "4     35.171004\n",
      "5     35.171004\n",
      "6     71.462848\n",
      "7     18.911488\n",
      "8     35.171004\n",
      "9     27.282410\n",
      "10    35.171004\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "print(ggf.conditional_expected_average_profit( summary_with_money_value['frequency'],summary_with_money_value['monetary_value'] ).head(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected conditional average profit: 35.25295949542014, Average profit: 35.07855179704026\n"
     ]
    }
   ],
   "source": [
    "print(\"Expected conditional average profit: %s, Average profit: %s\" % (\n",
    "    ggf.conditional_expected_average_profit(\n",
    "        summary_with_money_value['frequency'],\n",
    "        summary_with_money_value['monetary_value']\n",
    "    ).mean(),\n",
    "    summary_with_money_value[summary_with_money_value['frequency']>0]['monetary_value'].mean()\n",
    "))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "customer_id\n",
      "1      140.097046\n",
      "2       18.943419\n",
      "3       38.180625\n",
      "4       38.180625\n",
      "5       38.180625\n",
      "6     1003.881713\n",
      "7       28.109655\n",
      "8       38.180625\n",
      "9      167.419207\n",
      "10      38.180625\n",
      "Name: clv, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "# refit the BG model to the summary_with_money_value dataset\n",
    "bgf.fit(summary_with_money_value['frequency'], summary_with_money_value['recency'], summary_with_money_value['T'])\n",
    "\n",
    "print(ggf.customer_lifetime_value(\n",
    "    bgf, #the model to use to predict the number of future transactions\n",
    "    summary_with_money_value['frequency'],\n",
    "    summary_with_money_value['recency'],\n",
    "    summary_with_money_value['T'],\n",
    "    summary_with_money_value['monetary_value'],\n",
    "    time=12, # months\n",
    "    discount_rate=0.01 # monthly discount rate ~ 12.7% annually\n",
    ").head(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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