regression/binomial_regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bimonial regression alternatives to Logistic regression\n",
    "\n",
    "If we have a very large dataset it can be computationally expensive to train a logistic regression model.\n",
    "If we have categorical features or can convert features into categories we can summiarise the data and fit a binomial regression model instead, which are more data efficient.\n",
    "\n",
    "Here we we show their equivalence and how they scale.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First lets create a data generating function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Data sample:\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div><style>\n",
       ".dataframe > thead > tr > th,\n",
       ".dataframe > tbody > tr > td {\n",
       "  text-align: right;\n",
       "}\n",
       "</style>\n",
       "<small>shape: (5, 4)</small><table border=\"1\" class=\"dataframe\"><thead><tr><th>y</th><th>y_prob</th><th>x_0</th><th>x_1</th></tr><tr><td>i64</td><td>f64</td><td>i64</td><td>i64</td></tr></thead><tbody><tr><td>0</td><td>0.768634</td><td>1</td><td>1</td></tr><tr><td>0</td><td>0.539129</td><td>1</td><td>0</td></tr><tr><td>0</td><td>0.464949</td><td>0</td><td>0</td></tr><tr><td>1</td><td>0.433964</td><td>0</td><td>0</td></tr><tr><td>1</td><td>0.708297</td><td>0</td><td>1</td></tr></tbody></table></div>"
      ],
      "text/plain": [
       "shape: (5, 4)\n",
       "┌─────┬──────────┬─────┬─────┐\n",
       "│ y   ┆ y_prob   ┆ x_0 ┆ x_1 │\n",
       "│ --- ┆ ---      ┆ --- ┆ --- │\n",
       "│ i64 ┆ f64      ┆ i64 ┆ i64 │\n",
       "╞═════╪══════════╪═════╪═════╡\n",
       "│ 0   ┆ 0.768634 ┆ 1   ┆ 1   │\n",
       "│ 0   ┆ 0.539129 ┆ 1   ┆ 0   │\n",
       "│ 0   ┆ 0.464949 ┆ 0   ┆ 0   │\n",
       "│ 1   ┆ 0.433964 ┆ 0   ┆ 0   │\n",
       "│ 1   ┆ 0.708297 ┆ 0   ┆ 1   │\n",
       "└─────┴──────────┴─────┴─────┘"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "weights:\n",
      "[0.08365798 0.8965755 ]\n"
     ]
    }
   ],
   "source": [
    "from typing import Tuple\n",
    "import numpy as np\n",
    "import polars as pl\n",
    "\n",
    "\n",
    "def generate_data(\n",
    "    n_samples: int = 1000,\n",
    "    n_features: int = 4,\n",
    "    seed: int = None,\n",
    ") -> Tuple[pl.DataFrame, np.array]:\n",
    "    rand = np.random.default_rng(seed)\n",
    "\n",
    "    # binary covariates\n",
    "    covariates = rand.integers(0, 2, size=(n_samples, n_features))\n",
    "\n",
    "    weights = rand.normal(size=(n_features, 1))\n",
    "    outcome_logit = np.dot(covariates, weights) + rand.normal(\n",
    "        scale=0.1, size=(n_samples, 1)\n",
    "    )\n",
    "\n",
    "    def inv_logit(p):\n",
    "        return np.exp(p) / (1 + np.exp(p))\n",
    "\n",
    "    outcome_prob = inv_logit(outcome_logit)\n",
    "    outcome = rand.binomial(n=1, p=outcome_prob)\n",
    "\n",
    "    df = pl.concat(\n",
    "        [\n",
    "            pl.DataFrame(outcome, schema=[\"y\"]),\n",
    "            pl.DataFrame(outcome_prob, schema=[\"y_prob\"]),\n",
    "            pl.DataFrame(covariates, schema=[f\"x_{idx}\" for idx in range(n_features)]),\n",
    "        ],\n",
    "        how=\"horizontal\",\n",
    "    )\n",
    "\n",
    "    return df, weights\n",
    "\n",
    "\n",
    "df, weights = generate_data(n_samples=1000, n_features=2, seed=0)\n",
    "print(\"Data sample:\")\n",
    "display(df.head())\n",
    "\n",
    "print(\"weights:\")\n",
    "print(weights.flatten())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets fit a logistic regression model first. We predict the outcome column `y` from the `x` columns and we retrieve estimated weights that are close to the true weights:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.643229\n",
      "         Iterations 5\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Logit Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>           <td>y</td>        <th>  No. Observations:  </th>  <td>  1000</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                 <td>Logit</td>      <th>  Df Residuals:      </th>  <td>   998</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>                 <td>MLE</td>       <th>  Df Model:          </th>  <td>     1</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>            <td>Thu, 10 Aug 2023</td> <th>  Pseudo R-squ.:     </th>  <td>0.03417</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                <td>10:41:17</td>     <th>  Log-Likelihood:    </th> <td> -643.23</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>converged:</th>             <td>True</td>       <th>  LL-Null:           </th> <td> -665.99</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>     <td>nonrobust</td>    <th>  LLR p-value:       </th> <td>1.512e-11</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "   <td></td>      <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x_0</th> <td>    0.0825</td> <td>    0.105</td> <td>    0.786</td> <td> 0.432</td> <td>   -0.123</td> <td>    0.288</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x_1</th> <td>    0.8720</td> <td>    0.109</td> <td>    8.003</td> <td> 0.000</td> <td>    0.658</td> <td>    1.086</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/latex": [
       "\\begin{center}\n",
       "\\begin{tabular}{lclc}\n",
       "\\toprule\n",
       "\\textbf{Dep. Variable:}   &        y         & \\textbf{  No. Observations:  } &     1000    \\\\\n",
       "\\textbf{Model:}           &      Logit       & \\textbf{  Df Residuals:      } &      998    \\\\\n",
       "\\textbf{Method:}          &       MLE        & \\textbf{  Df Model:          } &        1    \\\\\n",
       "\\textbf{Date:}            & Thu, 10 Aug 2023 & \\textbf{  Pseudo R-squ.:     } &  0.03417    \\\\\n",
       "\\textbf{Time:}            &     10:41:17     & \\textbf{  Log-Likelihood:    } &   -643.23   \\\\\n",
       "\\textbf{converged:}       &       True       & \\textbf{  LL-Null:           } &   -665.99   \\\\\n",
       "\\textbf{Covariance Type:} &    nonrobust     & \\textbf{  LLR p-value:       } & 1.512e-11   \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lcccccc}\n",
       "              & \\textbf{coef} & \\textbf{std err} & \\textbf{z} & \\textbf{P$> |$z$|$} & \\textbf{[0.025} & \\textbf{0.975]}  \\\\\n",
       "\\midrule\n",
       "\\textbf{x\\_0} &       0.0825  &        0.105     &     0.786  &         0.432        &       -0.123    &        0.288     \\\\\n",
       "\\textbf{x\\_1} &       0.8720  &        0.109     &     8.003  &         0.000        &        0.658    &        1.086     \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "%\\caption{Logit Regression Results}\n",
       "\\end{center}"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                           Logit Regression Results                           \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   No. Observations:                 1000\n",
       "Model:                          Logit   Df Residuals:                      998\n",
       "Method:                           MLE   Df Model:                            1\n",
       "Date:                Thu, 10 Aug 2023   Pseudo R-squ.:                 0.03417\n",
       "Time:                        10:41:17   Log-Likelihood:                -643.23\n",
       "converged:                       True   LL-Null:                       -665.99\n",
       "Covariance Type:            nonrobust   LLR p-value:                 1.512e-11\n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "x_0            0.0825      0.105      0.786      0.432      -0.123       0.288\n",
       "x_1            0.8720      0.109      8.003      0.000       0.658       1.086\n",
       "==============================================================================\n",
       "\"\"\""
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "\n",
    "logit_model = sm.Logit(\n",
    "    df[\"y\"].to_pandas(), df.drop(columns=[\"y\", \"y_prob\"]).to_pandas()\n",
    ")\n",
    "logit_model_results = logit_model.fit()\n",
    "logit_model_results.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets fit with a Binomial model. First we need to group the data into counts of success and failure against each combination of the input categories:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><style>\n",
       ".dataframe > thead > tr > th,\n",
       ".dataframe > tbody > tr > td {\n",
       "  text-align: right;\n",
       "}\n",
       "</style>\n",
       "<small>shape: (4, 4)</small><table border=\"1\" class=\"dataframe\"><thead><tr><th>x_0</th><th>x_1</th><th>success</th><th>failure</th></tr><tr><td>i64</td><td>i64</td><td>i64</td><td>i64</td></tr></thead><tbody><tr><td>0</td><td>0</td><td>102</td><td>115</td></tr><tr><td>1</td><td>0</td><td>138</td><td>118</td></tr><tr><td>0</td><td>1</td><td>193</td><td>74</td></tr><tr><td>1</td><td>1</td><td>183</td><td>77</td></tr></tbody></table></div>"
      ],
      "text/plain": [
       "shape: (4, 4)\n",
       "┌─────┬─────┬─────────┬─────────┐\n",
       "│ x_0 ┆ x_1 ┆ success ┆ failure │\n",
       "│ --- ┆ --- ┆ ---     ┆ ---     │\n",
       "│ i64 ┆ i64 ┆ i64     ┆ i64     │\n",
       "╞═════╪═════╪═════════╪═════════╡\n",
       "│ 0   ┆ 0   ┆ 102     ┆ 115     │\n",
       "│ 1   ┆ 0   ┆ 138     ┆ 118     │\n",
       "│ 0   ┆ 1   ┆ 193     ┆ 74      │\n",
       "│ 1   ┆ 1   ┆ 183     ┆ 77      │\n",
       "└─────┴─────┴─────────┴─────────┘"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def group_data(df: pl.DataFrame):\n",
    "    x_cols = [col for col in df.columns if \"x_\" in col]\n",
    "    return df.groupby(x_cols).agg(\n",
    "        [\n",
    "            pl.col(\"y\").sum().alias(\"success\"),\n",
    "            (pl.count() - pl.col(\"y\").sum()).alias(\"failure\"),\n",
    "        ]\n",
    "    )\n",
    "\n",
    "\n",
    "df_group = group_data(df)\n",
    "df_group"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can fit a Binomial regression model. We get identical results to the logistic regression model, including confidence intervals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Generalized Linear Model Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>   <td>['success', 'failure']</td> <th>  No. Observations:  </th>  <td>     4</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                     <td>GLM</td>          <th>  Df Residuals:      </th>  <td>     2</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model Family:</th>           <td>Binomial</td>        <th>  Df Model:          </th>  <td>     1</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Link Function:</th>            <td>Logit</td>         <th>  Scale:             </th> <td>  1.0000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>                   <td>IRLS</td>          <th>  Log-Likelihood:    </th> <td> -12.717</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>               <td>Thu, 10 Aug 2023</td>    <th>  Deviance:          </th> <td>  1.9577</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                   <td>10:41:17</td>        <th>  Pearson chi2:      </th>  <td>  1.96</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Iterations:</th>             <td>4</td>           <th>  Pseudo R-squ. (CS):</th>  <td> 1.000</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>        <td>nonrobust</td>       <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "   <td></td>      <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x_0</th> <td>    0.0825</td> <td>    0.105</td> <td>    0.786</td> <td> 0.432</td> <td>   -0.123</td> <td>    0.288</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x_1</th> <td>    0.8720</td> <td>    0.109</td> <td>    8.003</td> <td> 0.000</td> <td>    0.658</td> <td>    1.086</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/latex": [
       "\\begin{center}\n",
       "\\begin{tabular}{lclc}\n",
       "\\toprule\n",
       "\\textbf{Dep. Variable:}   & ['success', 'failure'] & \\textbf{  No. Observations:  } &        4    \\\\\n",
       "\\textbf{Model:}           &          GLM           & \\textbf{  Df Residuals:      } &        2    \\\\\n",
       "\\textbf{Model Family:}    &        Binomial        & \\textbf{  Df Model:          } &        1    \\\\\n",
       "\\textbf{Link Function:}   &         Logit          & \\textbf{  Scale:             } &    1.0000   \\\\\n",
       "\\textbf{Method:}          &          IRLS          & \\textbf{  Log-Likelihood:    } &   -12.717   \\\\\n",
       "\\textbf{Date:}            &    Thu, 10 Aug 2023    & \\textbf{  Deviance:          } &    1.9577   \\\\\n",
       "\\textbf{Time:}            &        10:41:17        & \\textbf{  Pearson chi2:      } &     1.96    \\\\\n",
       "\\textbf{No. Iterations:}  &           4            & \\textbf{  Pseudo R-squ. (CS):} &    1.000    \\\\\n",
       "\\textbf{Covariance Type:} &       nonrobust        & \\textbf{                     } &             \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lcccccc}\n",
       "              & \\textbf{coef} & \\textbf{std err} & \\textbf{z} & \\textbf{P$> |$z$|$} & \\textbf{[0.025} & \\textbf{0.975]}  \\\\\n",
       "\\midrule\n",
       "\\textbf{x\\_0} &       0.0825  &        0.105     &     0.786  &         0.432        &       -0.123    &        0.288     \\\\\n",
       "\\textbf{x\\_1} &       0.8720  &        0.109     &     8.003  &         0.000        &        0.658    &        1.086     \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "%\\caption{Generalized Linear Model Regression Results}\n",
       "\\end{center}"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                   Generalized Linear Model Regression Results                    \n",
       "==================================================================================\n",
       "Dep. Variable:     ['success', 'failure']   No. Observations:                    4\n",
       "Model:                                GLM   Df Residuals:                        2\n",
       "Model Family:                    Binomial   Df Model:                            1\n",
       "Link Function:                      Logit   Scale:                          1.0000\n",
       "Method:                              IRLS   Log-Likelihood:                -12.717\n",
       "Date:                    Thu, 10 Aug 2023   Deviance:                       1.9577\n",
       "Time:                            10:41:17   Pearson chi2:                     1.96\n",
       "No. Iterations:                         4   Pseudo R-squ. (CS):              1.000\n",
       "Covariance Type:                nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "x_0            0.0825      0.105      0.786      0.432      -0.123       0.288\n",
       "x_1            0.8720      0.109      8.003      0.000       0.658       1.086\n",
       "==============================================================================\n",
       "\"\"\""
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "binom_model = sm.GLM(\n",
    "    df_group[[\"success\", \"failure\"]].to_pandas(),\n",
    "    df_group.drop(columns=[\"success\", \"failure\"]).to_pandas(),\n",
    "    family=sm.families.Binomial(),\n",
    ")\n",
    "binom_model_results = binom_model.fit()\n",
    "binom_model_results.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fitting time/data scaling\n",
    "\n",
    "Now that we've shown their equivalence how does each model scale with data size?\n",
    "\n",
    "We can test the fitting time on different number of samples to find out. We will not include the time for grouping the data as this can commonly be done via external tools such as data warehouses."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0/11 [00:00<?, ?it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/stantoon/miniconda3/envs/project_env/lib/python3.10/site-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals\n",
      "  warnings.warn(\"Maximum Likelihood optimization failed to \"\n",
      "100%|██████████| 11/11 [00:33<00:00,  3.08s/it]\n"
     ]
    }
   ],
   "source": [
    "import timeit\n",
    "import tqdm\n",
    "\n",
    "\n",
    "times = []\n",
    "n_features = 10\n",
    "n_trials = 10\n",
    "for n_samples in tqdm.tqdm([1e2, 5e2, 1e3, 5e3, 1e4, 5e4, 1e5, 5e5, 1e6, 5e6, 1e7]):\n",
    "    for _trial in range(n_trials):\n",
    "        _n_samples = int(n_samples)\n",
    "        df, weights = generate_data(\n",
    "            n_samples=_n_samples, n_features=10, seed=_n_samples + _trial\n",
    "        )\n",
    "\n",
    "        if _n_samples < 1e6:\n",
    "            t1 = timeit.default_timer()\n",
    "            logit_model = sm.Logit(\n",
    "                df[\"y\"].to_pandas(), df.drop(columns=[\"y\", \"y_prob\"]).to_pandas()\n",
    "            )\n",
    "            logit_model_results = logit_model.fit(disp=0)\n",
    "            times.append([\"logit\", _n_samples, timeit.default_timer() - t1])\n",
    "\n",
    "        df_group = group_data(df=df)\n",
    "        t1 = timeit.default_timer()\n",
    "        binom_model = sm.GLM(\n",
    "            df_group[[\"success\", \"failure\"]].to_pandas(),\n",
    "            df_group.drop(columns=[\"success\", \"failure\"]).to_pandas(),\n",
    "            family=sm.families.Binomial(),\n",
    "        )\n",
    "        binom_model_results = binom_model.fit()\n",
    "        times.append([\"binomial\", _n_samples, timeit.default_timer() - t1])\n",
    "\n",
    "times = pl.DataFrame(times, schema=[\"model_type\", \"n_samples\", \"fit_time\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting the results show that the Logistic regression model scales exponentially whilst the Binomial is approximately flat.\n",
    "The shaded region represents the confidence interval of the mean fit time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/_v/nlh4h1yx2n1gd6f3szjlgxt40000gr/T/ipykernel_90987/2954676713.py:4: MatplotlibDeprecationWarning: The seaborn styles shipped by Matplotlib are deprecated since 3.6, as they no longer correspond to the styles shipped by seaborn. However, they will remain available as 'seaborn-v0_8-<style>'. Alternatively, directly use the seaborn API instead.\n",
      "  plt.style.use(\"seaborn-whitegrid\")\n",
      "/var/folders/_v/nlh4h1yx2n1gd6f3szjlgxt40000gr/T/ipykernel_90987/2954676713.py:11: UserWarning: Matplotlib is currently using module://matplotlib_inline.backend_inline, which is a non-GUI backend, so cannot show the figure.\n",
      "  fig.show()\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.style.use(\"seaborn-whitegrid\")\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10, 6))\n",
    "sns.lineplot(\n",
    "    data=times, x=\"n_samples\", y=\"fit_time\", hue=\"model_type\", ax=ax, marker=\"x\"\n",
    ")\n",
    "ax.set(xscale=\"log\", ylabel=\"Fit time (s)\", title=\"Fit time against data length\")\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data size passed to the Binomial model always has the same upper group which is the number of possible groups in the data. If we have $n$ features we have $2^n$ possible groups. The counts for each group simply increase when our data size is larger, so we don't expect any change in fitting time. Therefore the Binomial model can scale very well to large problems if we have categorical features. If we don't have categorical features this won't apply, but we can always approximate continuous features with binary categories, such as through various sklearn transformers ([link](https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.Binarizer.html), [link2](https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.KBinsDiscretizer.html)). What's convenient here is that it allows us to do the heavy lifting and aggregation on a data warehouse and output a small dataset for modelling. Therefore we are not limited by the memory of our device used for building models.\n",
    "\n",
    "Note: there are alternative approaches for logistic regression to handle large data, such as fitting on a sample, though this will bias the confidence intervals to be larger than reality."
   ]
  }
 ],
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