mlrate.ipynb

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   "cell_type": "code",
   "execution_count": 51,
   "id": "0a835b1a-80fe-4ca4-a78c-a6381029fa4d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import multiprocessing as mp\n",
    "\n",
    "from sklearn.datasets import make_regression\n",
    "from sklearn.base import BaseEstimator\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.metrics import r2_score, mean_squared_error\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from matplotlib_inline.backend_inline import set_matplotlib_formats\n",
    "set_matplotlib_formats(\"svg\")\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "79789840-7bce-4720-bbf9-717d4cd8a4a1",
   "metadata": {},
   "source": [
    "paper: https://arxiv.org/pdf/2106.07263.pdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "2ca8cec4-346a-4c87-931b-4baa4b6f75e7",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "6b5b0138-e78b-49a1-b9a7-d1ceb7c20dbd",
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_data(true_effect: float = 0.) -> pd.DataFrame:\n",
    "    n_samples = 10_000\n",
    "    k = 5\n",
    "    \n",
    "    X, y = make_regression(\n",
    "        n_samples=n_samples,\n",
    "        n_features=5,\n",
    "        noise=40,\n",
    "    )\n",
    "\n",
    "    data = pd.DataFrame(X, columns=[f\"X_{i}\" for i in range(X.shape[1])])\n",
    "    data[\"y\"] = y\n",
    "    # treatment indicator\n",
    "    data[\"t\"] = np.random.randint(0, 2, n_samples)\n",
    "    # assign each sample into one of the k splits\n",
    "    data[\"k\"] = np.random.randint(0, k, n_samples)\n",
    "\n",
    "    treatment_mask = data[\"t\"] == 1\n",
    "    data.loc[treatment_mask, \"y\"] += true_effect \n",
    "\n",
    "    return data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "b2be201d-9e00-4f52-9097-d8f5bb16b4d1",
   "metadata": {},
   "outputs": [],
   "source": [
    "def train_and_predict(\n",
    "    data: pd.DataFrame,\n",
    "    show_r2: bool = False,\n",
    ") -> tuple[list[BaseEstimator], pd.DataFrame]:\n",
    "\n",
    "    features = [col for col in data.columns if \"X_\" in col]\n",
    "    models = []\n",
    "    data[\"g_hat\"] = np.nan\n",
    "    for k in range(data[\"k\"].max() + 1):\n",
    "        # k-th model is trained on the complement of the k-th split,\n",
    "        # (all samples that do not belong to the k-th split.\n",
    "        complement_mask = data[\"k\"] != k\n",
    "        split_mask = ~complement_mask\n",
    "\n",
    "        model = LinearRegression()\n",
    "        model.fit(\n",
    "            data.loc[complement_mask, features], \n",
    "            data.loc[complement_mask, \"y\"]\n",
    "        )\n",
    "        models.append(model)\n",
    "\n",
    "        # predict the samples in the k-th split\n",
    "        g_hat = model.predict(data.loc[split_mask, features])\n",
    "        data.loc[split_mask, \"g_hat\"] = g_hat\n",
    "\n",
    "        if show_r2:       \n",
    "            r2 = r2_score(\n",
    "                y_true=data.loc[split_mask, \"y\"],\n",
    "                y_pred=g_hat\n",
    "            )\n",
    "            print(f\"model_{k} r2={r2:.2f}\")\n",
    "\n",
    "    return models, data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "beccda9d-3200-4e76-b0ce-3732952040d3",
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_ols(data: pd.DataFrame):\n",
    "    g_bar = data[\"g_hat\"].mean()\n",
    "\n",
    "    ols_X = pd.DataFrame(\n",
    "        {\n",
    "            \"X_1\": data[\"t\"],\n",
    "            \"X_2\": data[\"g_hat\"],\n",
    "            \"X_3\": data[\"t\"] * (data[\"g_hat\"] - g_bar)\n",
    "        }\n",
    "    )\n",
    "    ols_y = data[\"y\"]\n",
    "\n",
    "    ols = LinearRegression()\n",
    "    ols.fit(ols_X, ols_y)\n",
    "    return ols"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "0f5cd4cb-ca89-47c3-80a6-a57ec9e99460",
   "metadata": {},
   "outputs": [],
   "source": [
    "def evaluate(data: pd.DataFrame) -> dict:\n",
    "    models, data = train_and_predict(data)\n",
    "    ols = compute_ols(data)\n",
    "\n",
    "    treatment_mask = data[\"t\"] == 1\n",
    "    ate = (\n",
    "        data.loc[treatment_mask, \"y\"].mean()\n",
    "        - data.loc[~treatment_mask, \"y\"].mean()\n",
    "    )\n",
    "\n",
    "    return {\n",
    "        \"effect_mlrate_adjusted\": ols.coef_[0],\n",
    "        \"effect\": ate,\n",
    "    }"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "d2aff468-2e39-4914-b332-fb74d20581ca",
   "metadata": {},
   "outputs": [],
   "source": [
    "true_effect = 4.\n",
    "experiments = pd.DataFrame(evaluate(generate_data(true_effect)) for _ in range(1000))"
   ]
  },
  {
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   "execution_count": 65,
   "id": "869e36c3-fefc-4019-9e8d-9a613f3f3172",
   "metadata": {},
   "outputs": [
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       "<Figure size 640x480 with 1 Axes>"
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   ],
   "source": [
    "experiments_long = (\n",
    "    experiments[[\"effect\", \"effect_mlrate_adjusted\"]]\n",
    "    .rename(columns={\"effect\": \"non-adjusted\", \"effect_mlrate_adjusted\": \"mlrate\"})\n",
    "    .melt(\n",
    "        value_vars=[\"non-adjusted\", \"mlrate\"],\n",
    "        var_name=\"method\",\n",
    "        value_name=\"effect\"\n",
    "    )\n",
    ")\n",
    "\n",
    "sns.histplot(experiments_long, x=\"effect\", hue=\"method\", kde=True)\n",
    "plt.title(f\"1000 Experiments (effect={true_effect}): MLRATE and Non-adjusted\")\n",
    "plt.show()"
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