{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Python: Basics of Double Machine Learning\n", "\n", "**Remark**: This notebook has a long computation time due to the large number of simulations.\n", "\n", "This notebooks contains the detailed simulations according to the introduction to double machine learning in the [User Guide](https://docs.doubleml.org/stable/guide/basics.html) of the DoubleML package." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import warnings\n", "import numpy as np\n", "from scipy import stats\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "\n", "from lightgbm import LGBMRegressor\n", "from sklearn.ensemble import RandomForestRegressor\n", "from sklearn.model_selection import train_test_split\n", "from sklearn.base import clone\n", "\n", "from doubleml import DoubleMLData\n", "from doubleml import DoubleMLPLR\n", "from doubleml.plm.datasets import make_plr_CCDDHNR2018\n", "\n", "face_colors = sns.color_palette('pastel')\n", "edge_colors = sns.color_palette('dark')\n", "\n", "warnings.filterwarnings(\"ignore\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Data Generating Process (DGP)\n", "\n", "We consider the following partially linear model:\n", "\n", "$$\n", "\\begin{align*}\n", "y_i &= \\theta_0 d_i + g_0(x_i) + \\zeta_i, & \\zeta_i \\sim \\mathcal{N}(0,1), \\\\\n", "d_i &= m_0(x_i) + v_i, & v_i \\sim \\mathcal{N}(0,1),\n", "\\end{align*}\n", "$$\n", "\n", "with covariates $x_i \\sim \\mathcal{N}(0, \\Sigma)$, where $\\Sigma$ is a matrix with entries $\\Sigma_{kj} = 0.7^{|j-k|}$. We are interested in performing valid inference on the causal parameter $\\theta_0$. The true parameter $\\theta_0$ is set to $0.5$ in our simulation experiment.\n", "\n", "The nuisance functions are given by:\n", "\n", "$$\n", "\\begin{align*}\n", "m_0(x_i) &= x_{i,1} + \\frac{1}{4} \\frac{\\exp(x_{i,3})}{1+\\exp(x_{i,3})}, \\\\\n", "g_0(x_i) &= \\frac{\\exp(x_{i,1})}{1+\\exp(x_{i,1})} + \\frac{1}{4} x_{i,3}.\n", "\\end{align*}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We generate ``n_rep`` replications of the data generating process with sample size ``n_obs`` and compare the performance of different estimators." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "np.random.seed(1234)\n", "n_rep = 1000\n", "n_obs = 500\n", "n_vars = 5\n", "alpha = 0.5\n", "\n", "data = list()\n", "\n", "for i_rep in range(n_rep):\n", " (x, y, d) = make_plr_CCDDHNR2018(alpha=alpha, n_obs=n_obs, dim_x=n_vars, return_type='array')\n", " data.append((x, y, d))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Regularization Bias in Simple ML-Approaches\n", "\n", "Naive inference that is based on a direct application of machine learning methods to estimate the causal parameter, $\\theta_0$, is generally invalid. The use of machine learning methods introduces a bias that arises due to regularization. A simple ML approach is given by randomly splitting the sample into two parts. On the auxiliary sample indexed by $i \\in I^C$ the nuisance function $g_0(X)$ is estimated with an ML method, for example a random forest learner. Given the estimate $\\hat{g}_0(X)$, the final estimate of $\\theta_0$ is obtained as ($n=N/2$) using the other half of observations indexed with $i \\in I$\n", "\n", "$$\n", "\\hat{\\theta}_0 = \\left(\\frac{1}{n} \\sum_{i\\in I} D_i^2\\right)^{-1} \\frac{1}{n} \\sum_{i\\in I} D_i (Y_i - \\hat{g}_0(X_i)).\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As this corresponds to a \"non-orthogonal\" score, which is not implemented in the DoubleML package, we need to define a custom callable." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def non_orth_score(y, d, l_hat, m_hat, g_hat, smpls):\n", " u_hat = y - g_hat\n", " psi_a = -np.multiply(d, d)\n", " psi_b = np.multiply(d, u_hat)\n", " return psi_a, psi_b" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Remark that the estimator is not able to estimate $\\hat{g}_0(X)$ directly, but has to be based on a preliminary estimate of $\\hat{m}_0(X)$. All following estimators with ``score=\"IV-type\"`` are based on the same preliminary procedure. Furthermore, remark that we are using external predictions to avoid cross-fitting (for demonstration purposes)." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Replication 1000/1000\r" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "np.random.seed(1111)\n", "\n", "ml_l = LGBMRegressor(n_estimators=300, learning_rate=0.1, verbose=-1)\n", "ml_m = LGBMRegressor(n_estimators=300, learning_rate=0.1, verbose=-1)\n", "\n", "ml_g = clone(ml_l)\n", "\n", "theta_nonorth = np.full(n_rep, np.nan)\n", "se_nonorth = np.full(n_rep, np.nan) \n", "\n", "for i_rep in range(n_rep):\n", " print(f'Replication {i_rep+1}/{n_rep}', end='\\r')\n", " (x, y, d) = data[i_rep]\n", " \n", " # choose a random sample for training and estimation\n", " i_train, i_est = train_test_split(np.arange(n_obs), test_size=0.5, random_state=42)\n", " \n", " # fit the ML algorithms on the training sample\n", " ml_l.fit(x[i_train, :], y[i_train])\n", " ml_m.fit(x[i_train, :], d[i_train])\n", "\n", " psi_a = -np.multiply(d[i_train] - ml_m.predict(x[i_train, :]), d[i_train] - ml_m.predict(x[i_train, :]))\n", " psi_b = np.multiply(d[i_train] - ml_m.predict(x[i_train, :]), y[i_train] - ml_l.predict(x[i_train, :]))\n", " theta_initial = -np.nanmean(psi_b) / np.nanmean(psi_a)\n", " ml_g.fit(x[i_train, :], y[i_train] - theta_initial * d[i_train])\n", "\n", " # create out-of-sample predictions\n", " l_hat = ml_l.predict(x[i_est, :])\n", " m_hat = ml_m.predict(x[i_est, :])\n", " g_hat = ml_g.predict(x[i_est, :])\n", "\n", " external_predictions = {\n", " 'd': {\n", " 'ml_l': l_hat.reshape(-1, 1),\n", " 'ml_m': m_hat.reshape(-1, 1),\n", " 'ml_g': g_hat.reshape(-1, 1)\n", " }\n", " }\n", "\n", " obj_dml_data = DoubleMLData.from_arrays(x[i_est, :], y[i_est], d[i_est])\n", " obj_dml_plr_nonorth = DoubleMLPLR(obj_dml_data,\n", " ml_l, ml_m, ml_g,\n", " n_folds=2,\n", " score=non_orth_score)\n", " obj_dml_plr_nonorth.fit(external_predictions=external_predictions)\n", " theta_nonorth[i_rep] = obj_dml_plr_nonorth.coef[0]\n", " se_nonorth[i_rep] = obj_dml_plr_nonorth.se[0]\n", "\n", "fig_non_orth, ax = plt.subplots(constrained_layout=True);\n", "ax = sns.histplot((theta_nonorth - alpha)/se_nonorth,\n", " color=face_colors[0], edgecolor = edge_colors[0],\n", " stat='density', bins=30, label='Non-orthogonal ML');\n", "ax.axvline(0., color='k');\n", "xx = np.arange(-5, +5, 0.001)\n", "yy = stats.norm.pdf(xx)\n", "ax.plot(xx, yy, color='k', label='$\\\\mathcal{N}(0, 1)$');\n", "ax.legend(loc='upper right', bbox_to_anchor=(1.2, 1.0));\n", "ax.set_xlim([-6., 6.]);\n", "ax.set_xlabel('$(\\hat{\\\\theta}_0 - \\\\theta_0)/\\hat{\\sigma}$');\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The regularization bias in the simple ML-approach is caused by the slow convergence of $\\hat{\\theta}_0$\n", "\n", "$$\n", "|\\sqrt{n} (\\hat{\\theta}_0 - \\theta_0) | \\rightarrow_{P} \\infty\n", "$$\n", "\n", "i.e., slower than $1/\\sqrt{n}$.\n", "The driving factor is the bias that arises by learning $g$ with a random forest or any other ML technique.\n", "A heuristic illustration is given by\n", "\n", "$$\n", "\\sqrt{n}(\\hat{\\theta}_0 - \\theta_0) = \\underbrace{\\left(\\frac{1}{n} \\sum_{i\\in I} D_i^2\\right)^{-1} \\frac{1}{n} \\sum_{i\\in I} D_i \\zeta_i}_{=:a}\n", "+ \\underbrace{\\left(\\frac{1}{n} \\sum_{i\\in I} D_i^2\\right)^{-1} \\frac{1}{n} \\sum_{i\\in I} D_i (g_0(X_i) - \\hat{g}_0(X_i))}_{=:b}.\n", "$$\n", "\n", "$a$ is approximately Gaussian under mild conditions.\n", "However, $b$ (the regularization bias) diverges in general." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Overcoming regularization bias by orthogonalization\n", "\n", "To overcome the regularization bias we can partial out the effect of $X$ from $D$ to obtain the orthogonalized regressor $V = D - m(X)$. We then use the final estimate\n", "\n", "$$\n", "\\check{\\theta}_0 = \\left(\\frac{1}{n} \\sum_{i\\in I} \\hat{V}_i D_i\\right)^{-1} \\frac{1}{n} \\sum_{i\\in I} \\hat{V}_i (Y_i - \\hat{g}_0(X_i)).\n", "$$\n", "\n", "The following figure shows the distribution of the resulting estimates $\\hat{\\theta}_0$ without sample-splitting. Again, we are using external predictions to avoid cross-fitting (for demonstration purposes)." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Replication 1000/1000\r" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "np.random.seed(2222)\n", "\n", "theta_orth_nosplit = np.full(n_rep, np.nan)\n", "se_orth_nosplit = np.full(n_rep, np.nan)\n", "\n", "for i_rep in range(n_rep):\n", " print(f'Replication {i_rep+1}/{n_rep}', end='\\r')\n", " (x, y, d) = data[i_rep]\n", "\n", " # fit the ML algorithms on the training sample\n", " ml_l.fit(x, y)\n", " ml_m.fit(x, d)\n", "\n", " psi_a = -np.multiply(d - ml_m.predict(x), d - ml_m.predict(x))\n", " psi_b = np.multiply(d - ml_m.predict(x), y - ml_l.predict(x))\n", " theta_initial = -np.nanmean(psi_b) / np.nanmean(psi_a)\n", " ml_g.fit(x, y - theta_initial * d)\n", "\n", " l_hat = ml_l.predict(x)\n", " m_hat = ml_m.predict(x)\n", " g_hat = ml_g.predict(x)\n", "\n", " external_predictions = {\n", " 'd': {\n", " 'ml_l': l_hat.reshape(-1, 1),\n", " 'ml_m': m_hat.reshape(-1, 1),\n", " 'ml_g': g_hat.reshape(-1, 1)\n", " }\n", " }\n", "\n", " obj_dml_data = DoubleMLData.from_arrays(x, y, d)\n", " \n", " obj_dml_plr_orth_nosplit = DoubleMLPLR(obj_dml_data,\n", " ml_l, ml_m, ml_g,\n", " score='IV-type')\n", " obj_dml_plr_orth_nosplit.fit(external_predictions=external_predictions)\n", " theta_orth_nosplit[i_rep] = obj_dml_plr_orth_nosplit.coef[0]\n", " se_orth_nosplit[i_rep] = obj_dml_plr_orth_nosplit.se[0]\n", "\n", "fig_orth_nosplit, ax = plt.subplots(constrained_layout=True);\n", "ax = sns.histplot((theta_orth_nosplit - alpha)/se_orth_nosplit,\n", " color=face_colors[1], edgecolor = edge_colors[1],\n", " stat='density', bins=30, label='Double ML (no sample splitting)');\n", "ax.axvline(0., color='k');\n", "xx = np.arange(-5, +5, 0.001)\n", "yy = stats.norm.pdf(xx)\n", "ax.plot(xx, yy, color='k', label='$\\\\mathcal{N}(0, 1)$');\n", "ax.legend(loc='upper right', bbox_to_anchor=(1.2, 1.0)); \n", "ax.set_xlim([-6., 6.]);\n", "ax.set_xlabel('$(\\hat{\\\\theta}_0 - \\\\theta_0)/\\hat{\\sigma}$');\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If the nuisance models $\\hat{g}_0()$ and $\\hat{m}()$ are estimated on the whole dataset, which is also used for obtaining the final estimate $\\check{\\theta}_0$, another bias is observed.\n", "\n", "## Sample splitting to remove bias induced by overfitting\n", "\n", "Using sample splitting, i.e., estimate the nuisance models $\\hat{g}_0()$ and $\\hat{m}()$ on one part of the data (training data) and estimate $\\check{\\theta}_0$ on the other part of the data (test data), overcomes the bias induced by overfitting. We can exploit the benefits of cross-fitting by switching the role of the training and test sample. Cross-fitting performs well empirically because the entire sample can be used for estimation.\n", "\n", "The following figure shows the distribution of the resulting estimates $\\hat{\\theta}_0$ with orthogonal score and sample-splitting." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Replication 1000/1000\r" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "np.random.seed(3333)\n", "\n", "theta_dml = np.full(n_rep, np.nan)\n", "se_dml = np.full(n_rep, np.nan)\n", "\n", "for i_rep in range(n_rep):\n", " print(f'Replication {i_rep+1}/{n_rep}', end='\\r')\n", " (x, y, d) = data[i_rep]\n", " obj_dml_data = DoubleMLData.from_arrays(x, y, d)\n", " obj_dml_plr = DoubleMLPLR(obj_dml_data,\n", " ml_l, ml_m, ml_g,\n", " n_folds=2,\n", " score='IV-type')\n", " obj_dml_plr.fit()\n", " theta_dml[i_rep] = obj_dml_plr.coef[0]\n", " se_dml[i_rep] = obj_dml_plr.se[0]\n", "\n", "fig_dml, ax = plt.subplots(constrained_layout=True);\n", "ax = sns.histplot((theta_dml - alpha)/se_dml,\n", " color=face_colors[2], edgecolor = edge_colors[2],\n", " stat='density', bins=30, label='Double ML with cross-fitting');\n", "ax.axvline(0., color='k');\n", "xx = np.arange(-5, +5, 0.001)\n", "yy = stats.norm.pdf(xx)\n", "ax.plot(xx, yy, color='k', label='$\\\\mathcal{N}(0, 1)$');\n", "ax.legend(loc='upper right', bbox_to_anchor=(1.2, 1.0));\n", "ax.set_xlim([-6., 6.]);\n", "ax.set_xlabel('$(\\hat{\\\\theta}_0 - \\\\theta_0)/\\hat{\\sigma}$');\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Double/debiased machine learning\n", "\n", "To illustrate the benefits of the auxiliary prediction step in the DML framework we write the error as\n", "\n", "$$\n", "\\sqrt{n}(\\check{\\theta}_0 - \\theta_0) = a^* + b^* + c^*\n", "$$\n", "\n", "Chernozhukov et al. (2018) argues that:\n", "\n", "The first term\n", "\n", "$$\n", "a^* := (EV^2)^{-1} \\frac{1}{\\sqrt{n}} \\sum_{i\\in I} V_i \\zeta_i\n", "$$\n", "\n", "will be asymptotically normally distributed.\n", "\n", "The second term\n", "\n", "$$\n", "b^* := (EV^2)^{-1} \\frac{1}{\\sqrt{n}} \\sum_{i\\in I} (\\hat{m}(X_i) - m(X_i)) (\\hat{g}_0(X_i) - g_0(X_i))\n", "$$\n", "\n", "vanishes asymptotically for many data generating processes.\n", "\n", "The third term $c^*$ vanishes in probability if sample splitting is applied. Finally, let us compare all distributions." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "tags": [ "nbsphinx-thumbnail" ] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig_all, ax = plt.subplots(constrained_layout=True);\n", "ax = sns.histplot((theta_nonorth - alpha)/se_nonorth,\n", " color=face_colors[0], edgecolor = edge_colors[0],\n", " stat='density', bins=30, label='Non-orthogonal ML');\n", "sns.histplot((theta_orth_nosplit - alpha)/se_orth_nosplit,\n", " color=face_colors[1], edgecolor = edge_colors[1],\n", " stat='density', bins=30, label='Double ML (no sample splitting)');\n", "sns.histplot((theta_dml - alpha)/se_dml,\n", " color=face_colors[2], edgecolor = edge_colors[2],\n", " stat='density', bins=30, label='Double ML with cross-fitting');\n", "ax.axvline(0., color='k');\n", "xx = np.arange(-5, +5, 0.001)\n", "yy = stats.norm.pdf(xx)\n", "ax.plot(xx, yy, color='k', label='$\\\\mathcal{N}(0, 1)$');\n", "ax.legend(loc='upper right', bbox_to_anchor=(1.2, 1.0));\n", "ax.set_xlim([-6., 6.]);\n", "ax.set_xlabel('$(\\hat{\\\\theta}_0 - \\\\theta_0)/\\hat{\\sigma}$');\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Partialling out score\n", "\n", "Another debiased estimator, based on the partialling-out approach of Robinson(1988), is\n", "\n", "$$\n", "\\check{\\theta}_0 = \\left(\\frac{1}{n} \\sum_{i\\in I} \\hat{V}_i \\hat{V}_i \\right)^{-1} \\frac{1}{n} \\sum_{i\\in I} \\hat{V}_i (Y_i - \\hat{\\ell}_0(X_i)),\n", "$$\n", "\n", "with $\\ell_0(X_i) = E(Y|X)$.\n", "All nuisance parameters for the estimator with `score='partialling out'` are conditional mean functions, which can be directly estimated using ML methods. This is a minor advantage over the estimator with `score='IV-type'`.\n", "In the following, we repeat the above analysis with `score='partialling out'`. In a first part of the analysis, we estimate $\\theta_0$ without sample splitting. Again we observe a bias from overfitting.\n", "\n", "The following figure shows the distribution of the resulting estimates $\\hat{\\theta}_0$ without sample-splitting." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Replication 1000/1000\r" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "np.random.seed(4444)\n", "\n", "theta_orth_po_nosplit = np.full(n_rep, np.nan)\n", "se_orth_po_nosplit = np.full(n_rep, np.nan)\n", "\n", "for i_rep in range(n_rep):\n", " print(f'Replication {i_rep+1}/{n_rep}', end='\\r')\n", " (x, y, d) = data[i_rep]\n", "\n", " # fit the ML algorithms on the training sample\n", " ml_l.fit(x, y)\n", " ml_m.fit(x, d)\n", "\n", " l_hat = ml_l.predict(x)\n", " m_hat = ml_m.predict(x)\n", "\n", " external_predictions = {\n", " 'd': {\n", " 'ml_l': l_hat.reshape(-1, 1),\n", " 'ml_m': m_hat.reshape(-1, 1),\n", " }\n", " }\n", "\n", " obj_dml_plr_orth_nosplit = DoubleMLPLR(obj_dml_data,\n", " ml_l, ml_m,\n", " score='partialling out')\n", " obj_dml_plr_orth_nosplit.fit(external_predictions=external_predictions)\n", " theta_orth_po_nosplit[i_rep] = obj_dml_plr_orth_nosplit.coef[0]\n", " se_orth_po_nosplit[i_rep] = obj_dml_plr_orth_nosplit.se[0]\n", "\n", "fig_po_nosplit, ax = plt.subplots(constrained_layout=True);\n", "ax = sns.histplot((theta_orth_po_nosplit - alpha)/se_orth_po_nosplit,\n", " color=face_colors[1], edgecolor = edge_colors[1],\n", " stat='density', bins=30, label='Double ML (no sample splitting)');\n", "ax.axvline(0., color='k');\n", "xx = np.arange(-5, +5, 0.001)\n", "yy = stats.norm.pdf(xx)\n", "ax.plot(xx, yy, color='k', label='$\\\\mathcal{N}(0, 1)$');\n", "ax.legend(loc='upper right', bbox_to_anchor=(1.2, 1.0));\n", "ax.set_xlim([-6., 6.]);\n", "ax.set_xlabel('$(\\hat{\\\\theta}_0 - \\\\theta_0)/\\hat{\\sigma}$');\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using sample splitting, overcomes the bias induced by overfitting.\n", "Again, the implementation automatically applies cross-fitting." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Replication 1000/1000\r" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "np.random.seed(5555)\n", "\n", "theta_dml_po = np.full(n_rep, np.nan)\n", "se_dml_po = np.full(n_rep, np.nan)\n", "\n", "for i_rep in range(n_rep):\n", " print(f'Replication {i_rep+1}/{n_rep}', end='\\r')\n", " (x, y, d) = data[i_rep]\n", " obj_dml_data = DoubleMLData.from_arrays(x, y, d)\n", " obj_dml_plr = DoubleMLPLR(obj_dml_data,\n", " ml_l, ml_m,\n", " n_folds=2,\n", " score='partialling out')\n", " obj_dml_plr.fit()\n", " theta_dml_po[i_rep] = obj_dml_plr.coef[0]\n", " se_dml_po[i_rep] = obj_dml_plr.se[0]\n", " \n", "fig_po_dml, ax = plt.subplots(constrained_layout=True);\n", "ax = sns.histplot((theta_dml_po - alpha)/se_dml_po,\n", " color=face_colors[2], edgecolor = edge_colors[2],\n", " stat='density', bins=30, label='Double ML with cross-fitting');\n", "ax.axvline(0., color='k');\n", "xx = np.arange(-5, +5, 0.001)\n", "yy = stats.norm.pdf(xx)\n", "ax.plot(xx, yy, color='k', label='$\\\\mathcal{N}(0, 1)$');\n", "ax.legend(loc='upper right', bbox_to_anchor=(1.2, 1.0));\n", "ax.set_xlim([-6., 6.]);\n", "ax.set_xlabel('$(\\hat{\\\\theta}_0 - \\\\theta_0)/\\hat{\\sigma}$');\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, let us compare all distributions." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig_po_all, ax = plt.subplots(constrained_layout=True);\n", "ax = sns.histplot((theta_nonorth - alpha)/se_nonorth,\n", " color=face_colors[0], edgecolor = edge_colors[0],\n", " stat='density', bins=30, label='Non-orthogonal ML');\n", "sns.histplot((theta_orth_po_nosplit - alpha)/se_orth_po_nosplit,\n", " color=face_colors[1], edgecolor = edge_colors[1],\n", " stat='density', bins=30, label='Double ML (no sample splitting)');\n", "sns.histplot((theta_dml_po - alpha)/se_dml_po,\n", " color=face_colors[2], edgecolor = edge_colors[2],\n", " stat='density', bins=30, label='Double ML with cross-fitting');\n", "ax.axvline(0., color='k');\n", "xx = np.arange(-5, +5, 0.001)\n", "yy = stats.norm.pdf(xx)\n", "ax.plot(xx, yy, color='k', label='$\\\\mathcal{N}(0, 1)$');\n", "ax.legend(loc='upper right', bbox_to_anchor=(1.2, 1.0));\n", "ax.set_xlim([-6., 6.]);\n", "ax.set_xlabel('$(\\hat{\\\\theta}_0 - \\\\theta_0)/\\hat{\\sigma}$');\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "# save all figures\n", "fig_non_orth.savefig('../guide/figures/py_non_orthogonal.svg', dpi=300, bbox_inches='tight', format='svg')\n", "fig_orth_nosplit.savefig('../guide/figures/py_dml_nosplit.svg', dpi=300, bbox_inches='tight', format='svg')\n", "fig_dml.savefig('../guide/figures/py_dml.svg', dpi=300, bbox_inches='tight', format='svg')\n", "fig_all.savefig('../guide/figures/py_all.svg', dpi=300, bbox_inches='tight', format='svg')\n", "\n", "fig_po_nosplit.savefig('../guide/figures/py_dml_po_nosplit.svg', dpi=300, bbox_inches='tight', format='svg')\n", "fig_po_dml.savefig('../guide/figures/py_dml_po.svg', dpi=300, bbox_inches='tight', format='svg')\n", "fig_po_all.savefig('../guide/figures/py_po_all.svg', dpi=300, bbox_inches='tight', format='svg')" ] } ], "metadata": { "kernelspec": { "display_name": ".venv", "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": "3.12.3" } }, "nbformat": 4, "nbformat_minor": 2 }