{ "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": 5, "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.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": 6, "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": 7, "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": 8, "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": 9, "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(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": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Replication 1000/1000\r" ] }, { "data": { "image/png": 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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": 12, "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": 13, "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": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "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": 15, "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": "dml_dev", "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": "3.12.4" } }, "nbformat": 4, "nbformat_minor": 2 }