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Escape backslashes in notebook LaTeX #956

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2 changes: 1 addition & 1 deletion ...rios/Case Study - Customer Segmentation at An Online Media Company - EconML + DoWhy.ipynb
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Expand Up @@ -123,7 +123,7 @@
"\n",
"\\begin{align}\n",
"\\gamma(X) & = -3 - 14 \\cdot \\{\\text{income}<1\\} \\\\\n",
"\\beta(X,W) & = 20 + 0.5 \\cdot \\text{avg_hours} + 5 \\cdot \\{\\text{days_visited}>4\\} \\\\\n",
"\\beta(X,W) & = 20 + 0.5 \\cdot \\text{avg\\_hours} + 5 \\cdot \\{\\text{days\\_visited}>4\\} \\\\\n",
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Maybe one more backslash than necessary?

image

"Y &= \\gamma(X) \\cdot T + \\beta(X,W)\n",
"\\end{align}\n",
"\n"
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2 changes: 1 addition & 1 deletion ...oks/CustomerScenarios/Case Study - Customer Segmentation at An Online Media Company.ipynb
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Expand Up @@ -109,7 +109,7 @@
"\n",
"\\begin{align}\n",
"\\gamma(X) & = -3 - 14 \\cdot \\{\\text{income}<1\\} \\\\\n",
"\\beta(X,W) & = 20 + 0.5 \\cdot \\text{avg_hours} + 5 \\cdot \\{\\text{days_visited}>4\\} \\\\\n",
"\\beta(X,W) & = 20 + 0.5 \\cdot \\text{avg\\_hours} + 5 \\cdot \\{\\text{days\\_visited}>4\\} \\\\\n",
"Y &= \\gamma(X) \\cdot T + \\beta(X,W)\n",
"\\end{align}\n",
"\n"
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2 changes: 1 addition & 1 deletion ...s/CustomerScenarios/Case Study - Multi-investment Attribution at A Software Company.ipynb
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Expand Up @@ -363,7 +363,7 @@
"The data was generated using the following underlying treatment effect function:\n",
"\n",
"$$\n",
"\\text{treatment_effect(Size)} = (5,000 + 2\\% \\cdot \\text{Size}) \\cdot I_\\text{Tech Support} + (5\\% \\cdot \\text{Size}) \\cdot I_\\text{Discount}\n",
"\\text{treatment\\_effect(Size)} = (5,000 + 2\\% \\cdot \\text{Size}) \\cdot I_\\text{Tech Support} + (5\\% \\cdot \\text{Size}) \\cdot I_\\text{Discount}\n",
"$$\n",
"\n",
"Therefore, the treatment effect depends on the customer's size as follows: tech support provides an consumption boost of \\$5,000 + 2\\% Size and a discount provides an consumption boost of 5\\% Size.**This is the relationship we seek to learn from the data.**"
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106 changes: 53 additions & 53 deletions ...ustomerScenarios/Case Study - Recommendation AB Testing at An Online Travel Company.ipynb
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Expand Up @@ -70,21 +70,21 @@
},
"outputs": [],
"source": [
"# Some imports to get us started\r\n",
"# Utilities\r\n",
"import numpy as np\r\n",
"import pandas as pd\r\n",
"\r\n",
"# Generic ML imports\r\n",
"import lightgbm as lgb\r\n",
"from sklearn.preprocessing import PolynomialFeatures\r\n",
"\r\n",
"# EconML imports\r\n",
"from econml.iv.dr import LinearIntentToTreatDRIV\r\n",
"from econml.cate_interpreter import SingleTreeCateInterpreter, \\\r\n",
" SingleTreePolicyInterpreter\r\n",
"\r\n",
"import matplotlib.pyplot as plt\r\n",
"# Some imports to get us started\n",
"# Utilities\n",
"import numpy as np\n",
"import pandas as pd\n",
"\n",
"# Generic ML imports\n",
"import lightgbm as lgb\n",
"from sklearn.preprocessing import PolynomialFeatures\n",
"\n",
"# EconML imports\n",
"from econml.iv.dr import LinearIntentToTreatDRIV\n",
"from econml.cate_interpreter import SingleTreeCateInterpreter, \\\n",
" SingleTreePolicyInterpreter\n",
"\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline"
]
},
Expand Down Expand Up @@ -335,7 +335,7 @@
"The data was generated using the following undelying treatment effect function:\n",
"\n",
"$$\n",
"\\text{treatment_effect} = 0.2 + 0.3 \\cdot \\text{days_visited_free_pre} - 0.2 \\cdot \\text{days_visited_hs_pre} + \\text{os_type_osx}\n",
"\\text{treatment\\_effect} = 0.2 + 0.3 \\cdot \\text{days\\_visited\\_free\\_pre} - 0.2 \\cdot \\text{days\\_visited\\_hs\\_pre} + \\text{os\\_type\\_osx}\n",
"$$\n",
"\n",
"The interpretation of this is that users who visited the website before the experiment and/or who use an iPhone tend to benefit from the membership program, whereas users who visited the hotels pages tend to be harmed by membership. **This is the relationship we seek to learn from the data.**"
Expand All @@ -352,7 +352,7 @@
"outputs": [],
"source": [
"# Define underlying treatment effect function\n",
"def TE_fn(X):\r\n",
"def TE_fn(X):\n",
" return (0.2 + 0.3 * X[\"days_visited_free_pre\"] - 0.2 * X[\"days_visited_hs_pre\"] + X[\"os_type_osx\"]).values\n",
"true_TE = TE_fn(X_data)\n",
"\n",
Expand Down Expand Up @@ -386,23 +386,23 @@
},
"outputs": [],
"source": [
"# Define nuissance estimators\r\n",
"lgb_T_XZ_params = {\r\n",
" 'objective' : 'binary',\r\n",
" 'metric' : 'auc',\r\n",
" 'learning_rate': 0.1,\r\n",
" 'num_leaves' : 30,\r\n",
" 'max_depth' : 5\r\n",
"}\r\n",
"\r\n",
"lgb_Y_X_params = {\r\n",
" 'metric' : 'rmse',\r\n",
" 'learning_rate': 0.1,\r\n",
" 'num_leaves' : 30,\r\n",
" 'max_depth' : 5\r\n",
"}\r\n",
"model_T_XZ = lgb.LGBMClassifier(**lgb_T_XZ_params)\r\n",
"model_Y_X = lgb.LGBMRegressor(**lgb_Y_X_params)\r\n",
"# Define nuissance estimators\n",
"lgb_T_XZ_params = {\n",
" 'objective' : 'binary',\n",
" 'metric' : 'auc',\n",
" 'learning_rate': 0.1,\n",
" 'num_leaves' : 30,\n",
" 'max_depth' : 5\n",
"}\n",
"\n",
"lgb_Y_X_params = {\n",
" 'metric' : 'rmse',\n",
" 'learning_rate': 0.1,\n",
" 'num_leaves' : 30,\n",
" 'max_depth' : 5\n",
"}\n",
"model_T_XZ = lgb.LGBMClassifier(**lgb_T_XZ_params)\n",
"model_Y_X = lgb.LGBMRegressor(**lgb_Y_X_params)\n",
"flexible_model_effect = lgb.LGBMRegressor(**lgb_Y_X_params)"
]
},
Expand All @@ -427,13 +427,13 @@
}
],
"source": [
"# Train EconML model\r\n",
"model = LinearIntentToTreatDRIV(\r\n",
" model_y_xw = model_Y_X,\r\n",
" model_t_xwz = model_T_XZ,\r\n",
" flexible_model_effect = flexible_model_effect,\r\n",
" featurizer = PolynomialFeatures(degree=1, include_bias=False)\r\n",
")\r\n",
"# Train EconML model\n",
"model = LinearIntentToTreatDRIV(\n",
" model_y_xw = model_Y_X,\n",
" model_t_xwz = model_T_XZ,\n",
" flexible_model_effect = flexible_model_effect,\n",
" featurizer = PolynomialFeatures(degree=1, include_bias=False)\n",
")\n",
"model.fit(Y, T, Z=Z, X=X_data, inference=\"statsmodels\")"
]
},
Expand All @@ -447,11 +447,11 @@
},
"outputs": [],
"source": [
"# Compare learned coefficients with true model coefficients\r\n",
"coef_indices = np.arange(model.coef_.shape[0])\r\n",
"# Calculate error bars\r\n",
"coef_error = np.asarray(model.coef__interval()) # 95% confidence interval for coefficients\r\n",
"coef_error[0, :] = model.coef_ - coef_error[0, :]\r\n",
"# Compare learned coefficients with true model coefficients\n",
"coef_indices = np.arange(model.coef_.shape[0])\n",
"# Calculate error bars\n",
"coef_error = np.asarray(model.coef__interval()) # 95% confidence interval for coefficients\n",
"coef_error[0, :] = model.coef_ - coef_error[0, :]\n",
"coef_error[1, :] = coef_error[1, :] - model.coef_"
]
},
Expand All @@ -478,10 +478,10 @@
}
],
"source": [
"plt.errorbar(coef_indices, model.coef_, coef_error, fmt=\"o\", label=\"Learned coefficients\\nand 95% confidence interval\")\r\n",
"plt.scatter(coef_indices, true_coefs, color='C1', label=\"True coefficients\")\r\n",
"plt.xticks(coef_indices, X_data.columns, rotation='vertical')\r\n",
"plt.legend()\r\n",
"plt.errorbar(coef_indices, model.coef_, coef_error, fmt=\"o\", label=\"Learned coefficients\\nand 95% confidence interval\")\n",
"plt.scatter(coef_indices, true_coefs, color='C1', label=\"True coefficients\")\n",
"plt.xticks(coef_indices, X_data.columns, rotation='vertical')\n",
"plt.legend()\n",
"plt.show()"
]
},
Expand Down Expand Up @@ -607,8 +607,8 @@
},
"outputs": [],
"source": [
"test_customers = X_data.iloc[:1000]\r\n",
"true_customer_TE = TE_fn(test_customers)\r\n",
"test_customers = X_data.iloc[:1000]\n",
"true_customer_TE = TE_fn(test_customers)\n",
"model_customer_TE = model.effect(test_customers)"
]
},
Expand Down Expand Up @@ -772,4 +772,4 @@
},
"nbformat": 4,
"nbformat_minor": 2
}
}