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@akelleh
Created January 25, 2019 03:28
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"from dowhy.do_why import CausalModel\n",
"import dowhy.datasets\n",
"import dowhy.api.causal_data_frame\n",
"import pandas as pd"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"data = dowhy.datasets.linear_dataset(beta=10,\n",
" num_common_causes=5,\n",
" num_instruments = 2,\n",
" num_samples=1000,\n",
" treatment_is_binary=True)\n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"INFO:root:Using backdoor.linear_regression for estimation.\n",
"INFO:dowhy.causal_identifier:Common causes of treatment and outcome:{'X4', 'X2', 'X0', 'X3', 'Z1', 'U', 'Z0', 'X1'}\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Error: Pygraphviz cannot be loaded. No module named 'pygraphviz'\n",
"Trying pydot ...\n",
"['X4', 'X2', 'X0', 'X3', 'Z1', 'U', 'Z0', 'X1']\n",
"yes\n",
"{'observed': 'yes'}\n",
"yes\n",
"{'observed': 'yes'}\n",
"yes\n",
"{'observed': 'yes'}\n",
"yes\n",
"{'observed': 'yes'}\n",
"yes\n",
"{'observed': 'yes'}\n",
"no\n",
"{'label': '\"Unobserved Confounders\"', 'observed': 'no'}\n",
"yes\n",
"{'observed': 'yes'}\n",
"yes\n",
"{'observed': 'yes'}\n",
"Model to find the causal effect of treatment v on outcome y\n",
"{'observed': 'yes'}\n",
"{'observed': 'yes'}\n",
"{'observed': 'yes'}\n",
"{'observed': 'yes'}\n",
"{'observed': 'yes'}\n",
"{'label': '\"Unobserved Confounders\"', 'observed': 'no'}\n",
"There are unobserved common causes. Causal effect cannot be identified.\n",
"WARN: Do you want to continue by ignoring these unobserved confounders? [y/n] yes\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"INFO:dowhy.causal_identifier:Instrumental variables for treatment and outcome:['Z0', 'Z1']\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"LinearRegressionEstimator\n",
"LinearRegressionEstimator\n",
"LinearRegressionEstimator\n",
"LinearRegressionEstimator\n",
"LinearRegressionEstimator\n",
"LinearRegressionEstimator\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"LinearRegressionEstimator\n",
"LinearRegressionEstimator\n",
"LinearRegressionEstimator\n",
"LinearRegressionEstimator\n",
"LinearRegressionEstimator\n",
"LinearRegressionEstimator\n",
"LinearRegressionEstimator\n",
"LinearRegressionEstimator\n",
"LinearRegressionEstimator\n",
"LinearRegressionEstimator\n",
"LinearRegressionEstimator\n",
"LinearRegressionEstimator\n",
"LinearRegressionEstimator\n",
"LinearRegressionEstimator\n",
"LinearRegressionEstimator\n",
"LinearRegressionEstimator\n",
"LinearRegressionEstimator\n",
"LinearRegressionEstimator\n",
"LinearRegressionEstimator\n",
"LinearRegressionEstimator\n",
"LinearRegressionEstimator\n",
"LinearRegressionEstimator\n",
"LinearRegressionEstimator\n",
"LinearRegressionEstimator\n",
"LinearRegressionEstimator\n",
"LinearRegressionEstimator\n",
"LinearRegressionEstimator\n",
"LinearRegressionEstimator\n",
"LinearRegressionEstimator\n",
"LinearRegressionEstimator\n",
"LinearRegressionEstimator\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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]
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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]
},
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"text": [
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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"LinearRegressionEstimator\n",
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"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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]
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"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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]
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"LinearRegressionEstimator\n",
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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]
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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]
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"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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]
},
{
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"text": [
"LinearRegressionEstimator\n",
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"text": [
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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]
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"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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]
},
{
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"text": [
"LinearRegressionEstimator\n",
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"text": [
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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"LinearRegressionEstimator\n",
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"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
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]
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n"
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"LinearRegressionEstimator\n",
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"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
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"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
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"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"data['df'].causal.plot(x='v', y='y', dot_graph=data['dot_graph'], kind='bar')"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"data['df'].causal.mean(x='v', y='y', common_causes=['X0', 'X1', 'X2', 'X3', 'X4'])"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"INFO:dowhy.causal_identifier:Common causes of treatment and outcome:{'X4', 'X2', 'X0', 'X3', 'Z1', 'U', 'Z0', 'X1'}\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Error: Pygraphviz cannot be loaded. No module named 'pygraphviz'\n",
"Trying pydot ...\n",
"['X4', 'X2', 'X0', 'X3', 'Z1', 'U', 'Z0', 'X1']\n",
"yes\n",
"{'observed': 'yes'}\n",
"yes\n",
"{'observed': 'yes'}\n",
"yes\n",
"{'observed': 'yes'}\n",
"yes\n",
"{'observed': 'yes'}\n",
"yes\n",
"{'observed': 'yes'}\n",
"no\n",
"{'label': '\"Unobserved Confounders\"', 'observed': 'no'}\n",
"yes\n",
"{'observed': 'yes'}\n",
"yes\n",
"{'observed': 'yes'}\n",
"Model to find the causal effect of treatment v on outcome y\n",
"{'observed': 'yes'}\n",
"{'observed': 'yes'}\n",
"{'observed': 'yes'}\n",
"{'observed': 'yes'}\n",
"{'observed': 'yes'}\n",
"{'label': '\"Unobserved Confounders\"', 'observed': 'no'}\n",
"There are unobserved common causes. Causal effect cannot be identified.\n",
"WARN: Do you want to continue by ignoring these unobserved confounders? [y/n] yes\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"INFO:dowhy.causal_identifier:Instrumental variables for treatment and outcome:['Z0', 'Z1']\n"
]
}
],
"source": [
"model= CausalModel(\n",
" data=data[\"df\"],\n",
" treatment=data[\"treatment_name\"],\n",
" outcome=data[\"outcome_name\"],\n",
" graph=data[\"dot_graph\"])\n",
"\n",
"identified_estimand = model.identify_effect()\n"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n",
"INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
"INFO:dowhy.causal_estimator:b: y~v+X4+X2+X0+X3+Z1+Z0+X1\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"LinearRegressionEstimator\n",
"LinearRegressionEstimator\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAANMAAAASCAYAAADBs+vIAAAABHNCSVQICAgIfAhkiAAAAulJREFUaIHt2s+r1UUYx/GXP66JhEIUiAhabVQMbFEh5EpskQjaKnAXCoILcRH6F0glSCIiVgsRoqWKQYooulGKVChzJZYIoiamVHgV67SYuXDuvXO9nTnnDiPMZzOHZ+b9PJ+BM8z3O/OlqalpSjQNm/E9/sLf+BFbMH2Kc+XULsHU6qvNpYyvEa3GEdzGY9zCSbw/EfA1OriDL7EXV2Ps8CTF+s2VU7sEU6uvNpcyvuCzOOYmvsCuyF+KfeO0IQLX8XJXfBaOx74PnlGwn1w5tUswtfpqcynji7CTdXAojh2roUTM4QhtTfStiH1nUuAAcuXULsHU6iuHqdVXDlPK1wu4ixvSC2mUZnb9nh/b64lxI7FVMemTSfL2miundgmmVl85TK2+cphSvtbgFXyOf7EWyzGMH3ChO0n3S9e92L6aKPZabGd2/X6Wes2VU7sEU6uvHKZWXzlMKV9vxXYYl/EtPhEW13mcExbbOG0UtrpreKkrPoRjsa+DlSm4z1w5tUswtfpqcynj60CMPcVPeBcv4g3hJK+DsxKagRNxwG0cFE47fsF94bmxg3dScJ+5cmqXYGr11eZSxtfBGBvGYqM1Rzjdm3CDGcIO/BwTPMBRLMGVCKa2yUHkyqldgqnVV5vL1Nf4NMYuSOur2L9tgv6kZgsXVb/3Ag0oV07tEkytvnKYWn3lMIOs8ZGwWL6bgNsd+3fy/79q+FA45fimB4ODypVTuwRTq68cplZfOcwga5wWFssy6bWyPLa/ppLOTcRWCCv2PhaM6Xtd2CJTF1e95up1fCmmVl85TK2+cphSvkYOJ7aPib8nHJf/gXmMvmeCU3gkPD/+iaXC2fojrBO+R+rWaSwSnjN/6zNXr+NLMbX6anMp42sr3sSeOPay8H9fj3+wCQ8TnI9xUXgxeyxcZu3HwtRgYQF1jD/pyMnV6/hSTK2+2lzK+CLcJe0TTvyeCHdWR/D2JFxTU1NTU1NTU9Pzr/8Aci+mxNAQYGYAAAAASUVORK5CYII=\n",
"text/latex": [
"$$9.999999999999996$$"
],
"text/plain": [
"9.999999999999996"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"model.do(1., \n",
" identified_estimand=identified_estimand,\n",
" method_name=\"backdoor.linear_regression\") - \\\n",
"model.do(0., \n",
" identified_estimand=identified_estimand,\n",
" method_name=\"backdoor.linear_regression\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"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": "3.6.7"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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