Overview of Causal Forest and examples of application and implementation in R and Python

Causal Forest

Causal Forest is a machine learning model for estimating causal effects from observed data, which is based on Random Forest and extended based on the conditions required for causal inference.

Causal Forest uses two models to estimate causal effects in observed data: one, called the “intervention model,” divides the data into intervention and non-intervention variables, and the intervention model predicts the value of the non-intervention variable given the value of the intervention variable with the The objective is to predict the value of the non-intervention variable given the value of the intervention variable. The other, called the “counterfactual model,” is used to predict the causal effect of changing the value of the intervention variable.

Causal Forest is characterized by its strong predictive performance on unstable data through ensemble learning as described in “Overview of Ensemble Learning and Examples of Algorithms and Implementations”, similar to random forests, and is able to capture nonlinear causal relationships compared to traditional causal inference methods such as linear models. Furthermore, Causal Forest can automatically select intervention and non-intervention variables, which facilitates interpretation of causal relationships.

Algorithm used for Causal Forest

The basic idea of Causal Forest will be to combine ensemble learning of random forests with causal inference methods. The steps of the Causal Forest algorithm are described below.

• Construction of a random forest: Similar to a random forest, multiple decision trees are constructed. Each decision tree is trained using pairs of input variables (features) and output variables (objective variables for estimating causal effects).
• Estimation of causal effects: In each decision tree, causal effects are considered as a criterion for segmentation. Specifically, conditions that maximize the causal effect are introduced at the time of splitting, thereby constructing a decision tree that focuses on the estimation of the causal effect. Two additional features are added for this causal effect estimation: one is node-level causal inference to reduce bias by randomizing feature sampling, and the other is branch level causal inference.
• Bagging: Similar to random forests, multiple decision trees are constructed using bootstrap sampling. However, in causal forests, the output variable (causal effect) is randomly permuted in the training data set of each decision tree. This improves the unbiasedness of the causal effect estimation.
• Ensemble averaging: averaging is performed to combine the results of each decision tree. In causal forests, the causal effect estimates from individual decision trees are averaged to obtain a final estimate of the causal effect.

Causal forests have attracted attention as a method that has the properties of random forests but can also be applied to the estimation of causal effects, making it particularly useful in problems such as clarifying causal relationships and evaluating intervention effects.

Libraries and platforms that can be used for Causal Forest

There are libraries and platforms available to implement Causal Forest. The following is a list of some of the most common ones.

• R packages: The R language is widely used for statistical analysis and machine learning analysis, and related packages are available for Causal Forest. For example, the grf package (Generalized Random Forest) provides tools to implement causal forests, including estimation of causal effects and visualization of results.
• Python libraries: Python is also widely used in data science and machine learning, and several libraries are available for implementing Causal Forest. For example, EconML provides a Causal Forest implementation for Python. The library DoWhy also provides tools and algorithms related to causal inference that can use some of the features of Causal Forest.
• Microsoft documentation: Microsoft Research is actively researching and developing causal forests and provides detailed documentation and implementation guidelines for Causal Forest. Microsoft documentation covers everything from basic principles to application examples of Causal Forest, making it a useful resource for researchers and developers.

Application of Causal Forest

The following are examples of applications of Causal Forest

• Marketing: It is used to measure the effectiveness of advertising campaigns and analyze the causal effects of product pricing, for example, to causally evaluate the effectiveness of specific marketing measures using data such as customer attributes and behavioral history.
• Economics: Used to estimate various causal effects, such as the effects of policies and business strategies, to evaluate economic policies, and to correct for biases.
• Medical care: Used to evaluate the effects of specific treatments and drugs, and to conduct causal analysis of individual differences in these effects.
• Policy making: used to evaluate policies and estimate the causal effects of those policies on specific groups (e.g., to assess the impact of a particular policy on economic indicators such as labor markets and education).
• Text Mining: allows causal estimation of the relationship between textual content and behavior or opinion. This is used, for example, to estimate the impact of a particular advertising phrase on customer purchasing behavior. It can also be used to evaluate whether factors such as text content, grammatical features, and contextual information contribute to causal estimation, to extract important features, and to extract causal factors such as product features and emotional expressions from the text when estimating causal effects for a particular product review, and to estimate causal relationships. It can also be used for this purpose. In addition, textual data and other information (e.g., user attributes, contextual information) can be combined to estimate causal effects in order to correct for bias.

Causal Forest is used when randomized experiments are difficult to perform or to validate the results of randomized experiments, and is particularly effective for big data and for data sets with a large number of features.

Example Implementation of Causal Forest in R

Here we describe an example implementation of Causal Forest using the R package grf. grf is an implementation of Causal Forest based on Random Forest, which is very fast and can handle large data sets. The following is an example of a simple Causal Forest implementation.

# Load the necessary libraries
library(grf)

# Read data
data("lalonde")

# Create an estimation model
cf <- causal_forest(lalonde$X, lalonde$Y, lalonde$T)

# Estimating causal effects
tau <- predict(cf, lalonde$X)

In this example, the lalonde dataset is used; the causal_forest() function is used to create a Causal Forest model, and the predict() function is used to estimate causal effects.

Causal Forest may require more advanced modeling, and the grf package provides a number of options. They can, for example, run Causal Forest for classification or dual treatment problems, or perform variable selection, interaction detection, quantile regression, etc.

About an example implementation of Causal Forest in Python

EconML (Economic Machine Learning) will be a library to support the application of machine learning in causal estimation and economic problems. Below is an example of implementing Causal Forest using EconML. First, install the EconML library.

pip install econml

Next, the following code implements EconML’s Causal Forest.

import numpy as np
from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split
from econml.dml import CausalForestDML

# Dummy data generation
X, y, treatment = make_regression(n_samples=1000, n_features=5, n_informative=3, treatment_effect=2.0, random_state=42)

# Data Division
X_train, X_test, y_train, y_test, treat_train, treat_test = train_test_split(X, y, treatment, test_size=0.2, random_state=42)

# Causal Forest Model Building and Learning
causal_forest = CausalForestDML(model_y=RandomForestRegressor(), model_t=RandomForestRegressor())
causal_forest.fit(Y=y_train, T=treat_train, X=X_train)

# Indication of estimated causal effects
effect = causal_forest.effect(X_test)
print("Causal effect:", effect)

In the above code, the make_regression function is used to generate dummy data, where Y is the objective variable, T is the intervention variable (treatment), and X is the feature. The Causal Forest model is then constructed using the CausalForestDML class, and the fit method is used to train the model on the data. model_y and model_t are the models used to estimate causal effects. In the above example, RandomForestRegressor is used to perform the regression task, but an appropriate model should be selected. Finally, the effect method is used to estimate the causal effects of the test data.

Example Python implementation for causal estimation and feature evaluation of text data using Causal Forest

In order to estimate causal relationships and evaluate features of text data using Causal Forest, it is necessary to convert text data into an appropriate format and apply appropriate methods for estimating causal relationships and evaluating features. Below is an example of a Python implementation for causal estimation and feature evaluation of text data using Causal Forest.

First, for causal estimation, it is necessary to apply text data to a causal model. Below is an example of a method for applying text data to a causal model.

import numpy as np
from sklearn.feature_extraction.text import CountVectorizer
from causallib.estimation import CausalForest

# Preparation of text data
texts = ["This is the first document.",
         "This document is the second document.",
         "And this is the third one.",
         "Is this the first document?"]
labels = [0, 1, 1, 0]  # 0: group A, 1: group B

# Vectorize text data
vectorizer = CountVectorizer()
X = vectorizer.fit_transform(texts).toarray()

# Causal Forest Model Building and Estimation
causal_forest = CausalForest()
causal_forest.estimate_ATE(X, labels)

# Display results of causal effect estimation
ate_estimate = causal_forest.ate_estimate_
ate_lower_bound = causal_forest.ate_lower_bound_
ate_upper_bound = causal_forest.ate_upper_bound_
print("ATE estimate:", ate_estimate)
print("ATE lower bound:", ate_lower_bound)
print("ATE upper bound:", ate_upper_bound)

The above code uses CountVectorizer to vectorize text data. This converts the text data into the form of numeric vectors. The CausalForest class is used to construct a Causal Forest model, and the estimate_ATE method is used to estimate causal effects, where X is the vectorized text data and labels are labels indicating groups of causal relationships.

The results of the causal effect estimation can be obtained as ate_estimate, ate_lower_bound, and ate_upper_bound. ate_estimate indicates the estimated value of the causal effect, and ate_lower_bound and ate_upper_bound indicate the lower and upper confidence intervals of the causal effect. lower and upper bounds of the confidence interval of the causal effect.

Next, we will discuss the evaluation of the features; to evaluate the features using Causal Forest, it is necessary to obtain the importance of the features and the estimation results of the causal effect. Below is an example for feature evaluation.

# Assessing the importance of features
feature_importances = causal_forest.feature_importances_
print("Feature importances:", feature_importances)

In the above code, feature_importances_ is used to obtain the importance of the features. This gives the importance of each feature.

Reference Information and Reference Books

For details on causal inference and causal search, see “Overview and Implementation of Causal Inference and Causal Search Techniques” and “Statistical Causal Inference and Causal Search. For more information on random forests, see “Decision Tree Algorithm (1)” and “Overview of LightBGM and its implementation in various languages.

Also on the web, there is information such as “Machine Learning Goes Causal II: Meet the Random “、”Causal tree v. causal forest – when to use which for HTE?“ etc.