Overview and implementation of causal inference and causal search techniques

Overview of Causal Inference and Causal Search

The following is an overview of causal inference and causal search.

<Causal Inference>

Causal inference is a methodology for inferring whether an event or phenomenon is a cause of another event or phenomenon. This methodology can be used in various fields, such as the social sciences and medicine, to identify causal relationships, to evaluate the effects of specific interventions or policies, and to better understand phenomena. Specific examples of causal inference include comparing an intervention group with a control group to evaluate the effect of a particular drug, or comparing pre- and post-intervention data to evaluate the effect of a policy.

Causal inference involves statistical methods for inferring causal relationships from observed data. In general, it is difficult to infer causal relationships from observed data, so it is necessary to construct hypotheses or models to clarify causal relationships.

One of the basic methods of causal inference is the randomized controlled trial (RCT), in which causal relationships are assessed by random assignment to intervention and non-intervention groups. The randomization will be such that the effect of the intervention can be isolated from other factors.

It is difficult to infer all circumstances in this RCT, and methods have therefore been developed to infer causality using observational data. These include, for example, natural experiments and propensity score matching, which take approaches that take other covariates (factors associated with the intervention) into account to reduce bias between groups that received the intervention and those that did not.

Because these causal inferences do not always yield reliable results, and because there can be a variety of biases and confounding factors in observational data, it is important to understand and carefully analyze the methods and limitations of causal inferences when interpreting results.

<Causal Search>

Causal exploration is the process of analyzing data to identify causal relationships and to search for potential causal candidates. Causal exploration is a method used for a variety of purposes, and is an approach that can be applied not only to scientific inquiry, such as discovering new causal relationships, testing theories, and improving predictive models, but also to real-world issues such as business analysis and policy making.

Causal searches may be based on known theories or hypotheses, but they are often data-driven approaches. They are conducted with observational data and take the approach of collecting data from existing data sets or databases and applying statistical methods or machine learning algorithms to help in the search for causal relationships.

One approach to causal search is causal graphical models. In graphical models, causal relationships are represented by nodes (nodes represent variables) and edges (edges represent causal relationships among variables), and by constructing graphical models, causal relationships among variables are visualized and potential causal relationships are identified.

In causal search, it is also important to consider covariates and confounding factors to explain causal results, and appropriate control of covariates and confounding factors can also improve the reliability of identifying and interpreting causal relationships.

However, causal search is a process based on speculation and hypothesis and does not establish the truth of causal relationships. Therefore, caution is required in identifying and interpreting causal relationships, causal search has various restrictions and limitations, and care must be taken in interpreting the results.

Application Examples of Causal Inference and Causal Search

<Cases of Application of Causal Inference>

The following are some specific applications of causal inference.

• Medical: Causal inference is used to evaluate the effectiveness of medical treatments and therapies. Specifically, causal inference is used in randomized experiments or observational studies to evaluate whether a particular treatment is effective in treating a particular disease.
• Education Policy: Causal inference is also important in the evaluation and improvement of education policy. Causal inference methods such as randomized experiments and quotient designs are used to evaluate the effects of the introduction of specific educational programs or policies on learning outcomes and student performance.
• Social Policy: Causal inference is applied in the evaluation and impact analysis of social policies. Examples include the use of causal inference methods such as difference-in-differences and instrumental variables methods to assess the impact of the introduction of minimum wage policies on employment and labor markets.
• Economics: In the field of economics, causal inference is important in policy evaluation and market analysis. In particular, causal inference is used in natural experiments and statistical methods to evaluate the impact of specific economic policies on economic growth and employment.
• Environmental Science: Causal inference is used in the evaluation of environmental policies and sustainability. Specifically, causal inference methods are used to assess the impact of specific environmental policies on air pollution and climate change.
• Business Analysis: Causal reasoning is also important in business areas such as marketing and advertising. Specifically, matching and causal search methods are used to evaluate the effectiveness of specific marketing campaigns and advertisements.

The following are some specific examples of causal search applications.

<Case Studies of Causality>

• Biology: In the field of biology, causal search is used to explore causal relationships in gene interactions and the developmental processes of organisms. This can help in the construction of gene networks and the elucidation of complex biological processes.
• Ecology: Causal search is also important in the study of ecological interactions and biodiversity. Specifically, causal search is needed to understand how interactions among organisms and environmental factors affect the structure and function of ecosystems.
• Marketing/Advertising: In the field of marketing and advertising, causal search is used to elucidate the effects of specific advertisements and marketing campaigns on customer behavior. These can help improve the effectiveness of advertising and marketing strategies.
• Social Media/Online Platforms: Social media and online platform operators are exploring causal relationships regarding user behavior and participation patterns. This unravels the factors that influence user engagement and decision making to improve services and operate more effectively.
• Transportation/Urban Planning: In the area of transportation and urban planning, causal search is used to elucidate the factors that cause traffic accidents and the impact of urban development. This helps to improve transportation policies and urban planning.
• Economics/Finance: In the field of economics and finance, causality searches are conducted on economic indicators and financial market trends. This helps to evaluate policies and assess the effectiveness of investments.

Elucidating these causal relationships enables more effective decision-making and policy-making.

The algorithms used for them are described next.

Algorithms used for causal inference and causal search

<Algorithms used for causal inference>

Various algorithms and methods are used for causal inference. Some of the most common are described below.

• Randomized controlled trials (RCTs): RCTs draw causal inferences by comparing the effects of randomized interventions to non-intervention groups; RCTs are widely recognized as the “gold standard” for establishing causal relationships.
• Matching methods: Matching methods reduce covariate bias and infer causality by matching intervention and non-intervention groups based on observed data. A typical method is propensity score matching.
• Difference-in-differences (DID): The difference-in-differences method estimates causal effects by comparing differences between intervention and non-intervention groups before and after an intervention. This method takes the approach of simultaneously collecting data for the intervention and non-intervention groups to isolate the intervention-induced change from other factors.
• Propensity score regression: Propensity score regression is a technique that builds a regression model to predict the probability of an intervention (propensity score) and uses the propensity score as a control variable. This method is used to estimate causal relationships between intervention and non-intervention groups.
• Instrumental variables (IV): The instrumental variables method uses unobserved latent causal factors (instrumental variables) to estimate causal relationships. Instrumental variables here are factors that influence the intervention but do not directly affect the outcome.
• Causal inference using machine learning: Causal Forest approach based on Random Forests as described in “Overview and Examples of Causal Forest and its Implementation in R and Python” and Meta-Learners (T-Learners, S-Learners, X-Learners) using Meta-Learners described in “Overview of causal inference using Meta-Learners and examples of algorithms and implementations“, which can also be used for Few-shot/Zero-shot Learning as described in “Overview and Example Implementation of Meta-Learners“,‘Doubly Robust Learners (Doubly Robust Learners), also described in ‘Overview of Doubly Robust Learners (Doubly Robust Learners), application examples and python implementation examples’.

Next, we discuss the algorithms used in causal search.

<Algorithms for Causal Search>

Algorithms for causal search are data-driven approaches that are useful for identifying and searching for causal relationships. Typical algorithms are described below.

• Causal Graphical Models: Causal Graphical Models use a graph structure to represent causal relationships between variables. In this approach, nodes on the graph represent variables and edges indicate causal relationships.
• Bayesian Networks: Bayesian networks are an approach that uses graph structures to model probabilistic relationships. They are also used to represent causal relationships and utilize Bayes’ theorem and conditional independence to infer causal relationships.
• Causal Structure Learning: Causal Structure Learning is a method for learning the graph structure of causal relationships from data. This approach allows the identification of causal relationships and the testing of hypotheses by estimating the structure of a causal graph model or Bayesian network from given data.
• Causal Discovery Algorithms: Causal Discovery Algorithms is a generic term for algorithms to search for causal relationships from data. They are mainly used to estimate causal graph structures and Bayesian networks. Typical algorithms include the PC algorithm, the GES algorithm, and the FGS algorithm.
• LiNGAM (Linear Non-Gaussian Acyclic Models): LiNGAM is a statistical method used for causal estimation and causal modeling. LiNGAM is able to estimate causal relationships among multiple variables and assumes that the data follow a non-Gaussian distribution, making it possible to identify causal relationships among variables that are not Gaussian.
• Causal search using deep learning: There are causal search model approaches that use deep learning to learn the relationship between input and output variables, generative model approaches that generate data considering causal relationships, and causal domain application approaches, and others.
• Causal search using GAN (Generative Adversarial Network): Although GAN described in “Overview of GANs and their various applications and implementations” itself is not a direct method for causal search, research is being conducted to estimate causal relationships and generate causal data by extending and transforming GAN in consideration of causal structure. See detail in “Causal search using GAN (Generative Adversarial Network)“
• Structural Agnostic Model: A statistical method used for causality estimation, which attempts to identify causal relationships by analyzing statistical dependencies and conditional distributions of data. to infer causal relationships based solely on the statistical properties of the data. See “Overview of the Structural Agnostic Model (SAM) and examples of algorithms and implementation” in detail.

The following sections describe examples of the application of causal inference and causal search.

Libraries and platforms used for causal reasoning and causal search

<Libraries and platforms used for causal inference>

Some of the libraries and platforms used for causal inference are described below.

• DoWhy: DoWhy is a causal inference library in Python that provides a framework for statistical causal inference. It provides functions for building causal graphs, estimating propensity scores, and estimating causal effects.
• CausalImpact: CausalImpact is a library for causal inference provided in the R language. It specializes in temporal causal inference and can estimate causal effects and visualize causal temporal effects.
• EconML: EconML (Econometric Machine Learning) is a Python causal inference library developed by Microsoft Research. It provides tools for estimating causal effects by combining machine learning and econometric methods.
• IBM Watson Causal Inference: IBM Watson Causal Inference is a causal inference platform from IBM that provides advanced tools for handling large data sets and complex causal relationships.
• DAGitty: DAGitty is an online causal graph visualization tool that provides a graphical representation of causal relationships and will assist in the construction and analysis of causal graphs as the basis for causal inference.

Next, we describe the libraries and platforms that can be used for causal search.

<Libraries and Platforms Used for Causal Search>

Some of the libraries and platforms used for causal search are described below.

• Tetrad: Tetrad is a Java-based library for causal search. It provides functions for estimating graphical models of causality and supports various causal search methods (Bayesian networks, constraint-based search, etc.).
• PC Algorithm: The PC Algorithm will be one of the widely used algorithms in causal search, implemented as a library in R or Python to build graphical models for estimating causal relationships among variables.
• GES (Greedy Equivalence Search): GES is a method that employs a constraint-based approach in causal search, implemented as a library in R or Python, to search for causal relationships to build graphical models, as well as to find equivalence classes between variables. It is also possible to find equivalences between variables as well as causal relationships to build graphical models.
• Causalnex: Causalnex is a Python-based causal search library. It provides tools for building Bayesian networks and causal graph models, and can be combined with methods for estimating causal relationships from data.
• DAGitty: DAGitty can be used not only as a causal visualization tool, but also for causal search. It can assist in the construction and analysis of causal graphs and help in exploring methods for exploring causal relationships from data.

Finally, we describe the specific implementation steps and concrete implementation of causal inference and causal search.

Implementation steps for causal inference and causal search

<Procedures for Implementing Causal Inference>

The implementation procedure for causal inference generally proceeds in the following steps

• Problem definition: First, clearly define the purpose of the research and the problem to be solved. Here, it is important to clarify what causal relationships you wish to infer and which variables are involved.
• Data collection: Collect the necessary data for causal inference. Here, appropriate data collection methods, such as randomized experiments or observational data, should be selected. The quality of the data and the appropriate sample size should be carefully considered, as they affect the reliability of the causal inference.
• Data preprocessing: Prepare the collected data in a format suitable for analysis. Specifically, preprocessing methods include processing missing values, removing outliers, and scaling variables.
• Selection of causal inference methods: Depending on the causal relationships to be inferred and the study design, an appropriate causal inference method should be selected. Common methods include randomized experiments, difference-in-differences methods, matching methods, propensity score matching, and instrumental variables methods.
• Causal inference: Estimate causal relationships using the selected causal inference method. Depending on the estimation method, appropriate statistical models and algorithms are applied, as well as appropriate statistical tests and confidence interval calculations to assess the reliability and statistical significance of the estimated results.
• Interpretation of results: Interpret the estimated causal relationships to gain insight into the purpose or problem of the study. Specifically, the direction, strength, and effect size of the causal relationship shall be considered in interpreting the results.

<Procedures for Implementing Causal Search>

The following is a general procedure for implementing causal search. The procedure for causal search is similar to that of causal inference, but because it is a data-driven approach, it differs in the selection of variables, visualization of causal relationships, and additional validation experiments.

• Problem definition: Clearly define the problem to be solved in order to search for causal relationships. It is important to clarify what causal relationships you wish to explore and which variables are involved.
• Data collection: Collect the data necessary for the causal search. Appropriate data collection methods, such as observational or experimental data, should be selected.
• Variable Selection: Select variables that may be involved in the search for causality. Select appropriate variables, taking into account factors and outcomes that are candidates for causal relationships.
• Causal visualization: visualize the data to explore possible causal relationships. Visualize correlations and causal patterns among variables using visualization techniques such as scatter plots, correlation matrices, and causal graphs.
• Application of causal search methods: select appropriate methods and frameworks for causal search and apply them to real data. For the Gede routine, correlation analysis, regression analysis, and causal search algorithms (e.g., counterfactual inference and structural equation modeling) will be used.
• Interpretation of results: Interpret the obtained results to identify possible causal relationships and important factors. Interpret the results, taking into account the statistical significance of the results and the direction of causality.
• Additional validation: confirm the obtained results with additional validation or verification experiments. It is important to re-examine the results using different data sets and different approaches.

For an example implementation of causal inference in python

In the following, we describe an example implementation of the PC algorithm, one of the causal discovery algorithms.

The PC algorithm is an algorithm for inferring causal relationships among variables, and it utilizes conditional independence among variables. An example implementation of the PC algorithm is shown below.

import numpy as np
from itertools import combinations
from sklearn.linear_model import LinearRegression

def conditional_independence(X, Y, Z, alpha=0.05):
    # Functions to test for conditional independence
    n = X.shape[0]
    XZ = np.column_stack((X, Z))
    XY = np.column_stack((X, Y))
    
    model_XZ = LinearRegression().fit(XZ, Y)
    res_XZ = Y - model_XZ.predict(XZ)
    
    model_XY = LinearRegression().fit(XY, Z)
    res_XY = Z - model_XY.predict(XY)
    
    r_XZ = np.corrcoef(X, res_XZ)[0, 1]
    r_XY = np.corrcoef(Y, res_XY)[0, 1]
    
    se_XZ = np.sqrt((1 - r_XZ**2) / (n - 2))
    se_XY = np.sqrt((1 - r_XY**2) / (n - 2))
    
    t_XZ = r_XZ / se_XZ
    t_XY = r_XY / se_XY
    
    crit_val = 1.96  # t-value for 95% confidence interval
    
    return abs(t_XZ) < crit_val and abs(t_XY) < crit_val

def pc_algorithm(data, alpha=0.05):
    # PC Algorithm Implementation
    num_vars = data.shape[1]
    graph = np.zeros((num_vars, num_vars), dtype=bool)
    
    # Test for conditional independence for all variable combinations
    for (i, j) in combinations(range(num_vars), 2):
        X = data[:, i]
        Y = data[:, j]
        Z = np.delete(data, [i, j], axis=1)
        
        if conditional_independence(X, Y, Z, alpha):
            graph[i, j] = True
            graph[j, i] = True
    
    return graph

For an example implementation of causal search in python

Here we describe an example implementation using the “PC algorithm” and “LiNGAM,” which are algorithms for estimating causal graph structure.

1. Example of PC algorithm implementation:.

The PC algorithm is a method for estimating causal graphs using conditional independence among variables. An example implementation of the PC algorithm is shown below.

import numpy as np
from causality.pc import PC

def pc_algorithm(data):
    # PC Algorithm Implementation
    pc = PC()
    estimated_graph = pc.estimate(data)
    return estimated_graph

This example implements the PC algorithm using the PC class from the causality library, which uses the estimate method to estimate a causal graph from the data and returns the result.

2. Example of LiNGAM implementation:.

LiNGAM is a method for estimating causal graphs using a linear causal model. An example implementation of LiNGAM is shown below.

import numpy as np
from causality.causal import LiNGAM

def lingam_algorithm(data):
    # LiNGAM implementation
    lingam = LiNGAM()
    estimated_graph = lingam.fit(data)
    return estimated_graph

In this example, the LiNGAM class from the causality library is used to implement LiNGAM, and the fit method is used to apply LiNGAM to the data to estimate the causal graph.

Reference Information and Reference Books

Details of causal inference and causal search are described in “Statistical Causal Inference and Causal Search. See also that contents.

Causal Inference in Statistics” is available as a reference book.

“Causal Inference and Discovery in Python: Unlock the secrets of modern causal machine learning with DoWhy, EconML, PyTorch and more“

“Causal Inference in Python: Applying Causal Inference in the Tech Industry“

“Causal Inference for Data Science“