In the digital age, machine learning (ML) algorithms are becoming increasingly important in decision-making processes across a wide range of domains, including criminal justice, healthcare, and finance. While these algorithms provide significant benefits, they also pose the risk of perpetuating and exacerbating societal biases, especially when fairness is not taken into account during their design and implementation. We address the critical issue of fairness in machine learning, with a focus on combining statistical and causal fairness metrics to provide a more comprehensive approach to evaluate and ensure fairness by selecting the most suitable metric. To tackle this problem, we developed a research methodology aimed at systematically reviewing the existing literature while focusing on four research questions targeting the relationship between statistical and causal fairness metrics, which drove our analysis and categorization of papers. Based on the results of this review, we built a new fairness decision tree that integrates both types of metrics, which can guide users to choose the most suitable metric.
In the digital age, machine learning (ML) systems have become essential to many aspects of daily living
and social functions. Machine learning covers a wide range of critical applications, from criminal
justice and credit scoring to healthcare diagnostics. However, a serious concern for justice has emerged
along with the technological advancements that machine learning has brought forth. It is imperative to
ensure that these systems do not perpetuate or exacerbate societal inequalities and biases that already
exist [
These examples show the need for a systematic approach to assessing and mitigating bias in machine learning systems. The problem’s complexity is increased by the fact that fairness in ML can be understood from multiple perspectives, including statistical fairness, which focuses on ensuring equitable outcomes, and causal fairness, which aims to understand and address the underlying causal mechanisms that lead to biased results.
In this paper, we study the topic of fairness in machine learning, with a focus on the diference between statistical and causal fairness metrics; in particular, we study the possibility of incorporating them into a common vision. Our key contributions are as follows: (J. Huang)
CEUR Workshop
ISSN1613-0073 • Research Methodology: We develop a systematic research methodology to identify and categorize the relevant literature. • Results of Literature Analysis: Our systematic analysis of selected papers brings significant insights into the distinction between statistical and causal fairness, and the datasets most commonly used. • Fairness Decision Tree: We present a new fairness decision tree framework that integrates both statistical and causal fairness metrics.
The rest of this paper is organized as follows. Section 2 introduces some preliminary concepts. Section 3 presents the adopted research methodology. Section 4 describes the analysis of the results. Section 5 presents the fairness decision tree. Section 6 concludes the paper.
Fairness can be defined as the absence of any prejudice or favoritism toward an individual or a group
based on their inherent or acquired characteristics [
Existing fairness definitions in ML algorithms can be classified into two categories: statistical fairness
and causal fairness. Statistical fairness focuses on frequency statistics, ensuring equitable outcomes
across demographic groups. In contrast, causal fairness explores causal relationships between attributes
and outcomes, intervening to eliminate biases rooted in causal mechanisms. Statistical-based fairness
metrics are categorized in [
While statistics ofer the tools to identify patterns and correlations within data [
Based on Pearl’s structural causal models [
The majority of causal-based fairness notions are defined in terms of the non-observable quantities of
interventions and counterfactuals, so their applicability depends heavily on the identification of those
quantities in the data. An overview of the principal causal-based fairness metrics is presented by [
It is defined as follows:
( ) = ( |( = 1)) − ( |( = 0))
3. Path-specific Efect [
It is defined as follows:
( ) = ( |( = 1| , = 0| ))̂ − ( |( = 0))
where ( |( = 1| , = 0| ))̂ represents the post-intervention distribution of where the efect
of intervention ( = 1) is transmitted only along while the efect of reference intervention
( = 0) is transmitted along the other paths.
4. No proxy discrimination [
It is defined as follows:
( |( = )) = ( |( =
′)) ∀ , ′ ∈ ()
5. Counterfactual Fairness [
It is defined as follows: ( =1 ( )| = , = 0) = ( =0 ( )| = , = 0) Where is the subset of observed variables except sensitive variables and decision variables.
Any context = represents a certain sub-group of the population.
6. Individual direct discrimination [
Causal inference is used to define the distance function (, ′) to measure similarity between individuals: given a causal graph, only the variables that are direct parent nodes of the decision variable are considered to compute the similarity between individuals, which are denoted as = ( )\{} . The formal definition of (, ′) is: || =1 (, ′) = ∑ |( , ′) ∗ ( , ′)| (
, ′) is defined as follows:
Where (
the causal efect of each of the selected variables ∈ on the actual outcome. In particular,
, ′) is a distance function proposed by Luong et al. in [
Where ( |()) ( |(
is the efect of the interventions that forces to take the set of values , and ′, \ )) is the efect of the intervention that forces to take value ′ and other attributes 7. Equality of Efort
[
Equality of efort notions are defined based on the potential outcome framework into individual Equal efort and system -Equal efort. Both criteria can be used to measure the efort discrepancy between protected and unprotected groups.
Let’s consider as the potential outcome for individual had been , [ ] the expected outcome under treatment for individual , and consider, similar to Individual direct discrimination, + and − as two sets of similar individuals of group = 0 and = 1 respectively.
+] is the expected outcome under treatment for the subgroup +. And the needed minimal value of treatment variable to achieve -level of outcome within the subgroup + is defined as follows: For a certain outcome level , individual -Equal efort is satisfied for individual if: Ψ +( ) =
∈ [ +] ≥
Ψ +( ) = Ψ −( )
Ψ +( ) = Ψ −( )
When + and − are extended to the entire group with sensitive attribute = 0 and = 1
respectively, + is used to denote the first set and − denoted the second one. The System
-Equal efort is satisfied for a sub-population if:
8. Path-specific Counterfactual Fairness (PC Fairness) [
corresponds to the Total Causal Efect .
Consequently, for example, if we set contains all causal paths and an empty set, PC-Fairness Finally, regarding unfairness mitigation, depending on the stage of the ML algorithm, pre-processing, in-processing, and post-processing mechanisms can be used to intervene in the algorithm to achieve fair ML, respectively.
This section defines the research questions and the methodological approach taken to address them, including the specific search techniques and keywords that were employed to locate pertinent material, discussing the inclusion and exclusion criteria employed to identify the most relevant studies.
The methodology is based on a set of structured research questions designed to explore fairness in ML, comprehending both statistical and causal dimensions. These questions guide the entire research process, from the initial literature review to the final analysis and synthesis. Here, we discuss each of these questions.
RQ1: What are the main concepts and diferences between statistical-based and causal-based fairness?
This question is to provide a clear and simple review of the fundamental ideas and diferences between statistical and causal approaches to fairness in ML. Understanding these diferences is important for comprehending each perspective’s specific advantages and limits.
RQ2: Which datasets are most commonly used in fairness research, and are there diferences between those used in causal-based and statistical-based studies?
Identifying commonly used datasets in both causal and statistical fairness is crucial as it helps in understanding the contexts in which fairness metrics are tested and validated. This question attempts to figure out not just the most often used datasets in general, but also if there are diferences in dataset utilization across causal and statistical fairness studies.
RQ3: Is it possible to have a common vision between causal and statistical fairness? This question investigates the theoretical feasibility and applicability of combining causal-based and statistical-based fairness metrics.
RQ4: How to choose the most suitable metric considering both perspectives? This final question discusses the research’s practical consequences, suggesting an approach for selecting the most appropriate fairness metric while balancing causal and statistical aspects.
By addressing these questions, this work provides the foundation for a detailed investigation of fairness research, ensuring an in-depth knowledge of both the theoretical foundations and practical applications of the subject.
We delineate the comprehensive search strategy employed to gather relevant literature, focusing on evaluating fairness in ML with a particular emphasis on fairness metrics.
The literature collection process is illustrated in Figure 1 and which delineates the steps from research question formulation to final paper selection that are: Keywords and Query Creation, Setting Database and Inclusion and Exclusion Criteria, Paper Analysis and Snowballing.
To ensure targeted and relevant database searches, keywords were identified from the research questions. These keywords, along with supportive terms, guide the search process efectively and are: AI, Machine Learning, ML, Data, Fairness, Metric, Definition, Solution, Mitigation, Ethic, Measure, Causal, Statistical, Group, Individual, Counterfactual, Interventional.
The query was constructed using boolean operators to refine search results and ensure relevance to our objectives. Furthermore, the search was conducted across prominent databases including Scopus, ACM Digital Library, IEEE Xplore, and Google Scholar, focusing on publications from the past five years in the field of computer science. The final query is the following:
(fair* OR discriminat* OR unfair* OR bias*) AND (causal* OR statistic* OR individual* OR group* OR counterfact* OR intervention* OR parity*) AND (metric* OR measur* OR defin* OR solut* OR mitigat*) AND ((machine learning) OR data* OR ethic* OR (artificial intelligence))
The search provided a significant number of results: Scopus 5,270, ACM Digital Library 910, IEEE Xplore 2,335, Google Scholar 16,800.
For the selection strategy, we present the inclusion and exclusion criteria utilized during the selection process for identifying relevant literature. These criteria serve as guidelines to ensure the systematic and targeted inclusion of papers that align with our objectives while excluding those that do not meet the specified thematic requirements. The Inclusion Criteria are: • Article or Paper: Articles, conference papers, or research papers that contribute to the discourse on fairness in ML. • More than 5 citations: Papers cited more than five times, indicating the paper’s impact and relevance. • Discussion on fairness: This includes any study that addresses fairness in the context of ML, covering both theoretical and practical aspects. • New mitigation technique: Studies that suggest methods to reduce or eliminate biases in ML models. • Tool: Studies that introduce software or tools designed to assess, measure, or enhance fairness in
ML models. • New perspective: Papers that provide innovative viewpoints or conceptual frameworks for understanding fairness. • New fairness metric: Studies that develop and validate new metrics for evaluating fairness in
ML.
The Exclusion Criteria are: • Theses or reports: Academic theses and technical reports, as these often serve as preliminary or non-peer-reviewed documents. • Surveys: Summary of existing research rather than contributing new findings or perspectives. • Papers that primarily focus on techniques without discussing fairness: Studies focusing on techniques or algorithms without addressing their fairness implications.
• Papers not written in English: Studies written in languages other than English.
Through the selection process based on inclusion and exclusion criteria, a total of 26 papers were
initially identified as relevant. Subsequently, employing a snowballing technique to expand the pool of
selected papers, an additional 3 papers were incorporated, bringing the total number of selected papers
to 29. Snowballing technique, also known as snowball sampling or iterative citation searching [
The following data were systematically collected from the papers found (besides paper’s title, authors, year of publication, venue and URL/DOI): • Fairness Metrics (Causal or Not or Both): Whether the paper discusses causal fairness metrics or statistical fairness metrics or both. • Analysis Type: The type of analysis conducted in the paper: Classification, Evaluation, Definition, or Solution Proposal (a new tool, perspective or algorithm). • Content: The paper’s main findings and contributions. • Context: The specific domain or application area of the research. • Experimental Datasets: The datasets used in the paper, if any.
• Methods: Mitigation techniques type, if pre-, in- or post-processing.
This comprehensive data collection approach ensures that each paper’s relevant information is captured accurately and thoroughly, facilitating further analysis and synthesis of findings in subsequent stages of the research process. A portion of our findings is encapsulated in Table 1.
In this section, we are going to address the research questions RQ1 and RQ2 by analyzing the selected papers. The distribution of causal and non-causal papers among selected papers is: 70% focus on causal fairness metrics and 30% on statistical fairness metrics.
RQ1: What are the main concepts and diferences between statistical-based and causal-based fairness?
Statistical-based fairness metrics are grounded in ensuring that the observed outcomes of a machinelearning model are distributed equitably. These metrics focus on the fairness of the model’s predictions without delving into the underlying causal mechanisms that generate the data. Causal-based fairness metrics, in contrast, emphasize the importance of understanding and addressing the causal relationships between variables. These metrics, including Counterfactual fairness and Interventional fairness, seek to identify and mitigate biases that arise from the causal influence of protected attributes on the outcomes. By examining the causal pathways, thus, causal fairness metrics aim to ensure that decisions are not only fair in an observational sense but also in a causal sense, addressing deeper, more systemic biases.
To summarize, the fundamental diference between statistical and causal fairness lies in their approach. While statistical fairness focuses on the distribution of outcomes, causal fairness delves into the root causes of biases, examining how and why these biases occur.
Q2: Which datasets are most commonly used in fairness research, and are there diferences between those used in causal-based and statistical-based studies?
The visualization in Figure 2 provides the number of datasets used across papers and shows a detailed
comparison of the frequency of dataset usage in these studies. From the chart, it is evident that the
Adult dataset [41] is predominantly used in both causal and statistical studies, highlighting its relevance
and utility in fairness research, given its rich demographic features and applicability to numerous
fairness metrics. The Compas [
DATE where use reflects the importance of ensuring equitable treatment in financial services, an important area where biases can impact individuals’ economic opportunities. The chart also highlights the use of synthetic datasets in causal studies, which are artificially created by researchers, and they are essential for testing causal metrics because they allow researchers to design experiments that can isolate and examine the efects of specific variables on fairness, providing insights that might not be possible with real-world data.
In this section, we are going to present our new fairness decision tree (Figure 3), which aims to extend
and update the original proposal by Baresi et al. [
First, we will provide a detailed summary of the original decision tree, covering nodes A to F and metrics 1 to 12. Following that, we will introduce the new causal part of the tree (nodes G, H, I, L, M, and metrics 13 to 19), which is the original contribution of this work.
The tree begins with the question, ”Is past knowledge relevant?” (A). If the answer is yes, the tree helps experts decide about the importance of past decisions compared to new predictions. If the answer is no, the focus shifts to predictions and legitimate attributes (B). Based on the responses, the tree suggests diferent statistical fairness definitions. When past knowledge is relevant, the next question (C) asks which type of predictions the expert is interested in: wrong, correct, or both. If the focus is on wrong predictions, the tree further asks whether the interest is in negative or positive predictions (D) and how conservative the decisions should be (E). Based on the responses, the tree suggests specific statistical fairness definitions. If the expert is interested in correct predictions, the next question (F) asks how to balance predictions and past decisions, leading to other three possible statistical definitions.
The introduction of causal fairness metrics expands the tree with new questions (G, H, I, L, M). These additions address the limitations of purely statistical approaches by also considering the causal relationships. The new causal fairness metrics section starts with the question, ”Are you interested in modifying the predictions?” (G). This question is important because modifying predictions involves engaging with causal relationships, it suggests an interest in not just observing what is but also in altering and understanding the causal relationships that lead to specific outcomes. If the answer is no, we move on (C), returning to the statistical part of the tree. If the answer is yes, the tree explores the possibility of adding or modifying the cause-efect relationships through the question ”Do you want to add or modify cause-efect relations?” (H). Here, it is essential to distinguish between two paths that follow from the response to this question. This leads to two diferent nodes depending on whether the expert chooses to add (Counterfactual fairness metrics) or modify (Interventional fairness metrics) cause-efect relationships. In both cases, the decision tree diferentiates between analyzing by group or by individual with the question ”Do you want to analyze by group or by individual?” (I), which separates the path into group-level and individual-level analysis. This distinction is significant as it acknowledges that fairness can be assessed by considering the overall impact on groups, where the focus is on collective fairness, or by individual circumstances, which demands a more granular, personalized assessment of fairness.
In the counterfactual case (ADD), if the interest is in the group analysis, we suggest using the
Unresolved Discrimination [
In the Interventional case (MODIFY), for group analysis, if the interest is on modifying the overall
impact of the causal relationships, the decision tree guides the expert to consider the Total Causal
Efect [
This integration of causal and statistical fairness metrics into a unique fairness decision tree answers the following research questions.
RQ3: Is it possible to have a common vision between causal and statistical fairness? While statistical fairness and causal fairness each take a diferent approach, they share a common vision of fairness in ML models. Both approaches recognize biases and inequities that may exist in the models that process data, but they address these issues from diferent angles: statistical metrics assess the fairness of a model by comparing observed data using conditional probabilities and conditional expectations, focusing on the distribution of model outputs and ensuring that the outcomes are equitable. Causal ones, instead, delve into the underlying causal relationships that drive model decisions. This approach is more concerned with understanding and eliminating the efects of sensitive attributes on model outputs through causal pathways. Thus, it provides a deeper analysis by examining how changes in a protected attribute causally influence the outcome, considering both direct and indirect efects. Despite their diferent methodologies, both statistical and causal fairness strive to achieve the same goal: reducing unfairness in ML models. Therefore, it is possible and also beneficial to have a common vision between causal and statistical fairness, as they complement each other in addressing diferent facets of bias and discrimination in ML.
RQ4: How to choose the most suitable metric considering both perspectives? Choosing the most suitable fairness metric requires an approach that balances insights from both statistical and causal perspectives. This decision is complex and context-dependent, necessitating a thorough understanding of the dataset, the model, and the specific fairness goals of the application. The fairness decision tree framework presented in this chapter provides a method for navigating these choices. Here is a detailed approach to selecting the most appropriate metric.
• Deeper Understanding of the Current Dataset and Model: The first step is to analyze the features and attributes contained in the dataset. It is crucial to focus on protected attributes that might trigger inequality, such as race, gender, and age. Understanding the distribution of these attributes is essential for selecting appropriate metrics, as it helps identify potential sources of bias. • Choose the Appropriate Fairness Metrics: Use the fairness decision tree as a guide to navigate through various fairness metrics. The definition of fairness can vary depending on the context. Thus, it is also crucial to clarify the specific fairness objectives to align the choice of metrics with the desired outcomes. • Comprehensive Assessment and Comparison: Use a combination of multiple metrics to perform a comprehensive assessment. Comparing the results of diferent metrics can provide a better understanding of fairness. Additionally, it is beneficial to compare the chosen metrics with those used in other studies to ensure consistency and validity.
This approach ensures a deeper understanding and mitigation of underlying biases, considering both perspectives.
We investigate the topic of fairness in machine learning (ML), with a focus on the diference between
statistical and causal fairness metrics, in particular, the possibility to incorporate them into a common
vision. Our approach was motivated by the need to investigate, understand, and unify existing fairness
metrics, which usually concentrate solely on statistical outcomes or delve into causal mechanisms
without considering both perspectives. We introduced the fairness decision tree, a novel solution that
integrates the causal fairness metrics into the original tree proposed by Baresi et al. [
One limitation of this work is that the fairness decision tree framework has yet to be validated and thoroughly tested in real-world scenarios. This validation could be achieved through user testing, surveys, or field experiments to determine its practicality and efectiveness in a variety of applications. Another limitation is that the reviewed literature covers only the last seven years, potentially excluding older but still relevant studies. Thus, expanding the time frame to include earlier work could provide a more comprehensive understanding of how fairness metrics have evolved over time. Furthermore, the fairness decision tree may need refinement when applied to various contexts, as real-world applications could present challenges not fully anticipated by the current framework.
Future research may improve the findings of this work in a variety of ways. One direction could be the application of the tree to various datasets, potentially through experiments involving real-world scenarios or user interactions to validate its utility and robustness across diferent domains. Furthermore, as fairness in ML evolves, new metrics and perspectives are likely to emerge. Thus, future research should be adaptive, incorporating these advancements while continuing to investigate the relationships between various fairness perspectives.
We thank Professor L. Tanca and T. Dolci for their support. This work was supported in part by project SERICS (PE00000014) under the NRRP MUR program funded by the EU - NGEU and from the Italian PRIN project 2022XERWK9 “S-PIC4CHU” – Semantics-based Provenance, Integrity, and Curation for Consistent, High-quality, and Unbiased data science.
During the preparation of this work, GPT-4 was used in order to check grammar and spelling. After using these tool, the authors reviewed and edited the content as needed and take full responsibility for the publication’s content.
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