Reasoning with counterfactuals is one of the hallmarks of human cognition, involved in various tasks such as explanation, credit assignment, blame, and responsibility. Counterfactual quantities that are not identifiable in the general non-parametric case may be identified under shape constraints on the functional mechanisms, such as monotonicity. One prominent example of such an approach is the celebrated result by Angrist and Imbens on identifying the Local Average Treatment Effect (LATE) in the instrumental variable setting. In this paper, we study the identification problem of more general settings under monotonicity constraints. We begin by proving the monotonicity reduction lemma, which simplifies counterfactual queries using monotonicity assumptions and facilitates the reduction of a larger class of these queries to interventional quantities. We then extend the existing identification results on Probabilities of Causation (PoCs) and LATE to a broader set of queries and graphs. Finally, we develop an algorithm, M-ID, for identifying arbitrary counterfactual queries from combinations of observational and experimental data, which takes as input a causal diagram with monotonicity constraints. We show that M-ID subsumes the previously known identification results in the literature. We demonstrate the applicability of our results using synthetic and real data.

With the widespread adoption of AI systems, many of the decisions once made by humans are now delegated to automated systems. Recent works in the literature demonstrate that these automated systems, when used in socially sensitive domains, may exhibit discriminatory behavior based on sensitive characteristics such as gender, sex, religion, or race. In light of this, various notions of fairness and methods to quantify discrimination have been proposed, also leading to the development of numerous approaches for constructing fair predictors. At the same time, imposing fairness constraints may decrease the utility of the decision-maker, highlighting a tension between fairness and utility. This tension is also recognized in legal frameworks, for instance in the disparate impact doctrine of Title VII of the Civil Rights Act of 1964 -- in which specific attention is given to considerations of \textit{business necessity} -- possibly allowing the usage of proxy variables associated with the sensitive attribute in case a high-enough utility cannot be achieved without them. In this work, we analyze the tension between fairness and accuracy from a causal lens for the first time. We introduce the notion of a path-specific excess loss (PSEL) that captures how much the predictor's loss increases when a causal fairness constraint is enforced. We then show that the total excess loss (TEL), defined as the difference between the loss of predictor fair along all causal pathways vs. an unconstrained predictor, can be decomposed into a sum of more local PSELs. At the same time, enforcing a causal constraint often reduces the disparity between demographic groups. Thus, we introduce a quantity that summarizes the fairness-utility trade-off, called the causal fairness/utility ratio, defined as the ratio of the reduction in discrimination vs. the excess in the loss from constraining a causal pathway. This quantity is particularly suitable for comparing the fairness-utility trade-off across different causal pathways. Finally, as our approach requires causally-constrained fair predictors, we introduce a new neural approach for causally-constrained fair learning. Our approach is evaluated across multiple real-world datasets, providing new insights into the tension between fairness and accuracy.

Since the rise of fair machine learning as a critical field of inquiry, many different notions on how to quantify and measure discrimination have been proposed in the literature. Some of these notions, however, were shown to be mutually incompatible. Such findings make it appear that numerous different kinds of fairness exist, thereby making a consensus on the appropriate measure of fairness harder to reach, hindering the applications of these tools in practice. In this paper, we investigate one of these key impossibility results that relates the notions of statistical and predictive parity. Specifically, we derive a new causal decomposition formula for the fairness measures associated with predictive parity, and obtain a novel insight into how this criterion is related to statistical parity through the legal doctrines of disparate treatment, disparate impact, and the notion of business necessity. Our results show that through a more careful causal analysis, the notions of statistical and predictive parity are not really mutually exclusive, but complementary and spanning a spectrum of fairness notions through the concept of business necessity. Finally, we demonstrate the importance of our findings on a real-world example.

As society increasingly relies on AI-based tools for decision-making in socially sensitive domains, investigating fairness and equity of such automated systems has become a critical field of inquiry. Most of the literature in fair machine learning focuses on defining and achieving fairness criteria in the context of prediction, while not explicitly focusing on how these predictions may be used later on in the pipeline. For instance, if commonly used criteria, such as independence or sufficiency, are satisfied for a prediction score $S$ used for binary classification, they need not be satisfied after an application of a simple thresholding operation on $S$ (as commonly used in practice). In this paper, we take an important step to address this issue in numerous statistical and causal notions of fairness. We introduce the notion of a margin complement, which measures how much a prediction score $S$ changes due to a thresholding operation. We then demonstrate that the marginal difference in the optimal 0/1 predictor $\widehat Y$ between groups, written $P(\hat y \mid x_1) - P(\hat y \mid x_0)$, can be causally decomposed into the influences of $X$ on the $L_2$-optimal prediction score $S$ and the influences of $X$ on the margin complement $M$, along different causal pathways (direct, indirect, spurious). We then show that under suitable causal assumptions, the influences of $X$ on the prediction score $S$ are equal to the influences of $X$ on the true outcome $Y$. This yields a new decomposition of the disparity in the predictor $\widehat Y$ that allows us to disentangle causal differences inherited from the true outcome $Y$ that exists in the real world vs. those coming from the optimization procedure itself. This observation highlights the need for more regulatory oversight due to the potential for bias amplification, and to address this issue we introduce new notions of weak and strong business necessity, together with an algorithm for assessing whether these notions are satisfied. We apply our method to three real-world datasets and derive new insights on bias amplification in prediction and decision-making.

One of the fundamental challenges found throughout the data sciences is to explain why things happen in specific ways, or through which mechanisms a certain variable $X$ exerts influences over another variable $Y$. In statistics and machine learning, significant efforts have been put into developing machinery to estimate correlations across variables efficiently. In causal inference, a large body of literature is concerned with the decomposition of causal effects under the rubric of mediation analysis. However, many variations are spurious in nature, including different phenomena throughout the applied sciences. Despite the statistical power to estimate correlations and the identification power to decompose causal effects, there is still little understanding of the properties of spurious associations and how they can be decomposed in terms of the underlying causal mechanisms. In this manuscript, we develop formal tools for decomposing spurious variations in both Markovian and Semi-Markovian models. We prove the first results that allow a non-parametric decomposition of spurious effects and provide sufficient conditions for the identification of such decompositions. The described approach has several applications, ranging from explainable and fair AI to questions in epidemiology and medicine, and we empirically demonstrate its use.

As society transitions towards an AI-based decision-making infrastructure, an ever-increasing number of decisions once under control of humans are now delegated to automated systems. Even though such developments make various parts of society more efficient, a large body of evidence suggests that a great deal of care needs to be taken to make such automated decision-making systems fair and equitable, namely, taking into account sensitive attributes such as gender, race, and religion. In this paper, we study a specific decision-making task called outcome control in which an automated system aims to optimize an outcome variable $Y$ while being fair and equitable. The interest in such a setting ranges from interventions related to criminal justice and welfare, all the way to clinical decision-making and public health. In this paper, we first analyze through causal lenses the notion of benefit, which captures how much a specific individual would benefit from a positive decision, counterfactually speaking, when contrasted with an alternative, negative one. We introduce the notion of benefit fairness, which can be seen as the minimal fairness requirement in decision-making, and develop an algorithm for satisfying it. We then note that the benefit itself may be influenced by the protected attribute, and propose causal tools which can be used to analyze this. Finally, if some of the variations of the protected attribute in the benefit are considered as discriminatory, the notion of benefit fairness may need to be strengthened, which leads us to articulating a notion of causal benefit fairness. Using this notion, we develop a new optimization procedure capable of maximizing $Y$ while ascertaining causal fairness in the decision process.