As machine learning (ML) algorithms are used in applications that involve humans, concerns have arisen that these algorithms may be biased against certain social groups. Counterfactual fairness (CF) is a fairness notion proposed in Kusner et al. (2017) that measures the unfairness of ML predictions; it requires that the prediction perceived by an individual in the real world has the same marginal distribution as it would be in a counterfactual world, in which the individual belongs to a different group. Although CF ensures fair ML predictions, it fails to consider the downstream effects of ML predictions on individuals. Since humans are strategic and often adapt their behaviors in response to the ML system, predictions that satisfy CF may not lead to a fair future outcome for the individuals. In this paper, we introduce lookahead counterfactual fairness (LCF), a fairness notion accounting for the downstream effects of ML models which requires the individual future status to be counterfactually fair. We theoretically identify conditions under which LCF can be satisfied and propose an algorithm based on the theorems. We also extend the concept to path-dependent fairness.

Leveraging the development of structural causal model (SCM), researchers can establish graphical models for exploring the causal mechanisms behind machine learning techniques. As the complexity of machine learning applications rises, single-world interventionism causal analysis encounters theoretical adaptation limitations. Accordingly, cross-world counterfactual approach extends our understanding of causality beyond observed data, enabling hypothetical reasoning about alternative scenarios. However, the joint involvement of cross-world variables, encompassing counterfactual variables and real-world variables, challenges the construction of the graphical model. Twin network is a subtle attempt, establishing a symbiotic relationship, to bridge the gap between graphical modeling and the introduction of counterfactuals albeit with room for improvement in generalization. In this regard, we demonstrate the theoretical breakdowns of twin networks in certain cross-world counterfactual scenarios. To this end, we propose a novel teleporter theory to establish a general and simple graphical representation of counterfactuals, which provides criteria for determining teleporter variables to connect multiple worlds. In theoretical application, we determine that introducing the proposed teleporter theory can directly obtain the conditional independence between counterfactual variables and real-world variables from the cross-world SCM without requiring complex algebraic derivations. Accordingly, we can further identify counterfactual causal effects through cross-world symbolic derivation. We demonstrate the generality of the teleporter theory to the practical application. Adhering to the proposed theory, we build a plug-and-play module, and the effectiveness of which are substantiated by experiments on benchmarks.

Transport policy assessment often involves causal questions, yet the causal inference capabilities of traditional travel behavioural models are at best limited. We present the deep CAusal infeRence mOdel for traveL behavIour aNAlysis (CAROLINA), a framework that explicitly models causality in travel behaviour, enhances predictive accuracy, and maintains interpretability by leveraging causal inference, deep learning, and traditional discrete choice modelling. Within this framework, we introduce a Generative Counterfactual model for forecasting human behaviour by adapting the Normalizing Flow method. Through the case studies of virtual reality-based pedestrian crossing behaviour, revealed preference travel behaviour from London, and synthetic data, we demonstrate the effectiveness of our proposed models in uncovering causal relationships, prediction accuracy, and assessing policy interventions. Our results show that intervention mechanisms that can reduce pedestrian stress levels lead to a 38.5% increase in individuals experiencing shorter waiting times. Reducing the travel distances in London results in a 47% increase in sustainable travel modes.

Counterfactual reasoning is pivotal in human cognition and especially important for providing explanations and making decisions. While Judea Pearl's influential approach is theoretically elegant, its generation of a counterfactual scenario often requires interventions that are too detached from the real scenarios to be feasible. In response, we propose a framework of natural counterfactuals and a method for generating counterfactuals that are natural with respect to the actual world's data distribution. Our methodology refines counterfactual reasoning, allowing changes in causally preceding variables to minimize deviations from realistic scenarios. To generate natural counterfactuals, we introduce an innovative optimization framework that permits but controls the extent of backtracking with a naturalness criterion. Empirical experiments indicate the effectiveness of our method.

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.

Counterfactual reasoning -- envisioning hypothetical scenarios, or possible worlds, where some circumstances are different from what (f)actually occurred (counter-to-fact) -- is ubiquitous in human cognition. Conventionally, counterfactually-altered circumstances have been treated as "small miracles" that locally violate the laws of nature while sharing the same initial conditions. In Pearl's structural causal model (SCM) framework this is made mathematically rigorous via interventions that modify the causal laws while the values of exogenous variables are shared. In recent years, however, this purely interventionist account of counterfactuals has increasingly come under scrutiny from both philosophers and psychologists. Instead, they suggest a backtracking account of counterfactuals, according to which the causal laws remain unchanged in the counterfactual world; differences to the factual world are instead "backtracked" to altered initial conditions (exogenous variables). In the present work, we explore and formalise this alternative mode of counterfactual reasoning within the SCM framework. Despite ample evidence that humans backtrack, the present work constitutes, to the best of our knowledge, the first general account and algorithmisation of backtracking counterfactuals. We discuss our backtracking semantics in the context of related literature and draw connections to recent developments in explainable artificial intelligence (XAI).

With the rapid development of chatbots and other AI systems, questions about whether they will ever gain true understanding, become conscious, or even develop a feeling agency have become more pressing. When it comes to making sense of these qualities in humans, our ability for counterfactual thinking is key. The existence of alternative worlds where things happen differently, however, is not just an exercise in imagination – it's a key prediction of quantum mechanics. Perhaps our brains are able to ponder how things could have been because in essence they are quantum computers, accessing information from alternative worlds, argues Tim Palmer. Ask a chatbot "How many prime numbers are there?"[i] Ask the chatbot "How do we know?" and it will reply that there are many ways to show this, the original going back to the mathematician Euclid of ancient Greece.

Named entity recognition (NER) is an essential task in natural language processing, but the internal mechanism of most NER models is a black box for users. In some high-stake decision-making areas, improving the interpretability of an NER method is crucial but challenging. In this paper, based on the existing Deterministic Talmudic Public announcement logic (TPK) model, we propose a novel binary tree model (called BTPK) and apply it to two widely used Bi-RNNs to obtain BTPK-based interpretable ones. Then, we design a counterfactual verification module to verify the BTPK-based learning method. Experimental results on three public datasets show that the BTPK-based learning outperform two classical Bi-RNNs with self-attention, especially on small, simple data and relatively large, complex data. Moreover, the counterfactual verification demonstrates that the explanations provided by the BTPK-based learning method are reasonable and accurate in NER tasks. Besides, the logical reasoning based on BTPK shows how Bi-RNNs handle NER tasks, with different distance of public announcements on long and complex sequences.

Actual causality is increasingly well understood. Recent formal approaches, proposed by Halpern and Pearl, have made this concept mature enough to be amenable to automated reasoning. Actual causality is especially vital for building accountable, explainable systems. Among other reasons, causality reasoning is computationally hard due to the requirements of counterfactuality and the minimality of causes. Previous approaches presented either inefficient or restricted, and domain-specific, solutions to the problem of automating causality reasoning. In this paper, we present a novel approach to formulate different notions of causal reasoning, over binary acyclic models, as optimization problems, based on quantifiable notions within counterfactual computations. We contribute and compare two compact, non-trivial, and sound integer linear programming (ILP) and Maximum Satisfiability (MaxSAT) encodings to check causality. Given a candidate cause, both approaches identify what a minimal cause is. Also, we present an ILP encoding to infer causality without requiring a candidate cause. We show that both notions are efficiently automated. Using models with more than $8000$ variables, checking is computed in a matter of seconds, with MaxSAT outperforming ILP in many cases. In contrast, inference is computed in a matter of minutes.

Cognitive systems with human-level intelligence must dis­play a wide range of abilities, including reasoning about the beliefs of others, hypothetical and future situations, quanti­fiers, probabilities, and counterfactuals. While each of these deals in some way with reasoning about alternative states of reality, no single knowledge representation framework deals with them in a unified and scalable manner. As a conse­quence it is difficult to build cognitive systems for domains that require each of these abilities to be used together. To enable this integration we propose a representational framework based on synchronizing beliefs between worlds. Using this framework, each of these tasks can be reformu­lated into a reasoning problem involving worlds. This demonstrates that the notions of worlds and inheritance can bring significant parsimony and broad new abilities to knowledge representation.