Counterfactual Fairness

We study causal logistic bandits with counterfactual fairness constraints. The causal structure is given through known factual and counterfactual feature maps that share an unknown logistic reward parameter, but the learner observes only factual rewards. Consequently, the directions determining counterfactual feasibility need not be identifiable from the available feedback. The closest prior analyses either omit a coverage condition or impose a comparatively strong one, and do not establish matching lower bounds. We first show that some coverage condition is necessary: without a coverage-type restriction, factually indistinguishable environments with different optimal fair actions force $Ω(T)$ expected joint loss. Under a weaker full-rank condition on the factual covariance pooled across actions, we identify a target-specific information scale $V_\star$ that measures the difficulty of estimating rewards and counterfactual effects from factual feedback. We construct worst-case families satisfying this condition on which every policy incurs expected joint loss $Ω\left(\left[V_\star\min\{\log K,d\}\right]^{1/3}T^{2/3}\right)$. We also give an explore--then--exploit procedure tuned using $V_\star$ and an adaptive algorithm that does not require its value. Both algorithms achieve $\max\{R_T,V_T\}=\widetilde{O}\left(\left[V_\star\min\{\log K,d\}\right]^{1/3}T^{2/3}+κd/σ_0^2\right)$, where $R_T$ is regret relative to the best fair action and $V_T$ denotes the cumulative stage-wise positive violations. Thus the upper and lower bounds match in their leading dependence on $T$, $V_\star$, and $\min\{\log K,d\}$, up to logarithmic factors.

Counterfactual audits are the standard tool for checking whether a clinical agent treats demographically distinct but clinically identical patients differently. They report a flip rate: how often an action changes when only the patient descriptor changes. We show that this quantity is uninterpretable on its own. Re-running an identical condition ten times over sixteen vignettes (same narrative, same descriptor string, nothing varied) moved a clinical agent's action in 8.7% of outcome-vignette cells, and instability was heterogeneous across actions by a factor of eight, from 0.022 for ICU escalation to 0.179 for controlled-substance caution. No demographic contrast in our data was distinguishable from that floor. A second model gives a pooled floor of 6.7% and ranks the six actions almost identically (Spearman 0.94, exact p=0.017), so the floor is not one system's artefact. Majority-vote aggregation over five draws removes 39% of it and then flattens, and a null simulation attributes the residue to heterogeneous per-cell rates, so replication mitigates without eliminating. Any counterfactual fairness estimate reported without a per-action floor beside it therefore cannot be read as evidence of disparity. The measurements were taken with FairMedAgent, an evaluation harness for disparity in the actions of clinical LLM agents whose estimand, the within-range counterfactual flip rate, counts only flips between actions a published decision rule admits and a clinician has adjudicated. That estimand requires band adjudication, which is under way; no disparity result is claimed here. Each synthetic vignette runs a six-stage trajectory (five model-facing decisions around a deterministic environment step) under fixed-form conditions spanning race, sex, age, insurance, English proficiency, and their intersections. The harness, the floor protocol, and every analysis script are released.

Reinforcement learning (RL) seeks to optimize sequential decisions to maximize population-level benefits over time. However, when deployed in high-stakes settings such as healthcare, RL decisions might systematically restrict some subpopulation's access to valuable services in a manner contrary to the values and goals of stakeholders. Counterfactual fairness (CF) offers a promising framework to address this problem based on causal reasoning. This paper develops a data preprocessing algorithm that, when used in tandem with policy learning, enables CF in RL. Our algorithm relies on a novel quantile distribution mapping method for sequentially estimating the counterfactual states and rewards in the data preprocessing step, subsuming common additivity assumptions used for counterfactual prediction as a special case. We theoretically prove that the per-step level of counterfactual unfairness and infinite-horizon suboptimality gap can be bounded under mild regularity conditions. We also empirically test our algorithm in numerical experiments as well as in application to a real-world interventional digital health dataset.

Causal discovery recovers directed structure from observational data and is increasingly used in clinical settings to support mechanism reasoning and fairness audits of predictive models. Path-specific counterfactual fairness asks whether a protected attribute influences an outcome through illegitimate pathways, but these estimands are defined relative to a supplied causal graph and therefore inherit whatever errors the discovery step introduces. Discovery methods are routinely scored on aggregate structural metrics that weight all edges equally, and no established evaluation asks whether the specific pathway an audit depends on survives discovery---or what the audit reports when that pathway is missing. Here we show that full-graph Graph-of-Thoughts reasoning yields acyclic discovered graphs that are structurally competitive with large language model (LLM) baselines, yet that structural fidelity alone does not guarantee fairness-faithful audits. We introduce GoT-CD, in which the reasoning unit is a complete candidate edge set: multiple graphs are generated in parallel, scored by a deterministic validity function, and merged under a hard union constraint that forbids invented edges, with greedy projection enforcing a DAG before commitment. GoT-CD returns a valid DAG on all five reported benchmarks and achieves the best DAG-valid F1 score among LLM methods on Asia, Alzheimer's, and COVID-Respiratory datasets. On an Alzheimer's benchmark with known unfair path, a post-hoc path-specific audit shows that five of eight discovered graphs recover no path from the sensitive attribute to the outcome and therefore report a null overall effect while mediated effects persist, necessitating downstream path-specific fairness analysis along with structural discovery.

The notion of algorithmic fairness has been actively explored from various aspects of fairness, such as counterfactual fairness (CF) and group fairness (GF). However, the exact relationship between CF and GF remains to be unclear, especially in image classification tasks; the reason is because we often cannot collect counterfactual samples regarding a sensitive attribute, essential for evaluating CF, from the existing images (\eg, a photo of the same person but with different secondary sex characteristics). In this paper, we construct new image datasets for evaluating CF by using a high-quality image editing method and carefully labeling with human annotators. Our datasets, \oursceleb and \ourslfw, build upon the popular image GF benchmarks; hence, we can evaluate CF and GF simultaneously. We empirically observe that CF does not imply GF in image classification, whereas previous studies on tabular datasets observed the opposite. We theoretically show that it could be due to the existence of a latent attribute $G$ that is correlated with, but not caused by, the sensitive attribute (\eg, secondary sex characteristics are highly correlated with hair length). From this observation, we propose a simple baseline, Counterfactual Knowledge Distillation (CKD), to mitigate such correlation with the sensitive attributes. Extensive experimental results on \oursceleb and \ourslfw demonstrate that CF-achieving models satisfy GF if we successfully reduce the reliance on $G$ (\eg, using CKD).

The application of machine learning-based predictive algorithms to Anti-Money Laundering (AML) has grown rapidly, driven by the vast volume of financial transaction data available to banks. These algorithms are typically trained not only on transactional data but also on sensitive client information, which may raise fairness concerns. Despite this, AML detection systems remain largely underexplored from a fairness perspective, even though deeper analytical methods based on counterfactuals are now available. Such techniques enable the decomposition of the direct and indirect effects of potentially sensitive features on model predictions, thereby supporting the evaluation of whether their influence is acceptable from a fairness perspective. Closing this gap, we consider the synthetic IBM AMLSim transaction dataset and construct additional features of the country of an account and its average behaviour. This improves the predictive performance of diverse machine learning models, ranging from baseline decision trees to state-of-the-art graph neural networks. We assess the potential unfairness associated with these features through a counterfactual, path-specific effect analysis. This reveals that fairness violations tend to be more pronounced for models whose predictive performance benefits the most from the extended features. Such a finding highlights a concrete instance of the trade-off between predictive accuracy and fairness in AML applications, thus underscoring the urgency of a systematic fairness analysis in such critical domains.

Large language model (LLM) agents increasingly take actions (screening applicants, recommending credit, triaging patients), yet fairness for LLMs is still measured by grading answers. We introduce AgentFairBench, a cheap, reproducible, multi-domain benchmark for demographic disparity in the actions of LLM agents. Grounded in a companion framework, the Bias Conduction Framework (BCF, restated here), it spans three regulator-anchored domains: hiring, lending, and medical triage. Synthetic, demographic-neutral profiles are evaluated in counterfactual matched sets that vary only a name-coded race x gender signal (in the Bertrand Mullainathan tradition), under four agent scaffolds of increasing agency (direct, chain-of-thought, multi-agent deliberation, tool-augmented). A NumPy-only harness computes counterfactual flip rate, mean absolute score difference (MASD), action-rate disparity, and tool-invocation disparity, with bootstrap confidence intervals, paired tests, and false-discovery-rate control, for single-digit dollars per model. A live leaderboard with a held-out private split and a contamination canary admits external models by submission. Our pilot (864 decisions plus a test-retest replication) carries a methodological lesson: comparing a six-group score spread against a two-run noise difference overstates disparity by ~ 2.4X through statistic arity alone. Against an arity matched noise floor and an omnibus group test, claude haiku 4 5 shows no demographic effect above sampling noise (0 of 120 pairwise and 0 of 9 omnibus contrasts survive correction); a planted-bias test confirms the instrument detects disparity when present. The contribution is a sound, sensitive, adoption-ready instrument, the arity matched null methodology, and open artifacts to scale it. Code, data, and harness are released under open licenses, with an anonymized review artifact.

Machine learning systems deployed in high stakes socioeconomic settings routinely display bias. We formalize bias as a symmetry breaking operation: a classifier is fair if its outputs remain invariant under the counterfactual operation of switching a sensitive attribute, with merit features held fixed. We implement loss based regularization as a symmetry restoring mechanism and evaluate the framework on four synthetic datasets with varying levels of noise, correlation, and bias. The framework achieves upwards of 90% violation reduction, with accuracy costs around 5%. This framework does not require causal graph knowledge, is computationally lightweight, and generalizes to any sensitive attribute definable as a bit-flip, making it suitable for contexts where local sources of discrimination remain absent from mainstream benchmarks.

Online link recommendation on evolving graphs is performative: by choosing which candidate links to show users, the system changes which links form and what feedback it later observes. Consequently, fairness estimates from logged outcomes can be misleading and may drift after deployment when the recommendation policy is updated. We introduce COPF (Counterfactual Online Performative Fairness), a decision-layer framework for deployment-stable fairness monitoring and control in online link recommendation. COPF (i) defines group-level opportunity gaps over exposure (shown vs. not shown) counterfactuals, (ii) makes them estimable by explicit exploration and by logging the probability (propensity) that each candidate is shown, and (iii) audits and controls fairness using residual outcome indistinguishability (OI) over a configurable auditor family with graph-aware doubly robust (GA-DR) estimators. We provide a noisy transfer theorem showing that Residual-OI on estimated GA-DR residuals implies bounds on exposure-counterfactual group gaps under temporal mixing and bounded local interference, and we instantiate an online multicalibration auditor together with a primal-dual controller. Experiments on two TGB streams and a controlled synthetic bipartite stream show that COPF reduces worst-case spikes in exposure-counterfactual group disparities with modest impact on ranking utility. Our code is available at https://github.com/lsnnnnnnnn/COPF.

Large language models (LLMs) can reveal and amplify societal biases during chain-of-thought (CoT) generation. We present COFT (Chain of Fair Thought), a training-free decoding method that applies token-level fairness control at decode time, with distribution-free marginal validity guarantees (under exchangeability) for any frozen causal language model. COFT operates in three stages. First, it creates a masked counterfactual prompt by replacing sensitive spans with neutral tokens. Second, it compares the factual and masked logit distributions through lightweight logit fusion to attenuate attribute-driven biases. Third, it uses dual-branch split-conformal calibration to certify per-step candidate token sets at a user-chosen risk level. We evaluate COFT across six models and multiple bias benchmarks. Our method reduces standard bias metrics by 30-55% (median 38%) while preserving task utility and language quality. Reasoning accuracies remain unchanged within run-to-run noise margins. The computational overhead is modest, equivalent to one additional cached forward pass (<=11%). COFT offers a clear, auditable path to safer CoT generation with significant bias reduction, negligible utility loss, and no requirement for retraining, auxiliary classifiers, or weight access.

We consider the problem of learning a counterfactually fair regressor. We adopt a causal uncertainty view in which counterfactual fairness is defined with resampled noise. We focus on obtaining theoretical fairness guarantees for a new post-processing estimator. We begin by showing that counterfactual fairness is equivalent to satisfying demographic parity conditional on the latent variable. This allows us to provide a closed-form expression of the optimal fair regressor via a barycentric quantile map. In order to handle continuous latent variables, we propose a discretized post-processing method. Then, under mild regularity assumptions, we prove high-probability finite-sample fairness guarantees for our estimator, providing an unfairness decay at rate $\tilde O(n^{-1/3})$, and establishing a matching risk bound of order $\tilde O(n^{-1/3})$. We provide a matching lower bound on the excess risk of almost fair predictions. Finally, we extend our results to the setting of relaxed counterfactual fairness. We validate our approach on real-world and synthetic data.

AutoML, intended as the process of automating the application of machine learning to real-world problems, is a key step for AI popularisation. Most AutoML frameworks are not accounting for the potential lack of fairness in the training data and in the corresponding predictions. We introduce \textsc{FairMind}, a software prototype aiming to automatise fairness analysis at the dataset level. We achieve that by resorting to the assumptions of the \emph{standard fairness model}, recently proposed by Plečko and Bareinboim. This allows for a sound fairness evaluation in terms of causal effects, based on \emph{counterfactual} queries involving the target, possibly confounders and mediators, and the different values of an input feature we regard as \emph{protected}. After the necessary data preprocessing, the tool implements a closed-form computation of the effects. LLMs are consequently exploited to generate accurate reports on the fairness levels detected in the training dataset. We achieve that in a zero-shot setup and show by examples the expected advantages with respect to a direct analysis performed by the LLM. To favour applications, extensions to ordinal protected variable and continuous targets and novel decomposition results are also discussed.

The growing reliance of machine learning models in high-stakes, highly regulated domains such as finance and insurance has created a growing tension between predictive performance, interpretability, and regulatory fairness requirements. In these settings, models are expected not only to deliver reliable predictions but also to provide transparent decision rationales and comply with strict fairness requirements. Attention-based transformers offer powerful mechanisms for modeling complex data relationships as demonstrated in various language tasks, yet their attention mechanisms alone do not ensure counterfactually fair predictions, even when combined with fairness-aware techniques. To address these limitations, we propose the Feature Correlation Transformer (FCorrTransformer), an attention-light architecture tailored for tabular data. In this design, the attention matrix admits a direct statistical interpretation as pairwise feature dependencies, enhancing both interpretability and efficiency. Leveraging this structure, we introduce Counterfactual Attention Regularization (CAR), a framework that enforces group-invariant fair representations of sensitive features at the attention level, promoting counterfactually fair predictions without relying on explicit causal assumptions. Empirical evaluations on imbalanced classification and regression benchmarks demonstrate that FCorrTransformer combined with CAR achieves strong counterfactual fairness while maintaining competitive predictive performance and substantially reducing model complexity compared with standard transformer-based baselines. Overall, this work bridges a critical gap between fairness theory and machine learning models, offering a practical framework for responsible AI in regulatory-sensitive domains.

Deep learning models exhibit fairness concerns when predictions are inadvertently influenced by sensitive attributes. However, existing attempts to make Path-Specific Counterfactual Fairness optimizable rely on estimating marginal potential outcome probabilities-an approach that fundamentally requires high-dimensional conditional density estimation and breaks down in modalities such as medical images, where the curse of dimensionality renders reliable estimation infeasible. To address this limitation, we reduce the problem of enforcing Path-Specific Counterfactual Fairness to a causal conditional independence constraint and prove that satisfying this constraint is sufficient to eliminate the unfair causal effect. This reduction replaces intractable counterfactual estimation with a discriminative optimization objective that remains scalable in high-dimensional settings.