Graphical models have been widely used as parsimonious encoders of assumptions of the underlying causal system and provide a basis for causal inferences. Models encoding stronger constraints tend to require higher expressive power, which are also harder, and sometimes impossible to empirically falsify. In this paper, we introduce two new collections of distributions that include counterfactual quantities which are experimentally accessible under counterfactual randomizations. Correspondingly, we define two new classes of graphical models for encoding empirically testable constraints in these distributions. We further present a sound and complete calculus, based on counterfactual calculus, which licenses inferences in these two new models with rules that are within the empirically falsifiable boundary. Finally, we formulate a hierarchy over several graphical models based on the constraints they encode and study the fundamental trade-off between the expressive power and empirical falsifiability of different models across the hierarchy.

Most counterfactual inference frameworks traditionally assume acyclic structural causal models (SCMs), i.e. directed acyclic graphs (DAGs).

Machine learning models now influence decisions that directly affect people's lives, making it important to understand not only their predictions, but also how individuals could act to obtain better results. Algorithmic recourse provides actionable input modifications to achieve more favorable outcomes, typically relying on counterfactual explanations to suggest such changes. However, when the Rashomon set - the set of near-optimal models - is large, standard counterfactual explanations can become unreliable, as a recourse action valid for one model may fail under another. We introduce ElliCE, a novel framework for robust algorithmic recourse that optimizes counterfactuals over an ellipsoidal approximation of the Rashomon set. The resulting explanations are provably valid over this ellipsoid, with theoretical guarantees on uniqueness, stability, and alignment with key feature directions. Empirically, ElliCE generates counterfactuals that are not only more robust but also more flexible, adapting to user-specified feature constraints while being substantially faster than existing baselines. This provides a principled and practical solution for reliable recourse under model uncertainty, ensuring stable recommendations for users even as models evolve.

Contextual Markov Decision Processes (cMDP) model this challenge, but existing methods often require explicit context variables (e.g., friction, gravity), limiting their use when contexts are latent or hard to measure. We introduce Dynamics-Aligned Latent Imagination (DALI), a framework integrated within the Dreamer architecture that infers latent context representations from agent-environment interactions. By training a self-supervised encoder to predict forward dynamics, DALI generates actionable representations conditioning the world model and policy, bridging perception and control. We theoretically prove this encoder is essential for efficient context inference and robust generalization. DALI's latent space enables counterfactual consistency: Perturbing a gravity-encoding dimension alters imagined rollouts in physically plausible ways. On challenging cMDP benchmarks, DALI achieves significant gains over contextunaware baselines, often surpassing context-aware baselines in extrapolation tasks, enabling zero-shot generalization to unseen contextual variations.

Counterfactual explanations play a pivotal role in explainable artificial intelligence (XAI) by offering intuitive, human-understandable alternatives that elucidate machine learning model decisions. Despite their significance, existing methods for generating counterfactuals often require constant access to the predictive model, involve computationally intensive optimization for each instance and lack the flexibility to adapt to new user-defined constraints without retraining. In this paper, we propose DiCoFlex, a novel model-agnostic, conditional generative framework that produces multiple diverse counterfactuals in a single forward pass. Leveraging conditional normalizing flows trained solely on labeled data, DiCoFlex addresses key limitations by enabling real-time user-driven customization of constraints such as sparsity and actionability at inference time. Extensive experiments on standard benchmark datasets show that DiCoFlex outperforms existing methods in terms of validity, diversity, proximity, and constraint adherence, making it a practical and scalable solution for counterfactual generation in sensitive decision-making domains.

Recent advances in vision-language models (VLMs) have greatly improved crossmodal semantic understanding, yet significant limitations remain in fine-grained discrimination and deep causal reasoning tasks. Existing VLMs often rely on superficial statistical correlations, lacking the ability to capture the underlying causal logic between visual and textual content. To address this, we propose CounterFactual Vision-Language Fine-tuning (CF-VLM), a novel framework that enhances the causal reasoning capabilities of VLMs through the targeted use of counterfactual samples. CF-VLM introduces three complementary training objectives: maintaining foundational cross-modal alignment, reinforcing the uniqueness, and stability of factual scene representations against coherent counterfactuals, and sharpening the model's sensitivity to minimal but critical causal edits. Extensive experiments demonstrate that CF-VLM consistently outperforms strong baselines and state-of-the-art methods on compositional reasoning and generalization benchmarks. Furthermore, it shows promise in mitigating visual hallucinations, indicating improved factual consistency. Our CF-VLM provides a robust foundation for deploying VLMs in high-stakes, real-world scenarios requiring reliable reasoning and interpretability code.

The advent of Machine Learning as a Service (MLaaS) has heightened the trade-off between model explainability and security.

Counterfactual inference is a powerful tool for analysing and evaluating autonomous agents, but its application to language model (LM) agents remains challenging. Existing work on counterfactuals in LMs has primarily focused on token-level counterfactuals, which are often inadequate for LM agents due to their open-ended action spaces. Unlike traditional agents with fixed, clearly defined action spaces, the actions of LM agents are often implicit in the strings they output, making their action spaces difficult to define and interpret. Furthermore, the meanings of individual tokens can shift depending on the context, adding complexity to token-level reasoning and sometimes leading to biased or meaningless counterfactuals. We introduce \emph{Abstract Counterfactuals}, a framework that emphasises high-level characteristics of actions and interactions within an environment, enabling counterfactual reasoning tailored to user-relevant features. Our experiments demonstrate that the approach produces consistent and meaningful counterfactuals while minimising the undesired side effects of token-level methods. We conduct experiments on text-based games and counterfactual text generation, while considering both token-level and latent-space interventions.

Machine learning systems increasingly make life-changing decisions about individuals, such as loan approvals, hiring, and cheating detection, raising a pressing question: how can individuals respond to negative decisions made by these opaque systems? While explainable artificial intelligence (XAI) has largely focused on algorithmic recourse -- helping individuals change their features to obtain a desired outcome -- the parallel problem of algorithmic contestability -- helping individuals review and correct erroneous algorithmic decisions -- has received far less attention, despite its central ethical and legal importance. We trace this neglect to the absence of clear formal definitions and a systematic operationalization of contestability as an algorithmic problem. To address it, we propose an operational definition of contestability as a natural complement to recourse: contestability starts from the presumption that a decision may be incorrect and focuses on identifying evidence to challenge and potentially overturn it, whereas recourse assumes the decision is valid and instead provides pathways for changing it. We show that standard XAI explanations, such as counterfactuals, LIME, or Anchors, even when combined with human intuitions about decision continuity or monotonicity, reveal only errors in the neighborhood of the individual, but provide insufficient grounds for overturning the decision at hand. Going thus beyond traditional XAI, we identify three types of evidence warranting reversal according to the decision maker's own ethical standards: predictive multiplicity, incorrect feature values, and neglected overruling evidence. We argue that these render decisions normatively indefensible and thus successfully contestable. Finally, we analyze how existing EU legislation connects to our framework and argue that individuals already hold some legal rights to these forms of evidence.

These appendices contain demonstrations of the results in the main text as well as additional technical notes.