Causal Graph

Causal graphs in text are typically populated by observable, predefined events. In contrast, we study implicit causal graph construction from text by treating each described cause-effect pair as the begin- and endpoint of an underlying latent causal graph and using large language models (LLMs) to infer intermediate causal events. We compare end-to-end graph construction with methods that frame the task as causal chain discovery. In the latter, graphs are built either by aggregating inferred chains or by progressively expanding partial chains through an iterative search process. We further explore Wisdom of the Crowd extensions that access causal knowledge from multiple LLMs in post-hoc aggregation and collaborative inference settings. We analyze trade-offs among these approaches and evaluate the validity of inferred causal relations using a manually curated database of 1,560 scientifically validated causal pairs. This database-based evaluation is proposed as reliable, resource-efficient, and transferable to settings where ground-truth graphs are unavailable.

We introduce causal-temporal event graphs (CTEGs) as a formal model for fully resolved recursive agent execution records under single-parenthood causal semantics. We formalise direct event emissions and recursive subagent invocations as extension procedures on generic typed temporal graphs and show that the recursive closure $\mathscr{E}_\infty$ of the induced maximal dynamics starting from single causal roots consists entirely of finite sequences of CTEGs. A CTEG is a rooted arborescence whose nodes carry timestamps and event types, subject to the constraint that timestamps be strictly increasing along causal paths. We realise $\mathscr{E}_\infty$ as the increasing union of a recursive hierarchy $\mathscr{E}_0 \subseteq \mathscr{E}_1 \subseteq \cdots$ of agent execution levels parametrised by recursion depth, which is recognised as the ascending Kleene chain of a monotone operator $\varphi$ admitting $\mathscr{E}_\infty$ as its least fixed point. Although the introduction of the full hierarchy is natural, stabilisation occurs already at $\mathscr{E}_1$ if one insists that the internal construction of a subagent execution trace be a delegated and opaque computational unit. The CTEG formalism supports compositional construction of globally well-formed execution traces from local agent behaviour without centralised coordination, preserves well-formedness under partial execution failure, and admits a natural relational database encoding. The arborescent structure of CTEGs is further compatible with cryptographic Merkle tree commitments for tamper-evident session verification.

Understanding climate change requires reasoning over complex causal networks. Yet, existing causal discovery datasets predominantly capture explicit, direct causal relations. We introduce ClimateCause, a manually expert-annotated dataset of higher-order causal structures from science-for-policy climate reports, including implicit and nested causality. Cause-effect expressions are normalized and disentangled into individual causal relations to facilitate graph construction, with unique annotations for cause-effect correlation, relation type, and spatiotemporal context. We further demonstrate ClimateCause's value for quantifying readability based on the semantic complexity of causal graphs underlying a statement. Finally, large language model benchmarking on correlation inference and causal chain reasoning highlights the latter as a key challenge.

Selective conformal prediction can yield substantially tighter uncertainty sets when we can identify calibration examples that are exchangeable with the test example. In interventional settings, such as perturbation experiments in genomics, exchangeability often holds only within subsets of interventions that leave a target variable "unaffected" (e.g., non-descendants of an intervened node in a causal graph). We study the practical regime where this invariance structure is unknown and must be estimated from data. Our main result quantifies how coverage degrades when the estimated safe calibration set accidentally includes interventions that affect the target, and gives a conservative correction when an upper bound on this error is available. Rather than learning a full causal graph, we learn only the intervention-target relationships needed to choose calibration interventions. We give algorithms for this partial learning task and evaluate them on synthetic structural equation models and Replogle K562 CRISPR-interference data, where the experiments illustrate synthetic gains from selective calibration and finite-sample tradeoffs on real perturbation screens.

Algorithmic decisions about individuals require predictions that are not only accurate but also fair with respect to sensitive attributes such as gender and race. Causal notions of fairness align with legal requirements, yet many methods assume access to detailed knowledge of the underlying causal graph, which is a demanding assumption in practice. We propose a learning framework that achieves interventional fairness by leveraging a causal graph over \textit{clusters of variables}, which is substantially easier to estimate than a variable-level graph. With possible \textit{adjustment cluster sets} identified from such a cluster causal graph, our framework trains a prediction model by reducing the worst-case discrepancy between interventional distributions across these sets. To this end, we develop a computationally efficient barycenter kernel maximum mean discrepancy (MMD) that scales favorably with the number of sensitive attribute values. Extensive experiments show that our framework strikes a better balance between fairness and accuracy than existing approaches, highlighting its effectiveness under limited causal graph knowledge.

Estimating causal quantities traditionally relies on bespoke estimators tailored to specific assumptions. Recently proposed Causal Foundation Models (CFMs) promise a more unified approach by amortising causal discovery and inference in a single step. However, in their current state, they do not allow for the incorporation of any domain knowledge, which can lead to suboptimal predictions. We bridge this gap by introducing methods to condition CFMs on causal information, such as the causal graph or more readily available ancestral information. When access to complete causal graph information is too strict a requirement, our approach also effectively leverages partial causal information. We systematically evaluate conditioning strategies and find that injecting learnable biases into the attention mechanism, together with a graph-convolutional encoder, is a highly effective method to utilise full and partial causal information. Our experiments show that this conditioning allows a general-purpose CFM to match the performance of specialised models trained on specific causal structures. Overall, our approach addresses a central hurdle on the path towards all-in-one causal foundation models: the capability to answer causal queries in a data-driven manner while effectively leveraging any amount of domain expertise.

Retrieval augmented generation (RAG) has enhanced large language models by enabling access to external knowledge, with graph-based RAG emerging as a powerful paradigm for structured retrieval and reasoning. However, existing graph-based methods often over-rely on entity-centric node matching and lack explicit causal modeling, leading to unfaithful or spurious answers. Prior attempts to incorporate causality are typically limited to local or single-document contexts and also suffer from information isolation that arises from modular graph structures, which hinders scalability and cross-module causal reasoning. To address these challenges, we propose CausalRAG2, a framework that rethinks knowledge organization for graph-based RAG through causal gating across hierarchical modules. CausalRAG2 explicitly models causal relationships to suppress spurious correlations while enabling scalable reasoning over large-scale knowledge graphs. We also introduce HolisQA, a benchmark for holistic comprehension beyond entity-centric matching. Extensive experiments demonstrate that CausalRAG2 consistently outperforms competitive graph-based RAG baselines across multiple datasets and evaluation metrics. Our work establishes a principled foundation for structured, scalable, and causally grounded RAG systems. Our code and HolisQA benchmark are available at https://github.com/Pwnb/CausalRAG2.

Failures are the norm in highly complex and heterogeneous devices spanning the distributed computing continuum (DCC), from resource-constrained IoT and edge nodes to high-performance computing systems. Ensuring reliability and global consistency across these layers remains a major challenge, especially for AI-driven workloads requiring real-time, adaptive coordination. This work-in-progress paper introduces a Probabilistic Active Inference Resilience Agent (PAIR-Agent) to achieve resilience in DCC systems. PAIR-Agent performs three core operations: (i) constructing a causal fault graph from device logs, (ii) identifying faults while managing certainties and uncertainties using Markov blankets and the free energy principle, and (iii) autonomously healing issues through active inference. Through continuous monitoring and adaptive reconfiguration, the agent maintains service continuity and stability under diverse failure conditions. Theoretical validations confirm the reliability and effectiveness of the proposed framework.

Uncovering the causal mechanisms of complex real-world systems remains a significant challenge, as these systems often entail high data collection costs and involve unknown interventions. We introduce MetaCaDI, the first framework to cast the identification of unknown interventions as a meta-learning problem, explicitly leveraging a jointly learned causal graph. MetaCaDI is a Bayesian framework that learns a shared causal structure across multiple environments and is optimized to rapidly adapt to new, few-shot intervention target identification tasks. A key innovation is our model's analytical adaptation, which uses a closed-form solution to bypass expensive and potentially unstable gradient-based bilevel optimization. Extensive experiments on synthetic and complex gene expression data demonstrate that MetaCaDI significantly outperforms state-of-the-art methods. It excels at identifying intervention targets from as few as 3 samples - where existing methods collapse to random chance - while robustly recovering the shared causal graph, proving its effectiveness in data-scarce scenarios.

We study the propagation of outliers in cyclic causal graphs with linear structural equations, tracing them back to one or several "root cause" nodes. We show that it is possible to identify a short list of potential root causes provided that the perturbation is sufficiently strong and propagates according to the same structural equations as in the normal mode. This shortlist consists of the true root causes together with those of its parents lying on a cycle with the root cause. Notably, our method does not require prior knowledge of the causal graph and yields encouraging results on simulated data and real data from biology and cloud computing.

Data fusion, the process of combining observational and experimental data, can enable the identification of causal effects that would otherwise remain non-identifiable. Although identification algorithms have been developed for specific scenarios, do-calculus remains the only general-purpose tool for causal data fusion, particularly when variables are present in some data sources but not others. However, approaches based on do-calculus may encounter computational challenges as the number of variables increases and the causal graph grows in complexity. Consequently, there exists a need to reduce the size of such models while preserving the essential features. For this purpose, we propose pruning (removing unnecessary variables) and clustering (combining variables) as preprocessing operations for causal data fusion. We generalize earlier results on a single data source and derive conditions for applying pruning and clustering in the case of multiple data sources. We give sufficient conditions for inferring the identifiability or non-identifiability of a causal effect in a larger graph based on a smaller graph and show how to obtain the corresponding identifying functional for identifiable causal effects. Examples from epidemiology and social science demonstrate the use of the results.

Fair machine learning seeks to identify and mitigate biases in predictions against unfavorable populations characterized by demographic attributes, such as race and gender. Recent research has extended fairness to graph data, such as social networks, but many studies neglect the causal relationships among data instances. This paper addresses a prevalent challenge in many fair machine learning research, which typically assumes independent and identically distributed (IID) data, from the causal perspective. Specifically, this work targets the circumstance where nodes with different neighborhood structures follow different causal mechanisms, violating the invariance assumptions required for classical structural causal models and do-calculus. We base our research on the Network Structural Causal Model (NSCM) framework and develop a Message Passing Variational Autoencoder for Causal Inference (MPVA) to compute interventional distributions for causally fair node classification. We establish theoretical soundness under two conditions: Decomposability and Graph Independence. These conditions formalize when causal mechanism heterogeneity can be overcome by constructing a structural representation that restores invariance and facilitates the computation of interventional distributions using do-calculus in non-IID settings. Empirical evaluations on semi-synthetic and real-world datasets demonstrate that MPVA outperforms conventional methods by effectively approximating interventional distributions and mitigating bias. Our findings demonstrate the potential of causality-based fairness in complex ML applications and motivate future work on relaxing the classic assumptions in algorithmic fairness.

Causal knowledge can be used to support decision-making problems. This has been recognized in the causal bandits literature, where a causal (multi-armed) bandit is characterized by a causal graphical model and a target variable. The arms are then interventions on the causal model, and rewards are samples of the target variable. Causal bandits were originally studied with a focus on hard interventions. We focus instead on cases where the arms are conditional interventions, which more accurately model many real-world decision-making problems by allowing the value of the intervened variable to be chosen based on the observed values of other variables. This paper presents a graphical characterization of the minimal set of nodes guaranteed to contain the optimal conditional intervention, which maximizes the expected reward. We then propose an efficient algorithm with a time complexity of $O(|V| + |E|)$ to identify this minimal set of nodes. We prove that the graphical characterization and the proposed algorithm are correct. Finally, we empirically demonstrate that our algorithm significantly prunes the search space and substantially accelerates convergence rates when integrated into standard multi-armed bandit algorithms.

We study a class of reinforcement learning (RL) tasks where the objective of the agent is to accomplish temporally extended goals. In this setting, a common approach is to represent the tasks as deterministic finite automata (DFA) and integrate them into the state-space for RL algorithms. However, while these machines model the reward function, they often overlook the causal knowledge about the environment. To address this limitation, we propose the Temporal-Logic-based Causal Diagram (TL-CD) in RL, which captures the temporal causal relationships between different properties of the environment. We exploit the TL-CD to devise an RL algorithm in which an agent requires significantly less exploration of the environment. To this end, based on a TL-CD and a task DFA, we identify configurations where the agent can determine the expected rewards early during an exploration. Through a series of case studies, we demonstrate the benefits of using TL-CDs, particularly the faster convergence of the algorithm to an optimal policy due to reduced exploration of the environment.