Causal-Copilot: An Autonomous Causal Analysis Agent

Causal analysis plays a foundational role in scientific discovery and reliable decision-making, yet it remains largely inaccessible to domain experts due to its conceptual and algorithmic complexity. This disconnect between causal methodology and practical usability presents a dual challenge: domain experts are unable to leverage recent advances in causal learning, while causal researchers lack broad, real-world deployment to test and refine their methods. To address this, we introduce Causal-Copilot, an autonomous agent that operationalizes expert-level causal analysis within a large language model framework. Causal-Copilot automates the full pipeline of causal analysis for both tabular and time-series data -- including causal discovery, causal inference, algorithm selection, hyperparameter optimization, result interpretation, and generation of actionable insights. It supports interactive refinement through natural language, lowering the barrier for non-specialists while preserving methodological rigor. By integrating over 20 state-of-the-art causal analysis techniques, our system fosters a virtuous cycle -- expanding access to advanced causal methods for domain experts while generating rich, real-world applications that inform and advance causal theory. Empirical evaluations demonstrate that Causal-Copilot achieves superior performance compared to existing baselines, offering a reliable, scalable, and extensible solution that bridges the gap between theoretical sophistication and real-world applicability in causal analysis. A live interactive demo of Causal-Copilot is available at https://causalcopilot.com/.

Causal DAG Summarization (Full Version)

Causal inference aids researchers in discovering cause-and-effect relationships, leading to scientific insights. Accurate causal estimation requires identifying confounding variables to avoid false discoveries. Pearl's causal model uses causal DAGs to identify confounding variables, but incorrect DAGs can lead to unreliable causal conclusions. However, for high dimensional data, the causal DAGs are often complex beyond human verifiability. Graph summarization is a logical next step, but current methods for general-purpose graph summarization are inadequate for causal DAG summarization. This paper addresses these challenges by proposing a causal graph summarization objective that balances graph simplification for better understanding while retaining essential causal information for reliable inference. We develop an efficient greedy algorithm and show that summary causal DAGs can be directly used for inference and are more robust to misspecification of assumptions, enhancing robustness for causal inference. Experimenting with six real-life datasets, we compared our algorithm to three existing solutions, showing its effectiveness in handling high-dimensional data and its ability to generate summary DAGs that ensure both reliable causal inference and robustness against misspecifications.

Meta-Dependence in Conditional Independence Testing

Constraint-based causal discovery algorithms utilize many statistical tests for conditional independence to uncover networks of causal dependencies. These approaches to causal discovery rely on an assumed correspondence between the graphical properties of a causal structure and the conditional independence properties of observed variables, known as the causal Markov condition and faithfulness. Finite data yields an empirical distribution that is "close" to the actual distribution. Across these many possible empirical distributions, the correspondence to the graphical properties can break down for different conditional independencies, and multiple violations can occur at the same time. We study this "meta-dependence" between conditional independence properties using the following geometric intuition: each conditional independence property constrains the space of possible joint distributions to a manifold. The "meta-dependence" between conditional independences is informed by the position of these manifolds relative to the true probability distribution. We provide a simple-to-compute measure of this meta-dependence using information projections and consolidate our findings empirically using both synthetic and real-world data.

Can LLMs Leverage Observational Data? Towards Data-Driven Causal Discovery with LLMs

Causal discovery traditionally relies on statistical methods applied to observational data, often requiring large datasets and assumptions about underlying causal structures. Recent advancements in Large Language Models (LLMs) have introduced new possibilities for causal discovery by providing domain expert knowledge. However, it remains unclear whether LLMs can effectively process observational data for causal discovery. In this work, we explore the potential of LLMs for data-driven causal discovery by integrating observational data for LLM-based reasoning. Specifically, we examine whether LLMs can effectively utilize observational data through two prompting strategies: pairwise prompting and breadth first search (BFS)-based prompting. In both approaches, we incorporate the observational data directly into the prompt to assess LLMs' ability to infer causal relationships from such data. Experiments on benchmark datasets show that incorporating observational data enhances causal discovery, boosting F1 scores by up to 0.11 point using both pairwise and BFS LLM-based prompting, while outperforming traditional statistical causal discovery baseline by up to 0.52 points. Our findings highlight the potential and limitations of LLMs for data-driven causal discovery, demonstrating their ability to move beyond textual metadata and effectively interpret and utilize observational data for more informed causal reasoning. Our studies lays the groundwork for future advancements toward fully LLM-driven causal discovery.

From Observation to Orientation: an Adaptive Integer Programming Approach to Intervention Design

Using both observational and experimental data, a causal discovery process can identify the causal relationships between variables. A unique adaptive intervention design paradigm is presented in this work, where causal directed acyclic graphs (DAGs) are for effectively recovered with practical budgetary considerations. In order to choose treatments that optimize information gain under these considerations, an iterative integer programming (IP) approach is proposed, which drastically reduces the number of experiments required. Simulations over a broad range of graph sizes and edge densities are used to assess the effectiveness of the suggested approach. Results show that the proposed adaptive IP approach achieves full causal graph recovery with fewer intervention iterations and variable manipulations than random intervention baselines, and it is also flexible enough to accommodate a variety of practical constraints.

eST$^2$ Miner -- Process Discovery Based on Firing Partial Orders

Process discovery generates process models from event logs. Traditionally, an event log is defined as a multiset of traces, where each trace is a sequence of events. The total order of the events in a sequential trace is typically based on their temporal occurrence. However, real-life processes are partially ordered by nature. Different activities can occur in different parts of the process and, thus, independently of each other. Therefore, the temporal total order of events does not necessarily reflect their causal order, as also causally unrelated events may be ordered in time. Only partial orders allow to express concurrency, duration, overlap, and uncertainty of events. Consequently, there is a growing need for process mining algorithms that can directly handle partially ordered input. In this paper, we combine two well-established and efficient algorithms, the eST Miner from the process mining community and the Firing LPO algorithm from the Petri net community, to introduce the eST$^2$ Miner. The eST$^2$ Miner is a process discovery algorithm that can directly handle partially ordered input, gives strong formal guarantees, offers good runtime and excellent space complexity, and can, thus, be used in real-life applications.

A Systematic Evaluation of Knowledge Graph Embeddings for Gene-Disease Association Prediction

Discovery gene-disease links is important in biology and medicine areas, enabling disease identification and drug repurposing. Machine learning approaches accelerate this process by leveraging biological knowledge represented in ontologies and the structure of knowledge graphs. Still, many existing works overlook ontologies explicitly representing diseases, missing causal and semantic relationships between them. The gene-disease association problem naturally frames itself as a link prediction task, where embedding algorithms directly predict associations by exploring the structure and properties of the knowledge graph. Some works frame it as a node-pair classification task, combining embedding algorithms with traditional machine learning algorithms. This strategy aligns with the logic of a machine learning pipeline. However, the use of negative examples and the lack of validated gene-disease associations to train embedding models may constrain its effectiveness. This work introduces a novel framework for comparing the performance of link prediction versus node-pair classification tasks, analyses the performance of state of the art gene-disease association approaches, and compares the different order-based formalizations of gene-disease association prediction. It also evaluates the impact of the semantic richness through a disease-specific ontology and additional links between ontologies. The framework involves five steps: data splitting, knowledge graph integration, embedding, modeling and prediction, and method evaluation. Results show that enriching the semantic representation of diseases slightly improves performance, while additional links generate a greater impact. Link prediction methods better explore the semantic richness encoded in knowledge graphs. Although node-pair classification methods identify all true positives, link prediction methods outperform overall.

Constraint-based causal discovery with tiered background knowledge and latent variables in single or overlapping datasets

In this paper we consider the use of tiered background knowledge within constraint based causal discovery. Our focus is on settings relaxing causal sufficiency, i.e. allowing for latent variables which may arise because relevant information could not be measured at all, or not jointly, as in the case of multiple overlapping datasets. We first present novel insights into the properties of the 'tiered FCI' (tFCI) algorithm. Building on this, we introduce a new extension of the IOD (integrating overlapping datasets) algorithm incorporating tiered background knowledge, the 'tiered IOD' (tIOD) algorithm. We show that under full usage of the tiered background knowledge tFCI and tIOD are sound, while simple versions of the tIOD and tFCI are sound and complete. We further show that the tIOD algorithm can often be expected to be considerably more efficient and informative than the IOD algorithm even beyond the obvious restriction of the Markov equivalence classes. We provide a formal result on the conditions for this gain in efficiency and informativeness. Our results are accompanied by a series of examples illustrating the exact role and usefulness of tiered background knowledge.

Causal Discovery and Counterfactual Reasoning to Optimize Persuasive Dialogue Policies

Tailoring persuasive conversations to users leads to more effective persuasion. However, existing dialogue systems often struggle to adapt to dynamically evolving user states. This paper presents a novel method that leverages causal discovery and counterfactual reasoning for optimizing system persuasion capability and outcomes. We employ the Greedy Relaxation of the Sparsest Permutation (GRaSP) algorithm to identify causal relationships between user and system utterance strategies, treating user strategies as states and system strategies as actions. GRaSP identifies user strategies as causal factors influencing system responses, which inform Bidirectional Conditional Generative Adversarial Networks (BiCoGAN) in generating counterfactual utterances for the system. Subsequently, we use the Dueling Double Deep Q-Network (D3QN) model to utilize counterfactual data to determine the best policy for selecting system utterances. Our experiments with the PersuasionForGood dataset show measurable improvements in persuasion outcomes using our approach over baseline methods. The observed increase in cumulative rewards and Q-values highlights the effectiveness of causal discovery in enhancing counterfactual reasoning and optimizing reinforcement learning policies for online dialogue systems.

An extensive simulation study evaluating the interaction of resampling techniques across multiple causal discovery contexts

Despite the accelerating presence of exploratory causal analysis in modern science and medicine, the available non-experimental methods for validating causal models are not well characterized. One of the most popular methods is to evaluate the stability of model features after resampling the data, similar to resampling methods for estimating confidence intervals in statistics. Many aspects of this approach have received little to no attention, however, such as whether the choice of resampling method should depend on the sample size, algorithms being used, or algorithm tuning parameters. We present theoretical results proving that certain resampling methods closely emulate the assignment of specific values to algorithm tuning parameters. We also report the results of extensive simulation experiments, which verify the theoretical result and provide substantial data to aid researchers in further characterizing resampling in the context of causal discovery analysis. Together, the theoretical work and simulation results provide specific guidance on how resampling methods and tuning parameters should be selected in practice.