Lower Bounds on the Size of Markov Equivalence Classes

Causal discovery algorithms typically recover causal graphs only up to their Markov equivalence classes unless additional parametric assumptions are made. The sizes of these equivalence classes reflect the limits of what can be learned about the underlying causal graph from purely observational data. Under the assumptions of acyclicity, causal sufficiency, and a uniform model prior, Markov equivalence classes are known to be small on average. In this paper, we show that this is no longer the case when any of these assumptions is relaxed. Specifically, we prove exponentially large lower bounds for the expected size of Markov equivalence classes in three settings: sparse random directed acyclic graphs, uniformly random acyclic directed mixed graphs, and uniformly random directed cyclic graphs.

Active Inference AI Systems for Scientific Discovery

The rapid evolution of artificial intelligence has led to expectations of transformative scientific discovery, yet current systems remain fundamentally limited by their operational architectures, brittle reasoning mechanisms, and their separation from experimental reality. Building on earlier work, we contend that progress in AI-driven science now depends on closing three fundamental gaps -- the abstraction gap, the reasoning gap, and the reality gap -- rather than on model size/data/test time compute. Scientific reasoning demands internal representations that support simulation of actions and response, causal structures that distinguish correlation from mechanism, and continuous calibration. We define active inference AI systems for scientific discovery as those that (i) maintain long-lived research memories grounded in causal self-supervised foundation models, (ii) symbolic or neuro-symbolic planners equipped with Bayesian guardrails, (iii) grow persistent knowledge graphs where thinking generates novel conceptual nodes, reasoning establishes causal edges, and real-world interaction prunes false connections while strengthening verified pathways, and (iv) refine their internal representations through closed-loop interaction with both high-fidelity simulators and automated laboratories - an operational loop where mental simulation guides action and empirical surprise reshapes understanding. In essence, we outline an architecture where discovery arises from the interplay between internal models that enable counterfactual reasoning and external validation that grounds hypotheses in reality. It is also argued that the inherent ambiguity in feedback from simulations and experiments, and underlying uncertainties makes human judgment indispensable, not as a temporary scaffold but as a permanent architectural component.

Tagged for Direction: Pinning Down Causal Edge Directions with Precision

Not every causal relation between variables is equal, and this can be leveraged for the task of causal discovery. Recent research shows that pairs of variables with particular type assignments induce a preference on the causal direction of other pairs of variables with the same type. Although useful, this assignment of a specific type to a variable can be tricky in practice. We propose a tag-based causal discovery approach where multiple tags are assigned to each variable in a causal graph. Existing causal discovery approaches are first applied to direct some edges, which are then used to determine edge relations between tags. Then, these edge relations are used to direct the undirected edges. Doing so improves upon purely type-based relations, where the assumption of type consistency lacks robustness and flexibility due to being restricted to single types for each variable. Our experimental evaluations show that this boosts causal discovery and that these high-level tag relations fit common knowledge.

Uncovering Bias Paths with LLM-guided Causal Discovery: An Active Learning and Dynamic Scoring Approach

Causal discovery (CD) plays a pivotal role in understanding the mechanisms underlying complex systems. While recent algorithms can detect spurious associations and latent confounding, many struggle to recover fairness-relevant pathways in realistic, noisy settings. Large Language Models (LLMs), with their access to broad semantic knowledge, offer a promising complement to statistical CD approaches, particularly in domains where metadata provides meaningful relational cues. Ensuring fairness in machine learning requires understanding how sensitive attributes causally influence outcomes, yet CD methods often introduce spurious or biased pathways. We propose a hybrid LLM-based framework for CD that extends a breadth-first search (BFS) strategy with active learning and dynamic scoring. Variable pairs are prioritized for LLM-based querying using a composite score based on mutual information, partial correlation, and LLM confidence, improving discovery efficiency and robustness. To evaluate fairness sensitivity, we construct a semi-synthetic benchmark from the UCI Adult dataset, embedding a domain-informed causal graph with injected noise, label corruption, and latent confounding. We assess how well CD methods recover both global structure and fairness-critical paths. Our results show that LLM-guided methods, including the proposed method, demonstrate competitive or superior performance in recovering such pathways under noisy conditions. We highlight when dynamic scoring and active querying are most beneficial and discuss implications for bias auditing in real-world datasets.

Conditional Local Independence Testing with Application to Dynamic Causal Discovery

In this note, we extend the conditional local independence testing theory developed in Christgau et al. (2024) to Ito processes. The result can be applied to causal discovery in dynamic systems.

Time-Varying Home Field Advantage in Football: Learning from a Non-Stationary Causal Process

In sports analytics, home field advantage is a robust phenomenon where the home team wins more games than the away team. However, discovering the causal factors behind home field advantage presents unique challenges due to the non-stationary, time-varying environment of sports matches. In response, we propose a novel causal discovery method, DYnamic Non-stAtionary local M-estimatOrs (DYNAMO), to learn the time-varying causal structures of home field advantage. DYNAMO offers flexibility by integrating various loss functions, making it practical for learning linear and non-linear causal structures from a general class of non-stationary causal processes. By leveraging local information, we provide theoretical guarantees for the identifiability and estimation consistency of non-stationary causal structures without imposing additional assumptions. Simulation studies validate the efficacy of DYNAMO in recovering time-varying causal structures. We apply our method to high-resolution event data from the 2020-2021 and 2021-2022 English Premier League seasons, during which the former season had no audience presence. Our results reveal intriguing, time-varying, team-specific field advantages influenced by referee bias, which differ significantly with and without crowd support. Furthermore, the time-varying causal structures learned by our method improve goal prediction accuracy compared to existing methods.

Paths to Causality: Finding Informative Subgraphs Within Knowledge Graphs for Knowledge-Based Causal Discovery

Inferring causal relationships between variable pairs is crucial for understanding multivariate interactions in complex systems. Knowledge-based causal discovery -- which involves inferring causal relationships by reasoning over the metadata of variables (e.g., names or textual context) -- offers a compelling alternative to traditional methods that rely on observational data. However, existing methods using Large Language Models (LLMs) often produce unstable and inconsistent results, compromising their reliability for causal inference. To address this, we introduce a novel approach that integrates Knowledge Graphs (KGs) with LLMs to enhance knowledge-based causal discovery. Our approach identifies informative metapath-based subgraphs within KGs and further refines the selection of these subgraphs using Learning-to-Rank-based models. The top-ranked subgraphs are then incorporated into zero-shot prompts, improving the effectiveness of LLMs in inferring the causal relationship. Extensive experiments on biomedical and open-domain datasets demonstrate that our method outperforms most baselines by up to 44.4 points in F1 scores, evaluated across diverse LLMs and KGs. Our code and datasets are available on GitHub: https://github.com/susantiyuni/path-to-causality

Supernova Event Dataset: Interpreting Large Language Model's Personality through Critical Event Analysis

Large Language Models (LLMs) are increasingly integrated into everyday applications. As their influence grows, understanding their decision making and underlying personality becomes essential. In this work, we interpret model personality using our proposed Supernova Event Dataset, a novel dataset with diverse articles spanning biographies, historical events, news, and scientific discoveries. We use this dataset to benchmark LLMs on extracting and ranking key events from text, a subjective and complex challenge that requires reasoning over long-range context and modeling causal chains. We evaluate small models like Phi-4, Orca 2, and Qwen 2.5, and large, stronger models such as Claude 3.7, Gemini 2.5, and OpenAI o3, and propose a framework where another LLM acts as a judge to infer each model's personality based on its selection and classification of events. Our analysis shows distinct personality traits: for instance, Orca 2 demonstrates emotional reasoning focusing on interpersonal dynamics, while Qwen 2.5 displays a more strategic, analytical style. When analyzing scientific discovery events, Claude Sonnet 3.7 emphasizes conceptual framing, Gemini 2.5 Pro prioritizes empirical validation, and o3 favors step-by-step causal reasoning. This analysis improves model interpretability, making them user-friendly for a wide range of diverse applications.

Learning Causality for Modern Machine Learning

In the past decades, machine learning with Empirical Risk Minimization (ERM) has demonstrated great capability in learning and exploiting the statistical patterns from data, or even surpassing humans. Despite the success, ERM avoids the modeling of causality the way of understanding and handling changes, which is fundamental to human intelligence. When deploying models beyond the training environment, distribution shifts are everywhere. For example, an autopilot system often needs to deal with new weather conditions that have not been seen during training, An Al-aided drug discovery system needs to predict the biochemical properties of molecules with respect to new viruses such as COVID-19. It renders the problem of Out-of-Distribution (OOD) generalization challenging to conventional machine learning. In this thesis, we investigate how to incorporate and realize the causality for broader tasks in modern machine learning. In particular, we exploit the invariance implied by the principle of independent causal mechanisms (ICM), that is, the causal mechanisms generating the effects from causes do not inform or influence each other. Therefore, the conditional distribution between the target variable given its causes is invariant under distribution shifts. With the causal invariance principle, we first instantiate it to graphs -- a general data structure ubiquitous in many real-world industry and scientific applications, such as financial networks and molecules. Then, we shall see how learning the causality benefits many of the desirable properties of modern machine learning, in terms of (i) OOD generalization capability; (ii) interpretability; and (iii) robustness to adversarial attacks. Realizing the causality in machine learning, on the other hand, raises a dilemma for optimization in conventional machine learning, as it often contradicts the objective of ERM...

Nonlinear Causal Discovery for Grouped Data

Inferring cause-effect relationships from observational data has gained significant attention in recent years, but most methods are limited to scalar random variables. In many important domains, including neuroscience, psychology, social science, and industrial manufacturing, the causal units of interest are groups of variables rather than individual scalar measurements. Motivated by these applications, we extend nonlinear additive noise models to handle random vectors, establishing a two-step approach for causal graph learning: First, infer the causal order among random vectors. Second, perform model selection to identify the best graph consistent with this order. We introduce effective and novel solutions for both steps in the vector case, demonstrating strong performance in simulations. Finally, we apply our method to real-world assembly line data with partial knowledge of causal ordering among variable groups.