Understanding and identifying controlled direct effects (CDEs) is crucial across numerous scientific domains, including public health. While existing methods can identify these effects from causal directed acyclic graphs (DAGs), the true underlying structure is often unknown in practice. Essential graphs, which represent a Markov equivalence class of DAGs characterized by the same set of $d$-separations, provide a more practical and realistic alternative. However, learning the full essential graph is computationally intensive and typically depends on strong, untestable assumptions. In this work, we characterize a local class of graphs, defined relative to a target variable, that share a specific subset of $d$-separations, and introduce a graphical representation of this class, called the local essential graph (LEG). We then present LocPC, a novel algorithm designed to recover the LEG from an observed distribution using only local conditional independence tests. Building on LocPC, we propose LocPC-CDE, an algorithm that discovers the portion of the LEG that is both sufficient and necessary to identify a CDE, bypassing the need of retrieving the full essential graph. Compared to global methods, our algorithms require less conditional independence tests and operate under weaker assumptions while maintaining theoretical guarantees. We illustrate the effectiveness of our approach through simulation studies.

We will reflect this discussion in the paper.

Weaknesses: The paper emphasizes its focus on causal structure learning. In doing so it assumes "causal sufficiency", that is, it assumes that there are no latent confounders of the measured variables. Generally, there are many latent confounders of the measured variables in most domains. In the past 20 years, there has been substantial progress in developing graphical representations and algorithms for learning equivalence classes of causal networks from observational data. When causal sufficiency is assumed, the learning of DAG structure is generally called Bayesian network structure learning, not causal structural learning, as in the title of the paper. It would be helpful for the paper to more prominently highlight this assumption.

Understanding the causal interactions in simple brain tasks, such as face detection, remains a challenging and ambiguous process for researchers. In this study, we address this issue by employing a novel causal discovery method -- Directed Acyclic Graphs via M-matrices for Acyclicity (DAGMA) -- to investigate the causal structure of the brain's face-selective network and gain deeper insights into its mechanism. Using natural movie stimuli, we extract causal network of face-selective regions and analyze how frames containing faces influence this network. Our findings reveal that the presence of faces in the stimuli have causal effect both on the number and strength of causal connections within the network. Additionally, our results highlight the crucial role of subcortical regions in satisfying causal sufficiency, emphasizing its importance in causal studies of brain. This study provides a new perspective on understanding the causal architecture of the face-selective network of the brain, motivating further research on neural causality.

Causal discovery is essential for understanding complex systems, yet traditional methods often depend on strong, untestable assumptions, making the process challenging. Large Language Models (LLMs) present a promising alternative for extracting causal insights from text-based metadata, which consolidates domain expertise. However, LLMs are prone to unreliability and hallucinations, necessitating strategies that account for their limitations. One such strategy involves leveraging a consistency measure to evaluate reliability. Additionally, most text metadata does not clearly distinguish direct causal relationships from indirect ones, further complicating the inference of causal graphs. As a result, focusing on causal orderings, rather than causal graphs, emerges as a more practical and robust approach. We propose a novel method to derive a distribution of acyclic tournaments (representing plausible causal orders) that maximizes a consistency score. Our approach begins by computing pairwise consistency scores between variables, yielding a cyclic tournament that aggregates these scores. From this structure, we identify optimal acyclic tournaments compatible with the original tournament, prioritizing those that maximize consistency across all configurations. We tested our method on both classical and well-established bechmarks, as well as real-world datasets from epidemiology and public health. Our results demonstrate the effectiveness of our approach in recovering distributions causal orders with minimal error.