Causal Graph Recovery in Neuroimaging through Answer Set Programming
Mohammadsajad Abavisani, Kseniya Solovyeva, David Danks, Vince Calhoun, Sergey Plis
TL;DR
This paper introduces a novel approach using answer set programming to recover causal graphs from sub-sampled neuroimaging data, improving accuracy and efficiency over existing methods.
Contribution
The study presents a new ASP-based method that accounts for sub-sampling effects, providing more accurate causal graph recovery and a framework for expert selection of possible graphs.
Findings
Achieved 12% average improvement in F1 score over established methods.
State-of-the-art precision and recall in causal graph reconstruction.
Robust performance across varying sub-sampling rates.
Abstract
Learning graphical causal structures from time series data presents significant challenges, especially when the measurement frequency does not match the causal timescale of the system. This often leads to a set of equally possible underlying causal graphs due to information loss from sub-sampling (i.e., not observing all possible states of the system throughout time). Our research addresses this challenge by incorporating the effects of sub-sampling in the derivation of causal graphs, resulting in more accurate and intuitive outcomes. We use a constraint optimization approach, specifically answer set programming (ASP), to find the optimal set of answers. ASP not only identifies the most probable underlying graph, but also provides an equivalence class of possible graphs for expert selection. In addition, using ASP allows us to leverage graph theory to further prune the set of possible…
Peer Reviews
Decision·ICLR 2026 Conference Desk Rejected Submission
A quite clear question, clear method, and clear assessment
1. The authors claim that the method works for neuroimaging data, but they only test for fMRI. Does this method extend to other modalities e.g., fNIRS? 2. What happens if we remove the constraints of 10-30% density? If the method fails to converge, are we truly finding a causal structure or do we have some level of circularity? 3. When does the method fail completely? I suspect if the u (delay) is varied and long, the method would completely fail. This is important because we know the undersam
* An idea to increase the robustness of the method by recovering multiple solutions * An interesting idea to use domain knowledge (about density) as a constraint * A very interesting point is made in Section 3.5, where the authors propose to integrate into the process of recovering a graph not only the output graph of some algorithm but also the uncertainty about the edge or knowledge about the strength of the relation. Such an approach seems like a step in a good direction, not to "waste" any i
* Subsections 3.2 and 3.4 both have a C(G) function, but they have different forms. Can you clarify which one you used? * There is no discussion about tuning parameters of this method like δ or λ_d and λ_c. * For all experiments, there is no hyperparameter tuning procedure described. However, since this is a heuristics method, I think it would be important to describe how robust they are, what is needed to tune them, and how general these hyperparameters are. * Subsection 4.1 - How did you selec
1. Exceptional clarity and structure. The exposition is unusually well-organized for an fMRI causal paper—each method component (density constraints, adaptive weighting, SCC-DAG decomposition, meta-solver function) is clearly explained and mathematically specified. 2. Strong contextual grounding. The introduction and background display excellent awareness of prior work in fMRI causal discovery—Granger, MVAR, FASK, PCMCI, RASL, and newer deep learning variants. The authors accurately summarize th
1. Limited empirical scale. Current experiments involve small networks (≤ 10 nodes in ASP runs, up to 50 nodes in discussion) . While understandable, it would help to show scaling behavior or runtime analysis beyond toy graphs. 2. Quantitative evaluation scope. Most comparisons are against the Sanchez-Romero synthetic dataset and a few standard algorithms. A more diverse benchmark (e.g., larger synthetic networks, real multi-subject fMRI) would better test generality. 3. Lack of undersampled-d
1. The paper takes undersampling into account when doing causal discovery and directly encodes the mathematical structure of undersampling (compressed paths and latent confounding) into the ASP formulation. 2. RnR retrieves all graphs within a small cost tolerance, effectively approximating the Markov equivalence class of causal structures compatible with data, which provides more robust solutions. 3. On simulated and real fMRI data, RnR improves F1-scores by an average of ≈12% over state-of-
1. RnR does not discover causal edges directly from raw time series. It starts from an input graph generated by another causal discovery algorithm (Granger, PCMCI, FASK, etc.). If the initial graph is not accurate, the output of RnR may be affected. 2. RnR needs to solve a combinatoric problem using ASP. For graphs with a lot of variables, this optimization problem may be intractable.
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Taxonomy
TopicsLogic, Reasoning, and Knowledge · Advanced Graph Neural Networks · Multimodal Machine Learning Applications
MethodsSparse Evolutionary Training