RnR: a meta-solver for causal discovery in undersampled time series data

Learning directed causal graphs from time-series data poses significant challenges, especially in fMRI where slow sampling rate obscures fast neural interactions. This temporal mismatch leads to undersampling, which can make multiple graphs equally plausible. We address this problem by explicitly modeling undersampling effects when recovering causal graphs. Our approach employs answer set programming (ASP) to enforce domain-specific constraints and optimize soft observational constraints, thereby identifying a Markov equivalence class for the resulting graph solutions. By customizing an ASP solver to collect multiple near-optimal solutions, we obtain not only the single best-fitting graph but an equivalence class of high-scoring graphs for expert consideration. This method, called Real-world noisy RASL (RnR), can also act as a meta-solver: it refines the output of other causal discovery algorithms by accounting for undersampling biases. In synthetic data and empirical brain network data, RnR produces more accurate causal graphs than state-of-the-art methods. When applied as a meta-solver (refining outputs of existing algorithms), it improves F1 scores by an average of 46\% over baseline methods; on standalone synthetic data benchmarks, it achieves a 64\% improvement. We demonstrate that RnR is robust to varying undersampling rates, maintaining high precision and recall even as sampling becomes more sparse, whereas baseline methods degrade significantly. Finally, we test RnR on real-world settings where ground truth connectivity is unknown such as human brain fMRI data, showing that incorporating undersampling-aware constraints via ASP yields more reliable and interpretable brain connectivity estimates from fMRI time series, bridging the gap between neural dynamics and observational data.