Dictionary Based Pattern Entropy for Causal Direction Discovery

arXiv:2603.04473v1 Announce Type: new
Abstract: Discovering causal direction from temporal observational data is particularly challenging for symbolic sequences, where functional models and noise assumptions are often unavailable. We propose a novel emph{Dictionary Based Pattern Entropy ($DPE$)} framework that infers both the direction of causation and the specific subpatterns driving changes in the effect variable. The framework integrates emph{Algorithmic Information Theory} (AIT) and emph{Shannon Information Theory}. Causation is interpreted as the emergence of compact, rule based patterns in the candidate cause that systematically constrain the effect. $DPE$ constructs direction-specific dictionaries and quantifies their influence using entropy-based measures, enabling a principled link between deterministic pattern structure and stochastic variability. Causal direction is inferred via a minimum-uncertainty criterion, selecting the direction exhibiting stronger and more consistent pattern-driven organization. As summarized in Table 7, $DPE$ consistently achieves reliable performance across diverse synthetic systems, including delayed bit-flip perturbations, AR(1) coupling, 1D skew-tent maps, and sparse processes, outperforming or matching competing AIT-based methods ($ETC_E$, $ETC_P$, $LZ_P$). In biological and ecological datasets, performance is competitive, while alternative methods show advantages in specific genomic settings. Overall, the results demonstrate that minimizing pattern level uncertainty yields a robust, interpretable, and broadly applicable framework for causal discovery.