Causal discovery using compression-complexity measures.

Causal inference is one of the most fundamental problems across all domains of science. We address the problem of inferring a causal direction from two observed discrete symbolic sequences X and Y. We present a framework which relies on lossless compressors for inferring context-free grammars (CFGs) from sequence pairs and quantifies the extent to which the grammar inferred from one sequence compresses the other sequence. We infer X causes Y if the grammar inferred from X better compresses Y than in the other direction. To put this notion to practice, we propose three models that use the Compression-Complexity Measures (CCMs) - Lempel-Ziv (LZ) complexity and Effort-To-Compress (ETC) to infer CFGs and discover causal directions without demanding temporal structures. We evaluate these models on synthetic and real-world benchmarks and empirically observe performances competitive with current state-of-the-art methods. Lastly, we present two unique applications of the proposed models for causal inference directly from pairs of genome sequences belonging to the SARS-CoV-2 virus. Using numerous sequences, we show that our models capture causal information exchanged between genome sequence pairs, presenting novel opportunities for addressing key issues in sequence analysis to investigate the evolution of virulence and pathogenicity in future applications.