Causal discovery using compression-complexity measures

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