Causal Discovery using Compression-Complexity Measures

TL;DR

This paper introduces a novel method for causal inference between discrete sequences using compression-based measures, demonstrating competitive performance and applications in viral genome analysis.

Contribution

It proposes a new framework leveraging lossless compression to infer causal directions from symbolic sequences, including three models based on CCMs and applications to SARS-CoV-2 genomes.

Findings

Models perform competitively with state-of-the-art methods.

Effective in inferring causal directions without temporal information.

Applied successfully to genome sequences for viral analysis.

Abstract

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 a large number of sequences, we show that our models capture directed causal information exchange between sequence pairs, presenting novel opportunities for addressing key issues such as contact-tracing, motif discovery, evolution of virulence and pathogenicity in future applications.