# Vistla: identifying influence paths with information theory

## TL;DR

Vistla is a new method that uses information theory to identify influence paths in complex systems, offering a clearer and more interpretable alternative to traditional network inference methods.

## Contribution

Vistla introduces a novel approach combining tri-variate mutual information and a generalized widest path problem for tracking influence paths.

## Key findings

- Vistla provides a streamlined and interpretable output compared to dense network inference methods.
- The method is effective in both synthetic and real-world applications.
- Vistla can be used in machine learning pipelines and for mediation analysis.

## Abstract

It is a challenging task to decipher the mechanisms of a complex system from observational data, especially in biology, where systems are sophisticated, measurements coarse, and multi-modality common. The typical approaches of inferring a network of relationships between a system’s components struggle with the quality and feasibility of estimation, as well as with the interpretability of the results they yield. Said issues can be avoided, however, when dealing with a simpler problem of tracking only the influence paths, defined as circuits relying on the information of an experimental perturbation as it spreads through the system. Such an approach can be formalized with information theory and leads to a relatively streamlined, interpretable output, in contrast to the incomprehensibly dense ‘haystack’ networks produced by typical tools.

Following this idea, the paper introduces Vistla, a novel method built around tri-variate mutual information and data processing inequality, combined with a higher-order generalization of the widest path problem. Vistla can be used standalone, in a machine learning pipeline to aid interpretability, or as a tool for mediation analysis; the paper demonstrates its efficiency both in synthetic and real-world problems.

The R package implementing the method is available at https://gitlab.com/mbq/vistla, as well as on CRAN.