# Transfer Entropy: where Shannon meets Turing

## TL;DR

This paper explores the mathematical foundations of transfer entropy, demonstrating its ability to identify causal relations in multivariate time series and deriving key theoretical properties like the Data Processing Inequality.

## Contribution

It introduces a tensor formalism for transfer entropy, showing that bivariate analysis can suffice for causal inference in certain multivariate systems.

## Key findings

- Tensor formalism clarifies transfer entropy's properties.
- Bivariate analysis can distinguish true from false relations.
- Derived the Data Processing Inequality for transfer entropy.

## Abstract

Transfer entropy is capable of capturing nonlinear source-destination relations between multi-variate time series. It is a measure of association between source data that are transformed into destination data via a set of linear transformations between their probability mass functions. The resulting tensor formalism is used to show that in specific cases, e.g., in the case the system consists of three stochastic processes, bivariate analysis suffices to distinguish true relations from false relations. This allows us to determine the causal structure as far as encoded in the probability mass functions of noisy data. The tensor formalism was also used to derive the Data Processing Inequality for transfer entropy.