Causal network discovery by iterative conditioning: comparison of algorithms

TL;DR

This paper compares various iterative conditioning algorithms for causal network discovery, analyzing their theoretical properties and computational demands, and proposes a hybrid method balancing accuracy and efficiency.

Contribution

It provides a comprehensive comparison of prominent algorithms for causal network discovery, highlighting their strengths, weaknesses, and proposing a hybrid approach for better performance.

Findings

Most algorithms have similar accuracy in causal detection.

Computational complexity varies significantly, from polynomial to exponential.

A hybrid approach offers a good balance between accuracy and efficiency.

Abstract

Estimating causal interactions in complex dynamical systems is an important problem encountered in many fields of current science. While a theoretical solution for detecting the causal interactions has been previously formulated in the framework of prediction improvement, it generally requires the computation of high-dimensional information functionals -- a situation invoking the curse of dimensionality with increasing network size. Recently, several methods have been proposed to alleviate this problem, based on iterative procedures for assessment of conditional (in)dependences. In the current work, we bring a comparison of several such prominent approaches. This is done both by theoretical comparison of the algorithms using a formulation in a common framework, and by numerical simulations including realistic complex coupling patterns. The theoretical analysis highlights the key similarities and differences between the algorithms, hinting on their comparative strengths and weaknesses. The method assumptions and specific properties such as false positive control and order dependence are discussed. Numerical simulations suggest that while the accuracy of most of the algorithms is almost indistinguishable, there are substantial differences in their computational demands, ranging theoretically from polynomial to exponential complexity, and leading to substantial differences in computation time in realistic scenarios depending on the density and size of networks. Based on analysis of the algorithms and numerical simulations, we propose a hybrid approach providing competitive accuracy with improved computational efficiency.