Algorithmic Identification of Essential Exogenous Nodes for Causal Sufficiency in Brain Networks

TL;DR

This paper introduces an algorithmic method to identify essential exogenous nodes in brain networks, ensuring causal sufficiency, and validates it using human connectome data to reveal confounders in neural interactions.

Contribution

The study presents a novel algorithm combining independence testing, Kolmogorov-Smirnov analysis, and NF-iVAE to identify confounders in brain causal networks, addressing a key gap in causal sufficiency assumptions.

Findings

Dorsal regions act as confounders for visual networks.

Interactions exist between dorsal and ventral brain regions.

Method shows consistent results across multiple runs.

Abstract

In the investigation of any causal mechanisms, such as the brain's causal networks, the assumption of causal sufficiency plays a critical role. Notably, neglecting this assumption can result in significant errors, a fact that is often disregarded in the causal analysis of brain networks. In this study, we propose an algorithmic identification approach for determining essential exogenous nodes that satisfy the critical need for causal sufficiency to adhere to it in such inquiries. Our approach consists of three main steps: First, by capturing the essence of the Peter-Clark (PC) algorithm, we conduct independence tests for pairs of regions within a network, as well as for the same pairs conditioned on nodes from other networks. Next, we distinguish candidate confounders by analyzing the differences between the conditional and unconditional results, using the Kolmogorov-Smirnov test. Subsequently, we utilize Non-Factorized identifiable Variational Autoencoders (NF-iVAE) along with the Correlation Coefficient index (CCI) metric to identify the confounding variables within these candidate nodes. Applying our method to the Human Connectome Projects (HCP) movie-watching task data, we demonstrate that while interactions exist between dorsal and ventral regions, only dorsal regions serve as confounders for the visual networks, and vice versa. These findings align consistently with those resulting from the neuroscientific perspective. Finally, we show the reliability of our results by testing 30 independent runs for NF-iVAE initialization.