A Game-theoretical Framework for Causal Inference: With Applications in Artificial Neural Networks and Large-scale Models of Brain Dynamics

Abstract

Causal inference is at the core of neuroscientific method. From hands-on experimental manipulations to complex models, many frameworks aim at uncovering the causal relationships among brain regions, and between brain and behavior. This large variety of tools, however, comes with the cost of conceptual confusions, since researchers use the same wording to describe different concepts. This confusion is particularly visible, and to some extent troubling, in interdisciplinary sciences dealing with highly sophisticated systems, e.g., neuroscience deciphering the brain.

In this thesis, I aim to provide a coherent, axiomatic, and rigorous conceptual framework based on game theory for causal inference with many desirable properties. This framework, known as Multi-perturbation Shapley value analysis (MSA) employs exhaustive multi-site manipulation of the system to uncover the exact causal contribution of each element to the collectively produced function. After reviewing the current developments in epistemology of causation, methodological advancements of brain manipulation, causal modeling, game theory, network science, and dynamical systems theory, I test MSA on in-silico models such as artificial neural networks (ANNs) and large-scale models of brain dynamics.

I first ask how MSA differs from the conventional lesioning approach in neuroscience, in which only one site is perturbed at the same time. I show that even in small and presumably simplistic ANNs the standard framework produces biased results due to complex higher-order interactions among different elements. However, MSA captures these interactions and provides the correct causal map of the network.

Using a second ANN, I ask if it is possible to infer the causal contribution of its elements from their recorded activity profiles, as done extensively in neuroscience. I show that neural activity is a poor indicator of causal contribution due to downstream nonlinear transformations.

Lastly, I use large-scale models of brain dynamics to investigate how different brain regions causally influence each other. I compare underlying network differences, local models of dynamics, graph theoretical measures, and models of communication in networks. I show that, firstly, some simple models of communication dynamics successfully capture the amount of influence among nodes. These models fall into the category of “broadcasting models” in which the signal is permeated in the network, using multiple pathways to reach the target. I then show that more complicated models of local dynamics add little explanatory power, suggesting that the total amount of influence from a node to another is largely defined by structure. I then show a handful of brain regions use their topological privileges, that is, their extensive connectivity, to influence regions that are not directly connected to them.

Together, I show that not only is MSA a versatile framework for causal inference in neuroscience, but also it can be used to infer causal links in other systems such as ANNs. With these findings and an open-source Python library, I encourage neuroscientists and scientists from other disciplines, including computational sociology, bioinformatics, explainable artificial intelligence, philosophy, and complexity science to consider MSA as a mathematically sound framework for causal inference.