Despite the growing deployment of network representation throughout psychological sciences, the question of whether and how networks can systematically describe the effects of psychological interventions remains elusive. Towards this end, we capitalize on recent breakthrough in network control theory, the engineering study of networked interventions, to investigate a representative psychological attitude modification experiment. This study examined 30 healthy participants who answered 11 questions about their attitude toward eating meat. They then received 11 arguments to challenge their attitude on the questions, after which they were asked again the same set of questions. Using this data, we constructed networks that quantify the connections between the responses and tested: 1) if the observed psychological effect, in terms of sensitivity and specificity, relates to the regional network topology as described by control theory, 2) if the size of change in responses relates to whole-network topology that quantifies the “ease” of change as described by control theory, and 3) if responses after intervention could be predicted based on formal results from control theory. We found that 1) the interventions that had higher regional topological relevance (the so-called controllability scores) had stronger effect (r > 0.5), the intervention sensitivities were systematically lower for the interventions that were “easier to control” (r = -0.49), and that the model offered substantial prediction accuracy (r = 0.36). Finally, we compared results based on subjective as well as data-driven models and found that, across all tests, the results from the data-driven approach explained a larger size of effect. Taken together, our results suggest that psychological interventions can be studied using network control theory and that data-driven models provide a reliable medium.

Recent progress in network sciences has made it possible to apply key findings from control theory to the study of networks. Referred to as network control theory, this framework describes how the interactions between interconnected system elements and external energy sources, potentially constrained by different optimality criteria, result in complex network behavior. A typical example is the quantification of the functional role certain brain regions or symptoms play in shaping the temporal dynamics of brain activity or the clinical course of a disease, a property that is quantified in terms of the so-called controllability metrics. Critically though, contrary to the engineering context in which control theory was originally developed, a mathematical understanding of the network nodes and connections in neurosciences cannot be assumed. For instance, in the case of psychological systems such as those studied to understand psychiatric disorders, a potentially large set of related variables are unknown. As such, while the measures offered by network control theory would be mathematically correct, in that they can be calculated with high precision, they could have little translational values with respect to their putative role suggested by controllability metrics. It is therefore critical to understand if and how the controllability metrics estimated over subnetworks would deviate, if access to the complete set of variables, as is common in neurosciences, cannot be taken for granted. In this paper, we use a host of simulations based on synthetic as well as structural MRI data to study the potential deviation of controllability metrics in sub- compared to the full networks. Specifically, we estimate average- and modal-controllability, two of the most widely used controllability measures in neurosciences, in a large number of settings where we systematically vary network type, network size, and edge density. We find out, across all network types we test, that average and modal controllability are systematically, over- or underestimated depending on the number of nodes in the sub- and full network and the edge density. Finally, we provide formal theoretical proof that our observations generalize to any network type and discuss the ramifications of this systematic bias and potential solutions to alleviate the problem.

Recent progress in network sciences has made it possible to apply key findings from control theory to the study of networks. Referred to as network control theory, this framework describes how the interactions between interconnected system elements and external energy sources, potentially constrained by different optimality criteria, result in complex network behavior. A typical example is the quantification of the functional role certain brain regions or symptoms play in shaping the temporal dynamics of brain activity or the clinical course of a disease, a property that is quantified in terms of the so-called controllability metrics. Critically though, contrary to the engineering context in which control theory was originally developed, a mathematical understanding of the network nodes and connections in neurosciences cannot be assumed. For instance, in the case of psychological systems such as those studied to understand the psychiatric disorders, a potentially large set variables are unknown. As such, while the measures offered by network control theory would be mathematically correct, in that they can be calculated with high precision, they could have little translational values with respect to their putative role suggested by controllability metrics. It is therefore critical to understand if and how the controllability metrics computer over subnetworks would deviate, if access to the complete set of variables, as in neurosciences, cannot be taken for granted. In this paper, we use a host of simulations based on synthetic as well as structural MRI data to study the potential deviation of controllability metrics in sub- compared to the full networks. Specifically, we estimate average- and modal-controllability, two of the most widely used controllability measures in neurosciences, in a large number of settings where we systematically vary network type, network size, and edge density. We find out, across all network types we test, that average and modal controllability are systematically, either over- or underestimated depending on the number of nodes in the sub- and full network and the edge density. Finally, we provide a formal theoretical proof that our observations generalize to any network type and discuss the ramifications of this systematic bias and potential solutions to alleviate the problem.