Fig. 1: Dependency decomposition in a multi-variate system using pairwise and network models.

a Simplified Partial information decomposition (PID) framework^35,36 based definition of types of information that multiple sources can have about a target (see Methods and Supp. Fig S1). b A synthetic ensemble of eight neural variables with two kinds of dependencies – unique or shared – between seven source variables (black) and one target variable (cyan). All interactions are excitatory. Strength of dependencies is determined by model parameters P_unique and P_shared (see “Methods”). c1, c2 Information fraction (reduction in the proportion of total entropy) as a function of parameters (P_unique, P_shared) that control unique and shared information in the model. Information fraction estimation as a function of P_shared (c2) was performed using a subset of variables in the simulated network for computational efficiency, (see Methods). c3 Normalized total mutual information, measured by uncertainty coefficient, as a function of the sum of model parameters (P_unique,P_shared) that varied unique and shared components of mutual information in a monotonic way. d Coefficients of a pairwise model (univariate logistic regression (UR)) as a function of P_unique and P_shared. White arrow provides a visual guide for direction of highest change in coefficients. e Coefficients of a network model (LASSO multivariate regularized regression (RR)) as a function of P_unique and P_shared. White arrow provides a visual guide for direction of highest change in coefficients. f Application of pairwise and network-based statistical models for approximate information decomposition in an example multivariate system. It illustrates interpretation of the modulation of these dependencies using the PID framework. g Schema for utilizing pairwise and network methods for the estimation of total (brown) and unique (green) information modulation respectively, and to infer the modulation of shared information (purple) based on the PID framework. Shaded blocks indicate indeterminate modulation direction of shared information in the network.