Construction of synergy networks from gene expression data related to disease

MAXENT3D_PID: An Estimator for the Maximum-Entropy Trivariate Partial Information Decomposition

Partial information decomposition (PID) separates the contributions of sources about a target into unique, redundant, and synergistic components of information. In essence, PID answers the question of “who knows what” of a system of random variables and hence has applications to a wide spectrum of fields ranging from social to biological sciences. The paper presents MaxEnt3D_Pid, an algorithm that computes the PID of three sources, based on a recently-proposed maximum entropy measure, using convex optimization (cone programming). We describe the algorithm and its associated software utilization and report the results of various experiments assessing its accuracy. Moreover, the paper shows that a hierarchy of bivariate and trivariate PID allows obtaining the finer quantities of the trivariate partial information measure.

Construction and Analysis of Protein-Protein Interaction Network of Heroin Use Disorder

Heroin use disorder (HUD) is a complex disease resulting from interactions among genetic and other factors (e.g., environmental factors). The mechanism of HUD development remains unknown. Newly developed network medicine tools provide a platform for exploring complex diseases at the system level. This study proposes that protein–protein interactions (PPIs), particularly those among proteins encoded by casual or susceptibility genes, are extremely crucial for HUD development. The giant component of our constructed PPI network comprised 111 nodes with 553 edges, including 16 proteins with large degree (k) or high betweenness centrality (BC), which were further identified as the backbone of the network. JUN with the largest degree was suggested to be central to the PPI network associated with HUD. Moreover, PCK1 with the highest BC and MAPK14 with the secondary largest degree and 9^th highest BC might be involved in the development HUD and other substance diseases.

Information Decomposition of Target Effects from Multi-Source Interactions: Perspectives on Previous, Current and Future Work

The formulation of the Partial Information Decomposition (PID) framework by Williams and Beer in 2010 attracted a significant amount of attention to the problem of defining redundant (or shared), unique and synergistic (or complementary) components of mutual information that a set of source variables provides about a target. This attention resulted in a number of measures proposed to capture these concepts, theoretical investigations into such measures, and applications to empirical data (in particular to datasets from neuroscience). In this Special Issue on “Information Decomposition of Target Effects from Multi-Source Interactions” at Entropy, we have gathered current work on such information decomposition approaches from many of the leading research groups in the field. We begin our editorial by providing the reader with a review of previous information decomposition research, including an overview of the variety of measures proposed, how they have been interpreted and applied to empirical investigations. We then introduce the articles included in the special issue one by one, providing a similar categorisation of these articles into: i. proposals of new measures; ii. theoretical investigations into properties and interpretations of such approaches, and iii. applications of these measures in empirical studies. We finish by providing an outlook on the future of the field.

The Identity of Information: How Deterministic Dependencies Constrain Information Synergy and Redundancy

Understanding how different information sources together transmit information is crucial in many domains. For example, understanding the neural code requires characterizing how different neurons contribute unique, redundant, or synergistic pieces of information about sensory or behavioral variables. Williams and Beer (2010) proposed a partial information decomposition (PID) that separates the mutual information that a set of sources contains about a set of targets into nonnegative terms interpretable as these pieces. Quantifying redundancy requires assigning an identity to different information pieces, to assess when information is common across sources. Harder et al. (2013) proposed an identity axiom that imposes necessary conditions to quantify qualitatively common information. However, Bertschinger et al. (2012) showed that, in a counterexample with deterministic target-source dependencies, the identity axiom is incompatible with ensuring PID nonnegativity. Here, we study systematically the consequences of information identity criteria that assign identity based on associations between target and source variables resulting from deterministic dependencies. We show how these criteria are related to the identity axiom and to previously proposed redundancy measures, and we characterize how they lead to negative PID terms. This constitutes a further step to more explicitly address the role of information identity in the quantification of redundancy. The implications for studying neural coding are discussed.