Discovering pair-wise genetic interactions: an information theory-based approach.

in PloS one (2014), 9(3), 92310

Phenotypic variation, including that which underlies health and disease in humans, results in part from multiple interactions among both genetic variation and environmental factors. While diseases or ... [more ▼]

Phenotypic variation, including that which underlies health and disease in humans, results in part from multiple interactions among both genetic variation and environmental factors. While diseases or phenotypes caused by single gene variants can be identified by established association methods and family-based approaches, complex phenotypic traits resulting from multi-gene interactions remain very difficult to characterize. Here we describe a new method based on information theory, and demonstrate how it improves on previous approaches to identifying genetic interactions, including both synthetic and modifier kinds of interactions. We apply our measure, called interaction distance, to previously analyzed data sets of yeast sporulation efficiency, lipid related mouse data and several human disease models to characterize the method. We show how the interaction distance can reveal novel gene interaction candidates in experimental and simulated data sets, and outperforms other measures in several circumstances. The method also allows us to optimize case/control sample composition for clinical studies. [less ▲]

Relations between the set-complexity and the structure of graphs and their sub-graphs

in EURASIP Journal on Bioinformatics and Systems Biology (2012), 13

We describe some new conceptual tools for the rigorous, mathematical description of the “set-complexity” of graphs. This set-complexity has been shown previously to be a useful measure for analyzing some ... [more ▼]

We describe some new conceptual tools for the rigorous, mathematical description of the “set-complexity” of graphs. This set-complexity has been shown previously to be a useful measure for analyzing some biological networks, and in discussing biological information in a quantitative fashion. The advances described here allow us to define some significant relationships between the set-complexity measure and the structure of graphs, and of their component sub-graphs. We show here that modular graph structures tend to maximize the set-complexity of graphs. We point out the relationship between modularity and redundancy, and discuss the significance of set-complexity in this regard. We specifically discuss the relationship between complexity and entropy in the case of complete-bipartite graphs, and present a new method for constructing highly complex, binary graphs. These results can be extended to the case of ternary graphs, and to other multi-edge graphs, which are fundamentally more relevant to biological structures and systems. Finally, our results lead us to an approach for extracting high complexity modular graphs from large, noisy graphs with low information content. We illustrate this approach with two examples. [less ▲]

Complexity of Networks II: The Set Complexity of Edge-Colored Graphs

in Complexity (2012), 17(5), 23-36

We previously introduced the concept of “set-complexity”, based on a context-dependent measure of information, and used this concept to describe the complexity of gene interaction networks. In the ... [more ▼]

We previously introduced the concept of “set-complexity”, based on a context-dependent measure of information, and used this concept to describe the complexity of gene interaction networks. In the previous paper in this series we analyzed the set-complexity of binary graphs. Here we extend this analysis to graphs with multi-colored edges that more closely match biological structures like the gene interaction networks. All highly complex graphs by this measure exhibit a modular structure. A principal result of this work is that for the most complex graphs of a given size the number of edge colors is equal to the number of “modules” of the graph. Complete multipartite graphs (CMGs) are defined and analyzed, and the relation between complexity and structure of these graphs is examined in detail. We establish that the mutual information between any two nodes in a CMG can be fully expressed in terms of entropy, and present an explicit expression for the set complexity of CMGs (Theorem 3). An algorithm for generating highly complex graphs from CMGs is described. We establish several theorems relating these concepts and connecting complex graphs with a variety of practical network properties. In exploring the relation between symmetry and complexity we use the idea of a similarity matrix and its spectrum for highly complex graphs. [less ▲]

Tree-Based computation in probalistic models

Doctoral thesis (2010)

Functions on Probabilistic Graphical Models

in Proceedings of the International Multiconference on Computer Science and Information Technology IMCSIT 2009 (2009)