Reconstruction of biological networks from profiling data is one of the most challenges in systems biology. Methods that use some measures in information theory to reconstruct local relationships in biological networks are often preferred over others due to their simplicity and low computation cost. Present mutual information-based methods cannot detect as well as provide relationships that take into account more than two variables (called multivariate relationships or
-wise relationships). Some previous studies have tried to extend mutual information from two to multiple variables; however the interpretation of these extensions is not clear. We introduce a novel interpretation and visualization of mutual information between two variables. With the new interpretation, we then extend mutual information to multiple variables that can capture different categories of multivariate relationships. We illustrate the prediction performance of these multivariate mutual information measures in reconstructing three-variable relationships on different benchmark networks.
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