Path Weights, Networked Partial Correlations and their Application to the Analysis of Genetic Interactions
Alberto Roverato, Robert Castelo

Gene coexpression is a common feature employed in predicting buffering relationships that explain genetic interactions, which constitute an important mechanism behind the robustness of cells to genetic perturbations. The complete removal of such buffering connections impacts the entire molecular circuitry, ultimately leading to cellular death. Coexpression is commonly measured through Pearson correlation coefficients. However, Pearson correlation values are sensitive to indirect effects and often partial correlations are used instead. Yet, partial correlation values convey no information on the (linear) influence of the association within the entire multivariate system or, in other words, of the represented edge within the entire network. Jones and West (2005) showed that covariance can be decomposed into the weights of the paths that connect two variables within the corresponding undirected network. Here we provide a precise interpretation of path weights and show that, in the particular case of single-edge paths, this interpretation leads to a quantity we call networked partial correlation whose value depends on both the partial correlation between the intervening variables and their association with the rest of the multivariate system. We show that this new quantity correlates better with quantitative genetic interactions in yeast than classical coexpression measures.