Abstract: Gaussian graphical models (GGMs) have been investigated to infer dependence (or network) structure among high-dimensional data by estimating a precision matrix. However, while many estimation methods for GGM have been developed, methods for testing the equality of two precision matrices are still limited. Because testing the equality of the precision matrix depends on other given precision matrices, we develop a weighted conditional network testing for considering other given precision matrices information and also provide theoretical properties. None of the existing methods can be applied to test conditional differences when other networks are conditionally given and different. We demonstrate the advantage of our approach using a simulation study and genetic pathway analysis.

Key words and phrases: Conditional difference, Gaussian graphical model, precision matrix.