We study asymptotic properties of expectation propagation (EP) -- a method\nfor approximate inference originally developed in the field of machine\nlearning. Applied to generalized linear models, EP iteratively computes a\nmultivariate Gaussian approximation to the exact posterior distribution. The\ncomputational complexity of the repeated update of covariance matrices severely\nlimits the application of EP to large problem sizes. In this study, we present\na rigorous analysis by means of free probability theory that allows us to\novercome this computational bottleneck if specific data matrices in the problem\nfulfill certain properties of asymptotic freeness. We demonstrate the relevance\nof our approach on the gene selection problem of a microarray dataset.\n