Variational approximation to posterior distributions has gained an enormous popularity in recent years as a computationally convenient alternative for Bayesian Inference. Beyond conjugate models, Variational approximations are challenging to implement and accordingly numerous majorization / minorization approaches are developed. In this poster, we focus on the tangent transform approach based on convex duality in generalized linear models. While such approaches and their variants are extremely popular, there are no theoretical guarantees on whether the Variational algorithm converges to the true parameter. In light of a recent developments of convergence of EM algorithm, we provide theoretical guarantees of the convergence of the Variational updates based on tangent transform approximations. In particular, we show that for random design matrix the updates converge to the truth with high probability.