New Variational Inference Framework with 135-Page Convergence Guarantee

Variational inference (VI) is a key alternative to MCMC for scalable Bayesian computation, but existing methods often rely on rigid model-specific formulations or stochastic black-box optimization. This paper introduces a principled alternative: a generalized tangent approximation framework designed for the broad class of 'strongly super-Gaussian' likelihoods. The approach uses convex duality to construct tangent minorants of the log-likelihood, effectively inducing conjugacy with Gaussian priors even in models where posterior inference is typically intractable. This geometric perspective enables structured, deterministic optimization rather than black-box sampling.

The authors provide rigorous theoretical guarantees that are uncommon in VI literature: algorithmic convergence proofs under mild data-generating assumptions and near-minimax optimal bounds for variational risk. These results ensure that the approximation quality scales properly with sample size and model complexity. Empirical evaluations on simulated and real-world datasets—including scenarios that challenge current state-of-the-art VI methods—demonstrate superior scalability and ability to recover complex underlying structures across diverse application domains.