In this SQUARE talk, Ola will discuss how variational inference can be understood as projections that decide the visible shape of a posterior.
SPEAKER: Ola Rønning, Postdoc at ITU.
ABSTRACT: Exact posterior inference is rarely available in Bayesian modeling. Variational methods provide a tractable substitute. However, this substitution is not neutral: the choice of approximation determines which posterior structure is even representable within the chosen approximation family.
While this perspective is implicit in much of the variational inference literature, it is rarely made explicit. In this talk, I frame variational inference methods as acting like geometric projections that shape the visible posterior. Through canonical examples, we will examine the three primary projection regimes: degenerate projection (MAP estimation), factorized projection (mean-field variational inference) and empirical measure projection (Stein variational gradient descent).
The goal is not to introduce new methods, but to clarify how different approximation choices systematically constrain what can be inferred and what is made invisible.