Operator Variational Inference
This work addresses limitations in variational inference for Bayesian inference practitioners, offering a more flexible framework with potential for improved approximations, though it appears incremental in building on existing optimization-based methods.
The authors tackled the problem of undesirable statistical properties in classical variational inference by designing variational objectives using operators, leading to a black box algorithm called operator variational inference (OPVI) that enables explicit tradeoffs between statistical and computational aspects, as illustrated on a mixture model and a generative image model.
Variational inference is an umbrella term for algorithms which cast Bayesian inference as optimization. Classically, variational inference uses the Kullback-Leibler divergence to define the optimization. Though this divergence has been widely used, the resultant posterior approximation can suffer from undesirable statistical properties. To address this, we reexamine variational inference from its roots as an optimization problem. We use operators, or functions of functions, to design variational objectives. As one example, we design a variational objective with a Langevin-Stein operator. We develop a black box algorithm, operator variational inference (OPVI), for optimizing any operator objective. Importantly, operators enable us to make explicit the statistical and computational tradeoffs for variational inference. We can characterize different properties of variational objectives, such as objectives that admit data subsampling---allowing inference to scale to massive data---as well as objectives that admit variational programs---a rich class of posterior approximations that does not require a tractable density. We illustrate the benefits of OPVI on a mixture model and a generative model of images.