Rates of Convergence of Generalised Variational Inference Posteriors under Prior Misspecification
We prove rates of convergence and robustness to prior misspecification within a Generalised Variational Inference (GVI) framework with bounded divergences. This addresses a significant open challenge for GVI and Federated GVI that employ a different divergence to the Kullback-Leibler under prior misspecification, operate within a subset of possible probability measures, and result in intractable posteriors. Our theoretical contributions extend to misspecified priors that lead to inconsistent Bayes posteriors. In particular, we are able to establish sufficient conditions for existence and uniqueness of GVI posteriors on arbitrary Polish spaces, prove that the GVI posterior measure concentrates on a neighbourhood of loss minimisers, and extend this to rates of convergence regardless of the prior measure.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Scalable Semi-Modular Inference with Variational Meta-Posteriors
The Cut posterior and related Semi-Modular Inference are Generalised Bayes methods for Modular Bayesian evidence combination. Analysis is broken up over modular sub-models of the joint posterior distribution. Model-missp…
Bayesian InferenceMeta-LearningConvergence Rates of Variational Posterior Distributions
We study convergence rates of variational posterior distributions for nonparametric and high-dimensional inference. We formulate general conditions on prior, likelihood, and variational class that characterize the conver…
On the Robustness to Misspecification of $α$-Posteriors and Their Variational Approximations
$\alpha$-posteriors and their variational approximations distort standard posterior inference by downweighting the likelihood and introducing variational approximation errors. We show that such distortions, if tuned appr…
Frequentist Consistency of Generalized Variational Inference
This paper investigates Frequentist consistency properties of the posterior distributions constructed via Generalized Variational Inference (GVI). A number of generic and novel strategies are given for proving consistenc…
Variational InferenceDenoising Diffusion Variational Inference: Diffusion Models as Expressive Variational Posteriors
We propose denoising diffusion variational inference (DDVI), a black-box variational inference algorithm for latent variable models which relies on diffusion models as flexible approximate posteriors. Specifically, our m…
DenoisingVariational Inference