Related papers: Stability of Mean-Field 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 consistency, relying on the…

We revisit Markowitz's mean-variance portfolio selection model by considering a distributionally robust version, where the region of distributional uncertainty is around the empirical measure and the discrepancy between probability measures…

Mean-field variational inference is one of the most popular approaches to inference in discrete random fields. Standard mean-field optimization is based on coordinate descent and in many situations can be impractical. Thus, in practice,…

Leveraging well-established MCMC strategies, we propose MCMC-interactive variational inference (MIVI) to not only estimate the posterior in a time constrained manner, but also facilitate the design of MCMC transitions. Constructing a…

Vanilla variational inference finds an optimal approximation to the Bayesian posterior distribution, but even the exact Bayesian posterior is often not meaningful under model misspecification. We propose predictive variational inference…

This paper is concerned with the approximation of probability distributions known up to normalization constants, with a focus on Bayesian inference for large-scale inverse problems in scientific computing. In this context, key challenges…

One of the core problems of modern statistics is to approximate difficult-to-compute probability densities. This problem is especially important in Bayesian statistics, which frames all inference about unknown quantities as a calculation…

We present stability estimates for the inverse source problem of the stochastic Helmholtz equation in two and three dimensions by either near-field or far-field data. The random source is assumed to be a microlocally isotropic generalized…

In Bayesian analysis, the posterior follows from the data and a choice of a prior and a likelihood. One hopes that the posterior is robust to reasonable variation in the choice of prior and likelihood, since this choice is made by the…

A new (unadjusted) Langevin Monte Carlo (LMC) algorithm with improved rates in total variation and in Wasserstein distance is presented. All these are obtained in the context of sampling from a target distribution $\pi$ that has a density…

Predicting extreme events is important in many applications in risk analysis. The extreme-value theory suggests modelling extremes by max-stable distributions. The Bayesian approach provides a natural framework for statistical prediction.…

We prove that, given a mean-field location-scale variational family, black-box variational inference (BBVI) with the reparametrization gradient converges at a rate that is nearly independent of explicit dimension dependence. Specifically,…

We consider Bayesian variable selection for binary outcomes under a probit link with a spike-and-slab prior on the regression coefficients. Motivated by the computational challenges encountered by Markov chain Monte Carlo (MCMC) samplers in…

Envelope models provide a sufficient dimension reduction framework for multivariate regression analysis. Bayesian inference for these models has been developed primarily using Markov chain Monte Carlo (MCMC) methods. Specifically, Gibbs…

We consider a mean-field control problem in which admissible controls are required to be adapted to the common noise filtration. The main objective is to show how the mean-field control problem can be approximates by time consistent…

We introduce and investigate a notion of multivalued $\lambda$-dissipative probability vector field (MPVF) in the Wasserstein space $\mathcal{P}_2(\mathsf X)$ of Borel probability measures on a Hilbert space $\mathsf X$. Taking inspiration…

Black-box variational inference (BBVI) now sees widespread use in machine learning and statistics as a fast yet flexible alternative to Markov chain Monte Carlo methods for approximate Bayesian inference. However, stochastic optimization…

Automatic differentiation variational inference (ADVI) offers fast and easy-to-use posterior approximation in multiple modern probabilistic programming languages. However, its stochastic optimizer lacks clear convergence criteria and…

Variational regression methods are an increasingly popular tool for their efficient estimation of complex. Given the mixed model representation of penalized effects, additive regression models with smoothed effects and scalar-on-function…

One-step generative modeling has emerged as a leading approach to amortize the inference cost of diffusion and flow-matching models. Among distillation-free methods, MeanFlow training is notoriously unstable, with non-decreasing loss and…