Mean Field Variational Inference (MFVI) is widely understood to underestimate posterior variance. By analysing conjugate Bayesian Linear Regression (BLR), we show that this characterization is incomplete: while MFVI underestimates the variance in parameter space, it can overestimate the predictive variance compared to the exact posterior.
arXiv:2606. 25745v1 Announce Type: cross Abstract: Mean Field Variational Inference (MFVI) is widely understood to underestimate posterior variance.
arXiv:2410. 14843v4 Announce Type: replace-cross Abstract: 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.
arXiv:2606. 25882v1 Announce Type: new Abstract: DGPs are probabilistic models with remarkable prediction performance that concatenate GPs across several layers.
arXiv:2607. 25376v1 Announce Type: cross Abstract: In Bayesian neural networks (BNNs), variational inference is a widely adopted framework for modeling uncertainty in a distributional way, with the evidence lower bound (ELBO) serving as the standard objective function.
arXiv:2608.29349v1 Announce Type: new Abstract: Gaussian process (GP) regression with a single global GP (GP-glo) incurs cubic computational cost, limiting scalability to large datasets. Product-of-e...
The paper presents a tuning‑free empirical Bayes framework for Bayesian generalized linear models that uses a novel mean‑field variational inference algorithm. By estimating the prior within the VI procedure and optimizing the posterior mean directly, the method reduces optimization complexity and supports scalable solvers like L‑BFGS and stochastic gradient descent. Applied to sparse logistic regression, the approach shows superior predictive performance compared to existing methods.
The paper introduces a new variational inference framework that uses tangent transformations to handle strongly super‑Gaussian likelihoods across a wide range of probability models. By constructing tangent minorants of the log‑likelihood through convex duality, the method achieves conjugacy with Gaussian priors, enabling tractable inference where traditional approaches struggle. The authors provide algorithmic convergence guarantees and near‑parametric risk bounds, and demonstrate superior scalability and accuracy on both simulated and real‑world datasets compared to existing variational algorithms.
arXiv:2602. 19126v2 Announce Type: replace Abstract: We propose a robust Bayesian formulation of random feature (RF) regression that accounts explicitly for prior and likelihood misspecification via Huber-style contamination sets.
The paper tackles two shortcomings of Gaussian‑process based active learning: (1) the posterior variance is independent of observed values, reducing sensitivity to data structure, and (2) it over‑inflates variance near domain boundaries, causing excessive edge sampling. The authors propose a reconstruction‑driven design density that warps sampling toward regions where the posterior mean changes rapidly, and a geometric equalizer that corrects boundary bias. Experiments on sixteen synthetic and two real‑data benchmarks show that the equalizer consistently improves function reconstruction, while the warp further enhances performance by concentrating measurements where the target function varies most.
arXiv:2606. 07841v1 Announce Type: cross Abstract: Black-box variational inference (BBVI) is a methodology for posterior approximation that relies on stochastic optimization.
arXiv:2606. 01954v1 Announce Type: new Abstract: Implicit-process priors define distributions over functions through flexible generative mechanisms, making them attractive for Bayesian function-space modelling.
Hierarchical data is ubiquitous in the empirical sciences and is most commonly analyzed with generalized linear mixed-effects models (GLMMs). Bayesian inference for GLMMs yields calibrated uncertainty...