The paper investigates how fast predictive regret guarantees of exact Bayesian online learning can be maintained when using approximate posterior methods. It establishes a general theorem linking the cumulative cost of posterior approximation to the contraction radius of the exact Gibbs posterior and the Wasserstein distance between approximate and exact posteriors. Three concrete online learning scenarios—linear models, infinite‑dimensional exponential families, and Gaussian process regression—illustrate that appropriately accurate approximations (projected Langevin, truncation, and sparse variational posteriors) preserve fast regret bounds while reducing computational demands.
By Ilsang Ohn
The paper introduces a structured posterior‑correction framework that blends a tractable Gaussian reference with data‑driven corrections learned via diffusion models. After applying mean correction and covariance calibration, the diffusion model focuses on a low‑dimensional subspace that captures discrepancies from the Gaussian reference, while the remaining space stays Gaussian. Experiments on three scientific inference tasks show that these corrections recover hidden modes, improve sample structure, and reduce prediction error compared to the Gaussian reference, with trade‑offs between accuracy and computational cost relative to full‑field generative models.
By Tobias Weber, Carla Sagebiel, Philipp Hennig
arXiv:2511. 16340v2 Announce Type: replace Abstract: Efficient Gaussian process (GP) inference is critical for sequential decision-making tasks such as active learning, online prediction, and Bayesian optimization.
By Alan Yufei Dong, Jihao Andreas Lin, Jos\'e Miguel Hern\'andez-Lobato
arXiv:2607. 24583v1 Announce Type: new Abstract: Large scale Bayesian nonparametrics (BNP) learner such as Stochastic Variational Inference (SVI) can handle datasets with large class number and large training size at fractional cost.
By Kart-Leong Lim
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.
By Dongyue Xie, Matthew Stephens
arXiv:2602. 10204v2 Announce Type: replace Abstract: We introduce MVN-Grad (Momentum on Variance-Normalized Gradients), an Adam-style optimizer that improves stability and performance by combining two complementary ideas: variance-based normalization and momentum applied after normalization.
By Francisco Patitucci, Aryan Mokhtari
The paper extends the classical conjugate Bayesian framework by leveraging the Fenchel‑Young inequality to define a generalized evidence lower bound that transcends the usual KL geometry. This leads to a new notion of conjugacy—closure of prior‑potential families that remain affine under loss translation—allowing additive canonical updates, parameter‑dependent support, and tunable heavy‑tailed posteriors. The authors also derive a Fenchel‑Young generalization of EM, encompassing both classical and hard EM, and demonstrate its utility in generalized Bayesian linear regression and sparse Gaussian mixture models.
By Sophia Sklaviadis, Thomas Moellenhoff, Emtiyaz Khan, Andre Martins, Mario Figueiredo
arXiv:2610.28256v1 Announce Type: cross
Abstract: Sparse variational Gaussian processes (SVGPs) are a widely used, principled approach to scalable Gaussian process modelling. Their success stems from...
By Matteo Hoxha
arXiv:2606. 07841v1 Announce Type: cross Abstract: Black-box variational inference (BBVI) is a methodology for posterior approximation that relies on stochastic optimization.
By Trevor Campbell, Jonathan H. Huggins, Kyurae Kim, Charles C. Margossian
The paper introduces DRO-NPE, a distributionally robust neural posterior estimation method that replaces the standard NPE objective with a worst‑case loss over a Wasserstein ambiguity set. It presents KL‑based metrics for miscoverage and miscalibration, demonstrating that the DRO‑NPE objective mitigates overfitting and reduces posterior overconfidence. Experiments on benchmark simulation‑based inference tasks show that DRO‑NPE consistently improves coverage and calibration while narrowing the gap between empirical and population NPE loss, especially in low‑simulation regimes.
By William Laplante, Yuga Hikida, Charita Dellaporta, Fran\c{c}ois-Xavier Briol, Ayush Bharti
arXiv:2412. 08951v3 Announce Type: replace Abstract: Scalable algorithms of posterior approximation allow Bayesian nonparametrics such as Dirichlet process mixture to scale up to larger dataset at fractional cost.
By Kart-Leong Lim, Xudong Jiang
The paper investigates how the Bayesian Learning Rule (BLR), traditionally tied to Kullback‑Leibler divergence, can be extended to other geometries. It demonstrates that additive BLR updates are possible using mixed‑space Bregman or Fenchel‑Young discrepancies, leading to generalized maximum‑entropy families and new canonical gradient updates. For example, applying the Tsallis negentropy with quadratic statistics yields bounded‑support, heavy‑tailed q‑Gaussian posteriors and a simple Newton‑like implementation, with experiments on CIFAR‑100 showing controllable support and tail behavior and competitive performance.
By Sophia Sklaviadis, Wu Lin, Andre Martins, Mario Figueiredo, Thomas Moellenhoff, Emtiyaz Khan