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
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.
By Somjit Roy, Pritam Dey, Debdeep Pati, Bani K. Mallick
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
arXiv:2606. 25882v1 Announce Type: new Abstract: DGPs are probabilistic models with remarkable prediction performance that concatenate GPs across several layers.
By Francisco Javier S\'aez-Maldonado, Juan Maro\~nas, Daniel Hern\'andez-Lobato
The paper introduces a two-way guidance framework that jointly learns summary statistics and posterior distributions for Bayesian simulation-based inference. By imposing a structural restriction on the learned summary, the method ensures that the posterior remains sufficient, while the posterior objective simultaneously steers the summary toward sufficiency. The authors provide theoretical guarantees on posterior estimation error and the deviation of the learned summary from sufficiency, outlining conditions on simulation budgets needed to recover increasingly concentrated posteriors as observation size grows.
By Percy S. Zhai, Max Pachman, Peverel D. Shipley, Jungeum Kim
arXiv:2509.10393v5 Announce Type: replace-cross
Abstract: Several methods in statistics and machine learning target a probability distribution for which an entropy-regularised variational objective i...
By Cl\'ementine Chazal, Heishiro Kanagawa, Zheyang Shen, Anna Korba, Chris. J. Oates
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
arXiv:2512. 01930v2 Announce Type: replace-cross Abstract: Stochastic Variance Reduced Gradient (SVRG) and its variants aim to speed-up training by using gradient corrections.
By Nico Daheim, Thomas M\"ollenhoff, Ming Liang Ang, Mohammad Emtiyaz Khan
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 extends active inference to incorporate learning of observation and transition parameters by assigning each factor its own Dirichlet prior, thereby preserving information‑gain corrections that vanish under standard mean‑field factorization. This approach yields a closed‑form objective whose stationary point is solved by sum‑product message passing with augmented factor functions. Experiments on two grid POMDPs demonstrate that the resulting planner reliably learns the model and reaches the goal in every episode, outperforming planners that lack this learning capability.
By Benedikt Waldeck
arXiv:2602. 23672v2 Announce Type: replace-cross Abstract: This study proposes a General Bayes framework for policy learning.
By Masahiro Kato
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.