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: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.
By Jinlin Lai, Antonio Linero, Yuling Yao
arXiv:2607. 26955v1 Announce Type: cross Abstract: Minimax-optimal rates for multivariate distribution estimation are known to suffer from the curse of dimensionality.
By Shuo-Chieh Huang, Chien-Ming Chi, Jau-er Chen
arXiv:2606. 15458v1 Announce Type: cross Abstract: Variational inference (VI) is a core engine of modern AI, enabling scalable approximate Bayesian learning and uncertainty-aware training of large probabilistic and generative models.
By Yuda Shao, Zhiling Gu, Shan Yu
arXiv:2604. 07635v2 Announce Type: replace-cross Abstract: This research considers a scalable inference for spatial data modeled through Gaussian intrinsic conditional autoregressive (ICAR) structures.
By Debjoy Thakur
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
The paper introduces an adaptive fitting procedure for mixtures of product distributions in Gaussian regression with a spike‑and‑slab prior, directly minimizing reverse Kullback‑Leibler divergence on inclusion indicators and active coefficients. This method jointly refines component parameters and weights as the mixture grows, avoiding extra divergence penalties on unused latent coefficients. Empirical results on 250 simulated datasets show that mixtures reduce errors in inclusion probabilities, grouped support probabilities, and coefficient covariance compared to multistart mean‑field approaches, and that direct joint refinement outperforms augmented or restricted refinement at fixed mixture size.
By Hanqing Li, Yaroslav Golub, Xuewen Lu
The paper introduces Compressed Active Subspaces (CAS), a scalable method for Bayesian inference in high‑dimensional models. CAS first compresses model parameters via a structured isometric embedding, then constructs the active subspace in this reduced space, dramatically lowering memory requirements. Experiments on neural networks of growing size show that CAS preserves predictive performance and provides robust uncertainty estimates while enabling inference where traditional active subspace methods fail.
By Thomas Flynn, Sanket Jantre, Byung-Jun Yoon, Kibaek Kim
arXiv:2507.23768v2 Announce Type: replace-cross
Abstract: Existing methods for transfer learning struggle to deal with situations where the source datasets are limited and not guaranteed to be well-a...
By Nathan Wycoff, Ali Arab, Lisa O. Singh
arXiv:2410.11771v4 Announce Type: replace
Abstract: Many spatial models exhibit locality structures that effectively reduce their intrinsic dimensionality, enabling efficient approximation and sampli...
By Tiangang Cui, Shuigen Liu, Xin T. Tong
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.
By Luis A. Ortega, Andr\'es R. Masegosa, Thomas D. Nielsen
arXiv:2606. 25188v1 Announce Type: new Abstract: Efficient uncertainty quantification (UQ) is essential for trustworthy large-scale learning.
By Kun Jin, James Harrison, Jiawei Li, Sihan Liu, Jiayi Liu, Randolph Linderman, Yuening Li, Arnab Bhadury, Sourabh Prakash Bansod, Liang Liu, Jasper Snoek