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arXiv Machine Learning

A Flexible Empirical Bayes Approach to Generalized Linear Models, with Applications to Sparse Logistic Regression

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.

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arXiv Machine Learning
Sep 14

A Generalized Tangent Approximation based Variational Inference Framework for Strongly Super-Gaussian Likelihoods

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
benchmarks
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arXiv Machine Learning
Aug 27

Gradient-based Sample Selection for Faster Bayesian Optimization

The paper introduces Gradient-based Sample Selection Bayesian Optimization (GSSBO), a method that builds the Gaussian process surrogate on a strategically chosen subset of samples rather than the full dataset. By using gradient information to eliminate redundant points while keeping diversity and representativeness, GSSBO achieves sublinear regret bounds and reduces the cubic computational cost of standard BO. Experiments on synthetic and real-world tasks show that this approach maintains comparable optimization performance while significantly cutting GP fitting time and resource usage.

By Qiyu Wei, Haowei Wang, Zirui Cao, Songhao Wang, Richard Allmendinger, Mauricio A \'Alvarez
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arXiv AI
Jun 9

SVRG and Beyond via Posterior Correction

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
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arXiv Machine Learning
Jul 27

Simulation-Based Empirical Bayes

arXiv:2607. 21843v1 Announce Type: cross Abstract: Empirical Bayes (EB) performs simultaneous inference across many related latent variables.

By Xinwei Shen, Diana Cai, Cheng Zhang, David M. Blei
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arXiv AI
Aug 19

Maximum Tsallis Entropy Distributions for Robust and Efficient Sparse Learning from Correlated Data

The paper proposes using the $q$Gaussian distribution, derived from Tsallis entropy maximization, to address the shortcomings of Gaussian assumptions in sparse learning with correlated and heterogeneous data. It introduces a new framework that adapts numerical equilibrium methods to composite optimization problems, applying it to the Hager‑Zhang conjugate gradient algorithm to create a stable, efficient sparse learning algorithm. The work offers both theoretical insights into alternative statistical distributions and practical tools for data analysis in fields like biostatistics.

By Kai Yang, Masoud Asgharian, Celia M. T. Greenwood
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