arXiv AI
Jun 26

XMSE-Aware Adaptive Empirical Bayes Estimation

arXiv:2606. 26975v1 Announce Type: cross Abstract: Empirical Bayes (EB) estimators can match the first-order asymptotic risk of maximum likelihood (ML) while behaving very differently at second order: recent excess mean squared error (XMSE) analysis shows that kernel-based EB estimation may be worse than ML when the kernel is poorly aligned with the true parameter.

By Minghao Chen, Jiale Zheng
arXiv Machine Learning
Sep 23

On Basis Function Selection for Sparse Gaussian Process Regression

The paper proposes three information‑theoretic criteria for selecting the most relevant basis functions in sparse Gaussian process regression, tailored to different levels of prior knowledge. Experiments on six UCI regression datasets and three basis families (HSGP, VFF, VISH) show that the no‑data criterion is a robust default, often outperforming simple truncation, while the data‑aware criteria yield significant improvements for HSGP. The study demonstrates that careful basis‑function selection can lead to better performance without increasing computational cost.

By Marnix Van Soom, Ivan De Boi
Hugging Face Trending Papers
Jun 25

XMSE-Aware Adaptive Empirical Bayes Estimation

Empirical Bayes (EB) estimators can match the first-order asymptotic risk of maximum likelihood (ML) while behaving very differently at second order: recent excess mean squared error (XMSE) analysis shows that kernel-based EB estimation may be worse than ML when the kernel is poorly aligned with the true parameter. This paper turns that diagnostic into a design principle.

arXiv Machine Learning
Aug 24

Amortized Bandwidth Learning for Kernel Density Estimation under Logarithmic Score

The paper introduces an amortized learning framework for selecting bandwidths in kernel density estimation by optimizing the logarithmic score across a distribution of tasks. It uses a truncated-and-renormalized bounded-support formulation and affine standardization to achieve stable learning and transferability across different intervals. Experiments on Gaussian samples, a multi-family benchmark, and randomized Gaussian mixtures demonstrate that the learned selector outperforms traditional methods such as Silverman’s rule, Sheather–Jones, and least‑squares cross‑validation, especially for small or heterogeneous samples.

By Junyi Liang, Hailiang Du