arXiv Machine Learning
Oct 8

Scalable Logistic Gaussian Process Density Regression with Kinetic Langevin Sampling

The paper introduces a scalable Bayesian method for conditional density estimation using a logistic Gaussian process. It models the log conditional density with a separable covariance— a Matérn kernel on the response dimension and a Nyström-feature kernel on covariates— and samples the latent field via kinetic Langevin dynamics instead of traditional approximations. Experiments on photometric‑redshift data with up to 3.9 million observations show the approach matches state‑of‑the‑art tabular foundation models on density and calibration metrics.

By Daniel Paulin, \'Ad\'am Jung, Andr\'as A. Bencz\'ur
arXiv Machine Learning
3d ago

Learn Only Where You Can't Compute: Structured Corrections to Gaussian Process Posteriors

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