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:2610.10080v1 Announce Type: cross
Abstract: Gaussian processes (GPs) are widely used across machine learning, spatial statistics, time-series analysis, optimization, Bayesian statistics, and sc...
By Ameer Qaqish, Didong Li
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 method to incorporate linear inequality constraints—such as nonnegativity, monotonicity, and no‑arbitrage—into Gaussian process solvers for linear partial differential equations. By proving that conditioning a Gaussian process jointly on equality observations and a finite‑dimensional inequality event is equivalent to sequential conditioning, the authors obtain a non‑Gaussian but computable posterior that respects both PDE physics and inequality constraints. Experiments on Poisson problems, option‑price surfaces, and air‑quality data show substantial error reductions and improved adherence to constraints when the new method is applied.
By Boyuan Deng, Kshitiz Upadhyay, Michael Shields
arXiv:2610.09452v1 Announce Type: cross
Abstract: Conditional density estimation describes how the entire distribution of a response changes with covariates, and in imaging studies also with location...
By Jaehoan Kim, Indrajit Ghosh, Debdeep Pati, Dipankar Bandyopadhyay
arXiv:2609. 21085v1 Announce Type: cross Abstract: Gaussian processes (GPs) provide principled probabilistic predictions while encoding prior knowledge, including equivariances.
By Tim Steinert, David Ginsbourger
arXiv:2610.39855v2 Announce Type: replace-cross
Abstract: Probabilistic meshless methods solve partial differential equations (PDEs) by placing a Gaussian process prior on the solution and conditioni...
By Federico Pavesi, No\'emie Jaquier, Antonio Candelieri
The paper tackles the challenge of predicting multiple high‑dimensional physical fields that must satisfy linear equality constraints, a common scenario in physics‑informed machine learning. It critiques the conventional approach of deducing one field from others, showing its sensitivity to arbitrary choices and its impact on accuracy and uncertainty. To address this, the authors introduce a symmetric framework that first applies a row‑wise PCA to preserve constraints in a latent space, then trains a linearly‑constrained multi‑output Gaussian process using a specially parametrized kernel, and validate the method on population dynamics and CFD problems involving Reynolds stress tensors.
By Mahamat Hamdan Nassouradine, Cl\'ement Gauchy, Pierre-Emmanuel Angeli, S\'ebastien da Veiga
arXiv:2510. 12744v2 Announce Type: replace-cross Abstract: We develop a unified statistical framework for softmax-gated Gaussian mixture of experts (SGMoE) that addresses three long-standing obstacles in parameter estimation and model selection: (i) non-identifiability of gating parameters up to common translations, (ii) intrinsic gate-expert interactions that induce coupled differential relations in the likelihood, and (iii) the tight numerator-denominator coupling in the softmax-induced conditional density.
By Do Tien Hai, Trung Nguyen Mai, TrungTin Nguyen, Nhat Ho, Binh T. Nguyen, Christopher Drovandi
The paper introduces improvements to FlowGP, a method for conditional sampling from Gaussian processes outside the linear-Gaussian regime. It adds kernel approximations to scale to high-resolution domains and a new technique for computing marginal likelihood by measuring the work required to steer diffusion toward conditioning statements. These advances enable hyperparameter optimisation within FlowGP and are demonstrated on tasks such as probabilistic downscaling, PDE solution inference on irregular domains, and sea level anomaly field recovery from non-Gaussian satellite data.
By Thomas Cowperthwaite, Louis Sharrock, Lachlan Astfalck, Henry Moss
The paper presents an exact, efficient solution for the Linear Model of Co‑regionalization (LMC) multitask Gaussian Process by decoupling latent processes under a mild noise‑model assumption. It introduces a full parametrization of the resulting projected LMC, enabling linear‑time optimization and simplifying tasks such as training updates and leave‑one‑out cross‑validation. Experiments on synthetic and real data demonstrate that projected LMC is competitive with state‑of‑the‑art multitask GP models while offering greater interpretability and computational ease.
By Olivier Truffinet (CEA Saclay), Karim Ammar (CEA Saclay), Jean-Philippe Argaud (EDF R&D), Bertrand Bouriquet (EDF)
arXiv:2606. 25169v2 Announce Type: replace-cross Abstract: Sampling from an unnormalized target by reversing an Ornstein-Uhlenbeck diffusion requires the score of each noise-perturbed marginal.
By Alois Duston, Tan Bui-Thanh