Generalized Matheron Variational Implicit Processes (GMVIP) provide a pathwise variational family for posterior inference with implicit-process priors, such as Bayesian neural networks and stochastic simulators. For Gaussian‑process priors, GMVIP reproduces the standard inducing‑variable variational GP construction, while for general implicit priors it preserves the prior mean and covariance in the population limit. The method constructs posterior samples by drawing a function from the prior and applying a correction anchored at inducing inputs, with the correction determined directly from prior samples, and achieves a tractable coefficient‑space Kullback‑Leibler divergence. Experiments on regression, classification, and forecasting demonstrate that GMVIP is broadly competitive with existing methods.
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.
arXiv:2606. 25882v1 Announce Type: new Abstract: DGPs are probabilistic models with remarkable prediction performance that concatenate GPs across several layers.
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.
arXiv:2610.22763v1 Announce Type: new Abstract: Bayesian optimization (BO) over discrete spaces is challenging due to missing gradients and the sparsity of valid solutions. Latent-space BO sidesteps...
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.
The paper introduces a continuous-depth formulation of Deep Gaussian Processes (DGPs), treating depth as a latent continuous evolution rather than a discrete stack. It proposes two instantiations—CDGP, which applies a GP prior directly to the state–depth drift, and FlowDGP, which uses a flow-evolved prior to capture richer depth dependence at lower training cost. Experiments on synthetic, benchmark, and large-scale regression tasks demonstrate that residual DGP outperforms plain DGP, while CDGP and FlowDGP provide stronger overall performance across the studied regimes.
The paper proposes a continuous-depth formulation for Deep Gaussian Processes (DGPs), treating depth as a latent continuous evolution rather than a discrete stack. It introduces two instantiations—CDGP, which applies a GP prior directly to the state–depth drift, and FlowDGP, which uses a flow-evolved prior to capture richer depth dependence at lower training cost. Experiments on synthetic, benchmark, and large-scale regression tasks demonstrate that residual DGP improves over plain DGP, while CDGP and FlowDGP offer stronger performance across the studied regimes.
arXiv:2610.28256v1 Announce Type: cross Abstract: Sparse variational Gaussian processes (SVGPs) are a widely used, principled approach to scalable Gaussian process modelling. Their success stems from...
Hierarchical data is ubiquitous in the empirical sciences and is most commonly analyzed with generalized linear mixed-effects models (GLMMs). Bayesian inference for GLMMs yields calibrated uncertainty...
arXiv:2609.24422v1 Announce Type: new Abstract: Hierarchical data is ubiquitous in the empirical sciences and is most commonly analyzed with generalized linear mixed-effects models (GLMMs). Bayesian...
arXiv:2606. 06351v1 Announce Type: cross Abstract: Vessel trajectory prediction from Automatic Identification System (AIS) data is essential for maritime situational awareness, yet it remains challenging due to irregular sampling, missing reports, and complex dynamics.
arXiv:2610.03201v1 Announce Type: cross Abstract: Gaussian Processes (GPs) are a powerful tool for modelling and quantifying uncertainty in functional relationships. However, they require practitione...