The paper introduces a scalable variational inference framework for latent field models with non‑Gaussian likelihoods. It mirrors the sparse nearest‑neighbor autoregressive structure of the Gaussian process prior in the variational family, employs normalizing‑flow conditionals for expressiveness, and amortizes all variational parameters through a single shared neural conditioner. The method achieves polylogarithmic per‑iteration complexity via doubly stochastic optimization with reduced ancestor sets.
The paper introduces Amortized Structured Stochastic Variational Inference for Gaussian Process Latent Variable Models, enabling the variational posterior over latent variables to depend on GP inducing points. This approach addresses limitations of mean‑field approximations and yields improved reconstruction metrics for data manifold points.
arXiv:2604. 07635v2 Announce Type: replace-cross Abstract: This research considers a scalable inference for spatial data modeled through Gaussian intrinsic conditional autoregressive (ICAR) structures.
arXiv:2606. 15458v1 Announce Type: cross Abstract: Variational inference (VI) is a core engine of modern AI, enabling scalable approximate Bayesian learning and uncertainty-aware training of large probabilistic and generative models.
The paper introduces Latent Annealed Posterior Sampling (LAPS), a method that maps sparsely observed random fields into a lower‑dimensional latent space and performs posterior sampling there. A variance‑preserving bridge controls local covariance inflation, while flow matching learns the latent prior. Experiments on Gaussian benchmarks, a bimodal posterior, and a Navier‑Stokes field show that LAPS accurately approximates posterior distributions, preserves multiple modes, and keeps conditional sampling costs nearly constant as spatial resolution increases.
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.
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.
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.
arXiv:2406. 12659v3 Announce Type: replace-cross Abstract: We propose a scalable variational Bayes method for statistical inference for a single or pre-specified low-dimensional subset of the coordinates of a high-dimensional parameter in sparse linear regression.
arXiv:2505. 04486v4 Announce Type: replace-cross Abstract: Flow matching models have shown great potential in image generation tasks among probabilistic generative models.
arXiv:2602. 02948v3 Announce Type: replace Abstract: Inverse problems are fundamental to many scientific and engineering disciplines; they arise when one seeks to reconstruct hidden, underlying quantities from noisy measurements.
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:2606. 25882v1 Announce Type: new Abstract: DGPs are probabilistic models with remarkable prediction performance that concatenate GPs across several layers.