Neural Conditional Simulation for Complex Spatial Processes

A new nonparametric density estimator based on Gaussian processes (GP) has been proposed, featuring three novel closed-form learning algorithms derived from Fisher divergence (FD) score matching. This estimator combines a base multivariate normal distribution with an exponentiated GP refinement, referred to as GP-tilted nonparametric density. The optimization for these algorithms can be solved in closed form, including basic and noise conditional versions of Fisher divergence, along with a variational inference-based alternative.

The article titled 'Bayesian ICA with super-Gaussian Source Priors' discusses advancements in Independent Component Analysis (ICA), a key method in machine learning for feature extraction. The authors introduce a horseshoe-type prior with a latent Polya-Gamma scale mixture representation, enabling scalable algorithms for point estimation and full posterior inference. The study establishes theoretical guarantees for hierarchical Bayesian ICA, including results for the unmixing matrix. Simulation studies indicate that the proposed methods are competitive with existing ICA tools.