A Unified and Computationally Efficient Non-Gaussian Statistical Modeling Framework

2026-02-27

AI Summary

Existing approaches to modeling non-Gaussian data lack a unified, efficient, and scalable framework. This work proposes Linear Latent non-Gaussian Models (LLnGMs), a natural extension of latent Gaussian models to the non-Gaussian setting, which unifies a broad class of structures ranging from time series to multivariate spatiotemporal models. Leveraging stochastic gradient descent, we develop an efficient Bayesian inference algorithm with theoretical guarantees, implemented in the R package ngme2. The framework demonstrates remarkable versatility, computational efficiency, and practical utility across several novel non-Gaussian spatial and spatiotemporal models. To our knowledge, this is the first statistical modeling paradigm for non-Gaussian data that simultaneously achieves flexibility, scalability, and theoretical rigor.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Reasoning under Uncertainty: Relational Probabilistic Models
• Natural Language Processing: (Large) Language Models

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Datasets that exhibit non-Gaussian characteristics are common in many fields, while the current modeling framework and available software for non-Gaussian models is limited. We introduce Linear Latent Non-Gaussian Models (LLnGMs), a unified and computationally efficient statistical modeling framework that extends a class of latent Gaussian models to allow for latent non-Gaussian processes. The framework unifies several popular models, from simple temporal models to complex spatial-temporal and multivariate models, facilitating natural non-Gaussian extensions. Computationally efficient Bayesian inference, with theoretical guarantees, is developed based on stochastic gradient descent estimation. The R package \texttt{ngme2}, which implements the framework, is presented and demonstrated through a wide range of applications including novel non-Gaussian spatial and spatio-temporal models.

Problem

• non-Gaussian
• statistical modeling
• latent models
• spatio-temporal
• computational efficiency

Innovation

• Non-Gaussian modeling
• Latent variable models
• Bayesian inference
• Stochastic gradient descent
• Spatio-temporal models