New framework brings automation and flexibility to Gaussian Processes
Hoang Nguyen defended his PhD thesis at the Department of Electrical Engineering on June 4th.
Gaussian Processes (GPs) are widely valued in Bayesian inference because they are powerful, flexible, and require only limited assumptions about the data. Despite these advantages, they can be difficult to use in practice because their inference procedures are often complex and require significant model-specific work. Within his PhD research Hoang Nguyen addresses that challenge by introducing a way to represent Gaussian Processes within Forney-style factor graphs (FFGs), enabling more automated, modular, and reusable probabilistic modeling. The result is a framework that makes GPs easier to integrate into larger models and more aligned with modern probabilistic programming practices.
Gaussian Processes offer a nonparametric approach to Bayesian inference, allowing researchers to model complex relationships without having to define a fixed structure in advance. However, this flexibility comes at a cost. Inference with GPs can be computationally demanding, and even when sparse approximations are used to reduce that burden, researchers often need to derive custom update rules for each new model. This manual work limits both scalability and accessibility, especially when GPs are combined with other probabilistic model components.
The need for automation and composability
To make probabilistic modeling more efficient, two important properties are needed: automation and composability. Automation allows inference procedures to be generated automatically rather than being derived by hand for every model. Composability makes it possible to build complex models from reusable building blocks. Together, these properties can significantly simplify the development of advanced probabilistic models.
A natural fit: forney-style factor graphs
Forney-style factor graphs provide a framework that naturally supports both automation and composability. They represent probabilistic models as networks of interconnected components and enable automated inference through message passing. Because model components can be reused and combined in different ways, FFGs offer an attractive foundation for scalable probabilistic modeling.
Bridging a long-standing gap
Despite their advantages, forney-style factor graphs have traditionally not been well suited for Gaussian Processes. The main reason is that GPs are infinite-dimensional objects, making them difficult to represent within the graph-based framework. This dissertation of closes that gap by introducing methods that allow Gaussian Processes to be represented within FFGs. The work covers not only standard GPs but also sparse and structured variants.
Towards modular and reusable probabilistic models
By bringing Gaussian Processes into the FFG framework, the dissertation enables a more modular approach to probabilistic modeling. Models can be built from reusable components while benefiting from automated inference procedures.
This combination of flexibility, automation, and reusability helps make Gaussian Processes more practical for larger and more complex probabilistic models, bringing them closer to the goals of modern probabilistic programming.
Title of PhD thesis: . Supervisors: Prof. Bert de Vries, Ismail 葮en枚z, and Dr. Thijs van de Laar.