Sequential Inference for Gaussian Processes: A Signal Processing Perspective

Problem
This paper addresses the gap in the literature regarding the application of Gaussian Processes (GPs) in sequential inference within the context of signal processing (SP). The authors highlight that while machine learning models have transformed SP methodologies, the existing frameworks often assume independent and identically distributed (i.i.d.) data, which is not suitable for sequential data scenarios. This work is presented as a preprint, indicating that it has not yet undergone peer review.

Method
The authors provide a comprehensive overview of GPs, emphasizing recent advancements in sequential, incremental, and streaming inference techniques. They frame these methodologies within a signal processing context, bridging them with contemporary machine learning developments. Key contributions include a detailed exposition of state-space modeling, sequential regression, and forecasting techniques, as well as applications in anomaly detection, sequential Bayesian optimization, adaptive sensing, and decision-making. The paper serves as a tutorial, equipping practitioners with practical tools for implementing sequential GP models in real-world applications.

Results
While the paper does not present empirical results or quantitative comparisons against specific baselines, it synthesizes existing methodologies and applications of GPs in sequential contexts. The authors discuss the theoretical underpinnings and practical implications of these techniques, suggesting that they can significantly enhance predictive accuracy and adaptability in SP systems. The lack of explicit benchmark comparisons limits the ability to quantify effect sizes or improvements over traditional methods.

Limitations
The authors acknowledge that their work is primarily a survey and tutorial, which may not provide novel empirical results or extensive case studies. They do not address potential computational challenges associated with implementing sequential GPs, such as scalability issues in high-dimensional spaces or the computational burden of maintaining and updating GP priors in real-time applications. Additionally, the paper does not explore the limitations of GPs in terms of their assumptions about the underlying data distribution or the potential for overfitting in complex models.

Why it matters
This work is significant as it consolidates recent advancements in sequential inference for GPs, providing a structured approach for practitioners in signal processing and machine learning. By framing these techniques within a signal processing perspective, the authors facilitate the adoption of GPs in various applications, including real-time anomaly detection and adaptive sensing. The insights offered could lead to improved methodologies in fields where sequential data is prevalent, thereby influencing future research directions and practical implementations in both SP and ML domains.

Authors: Daniel Waxman, Fernando Llorente, Petar M. Djurić
Source: arXiv:2604.28163
URL: https://arxiv.org/abs/2604.28163v1