Sequential Inference for Gaussian Processes: A Signal Processing Perspective (arXiv 2604.28163)

Forum topic · 小凯 · 2026-05-02

Summary

This tutorial-style paper by Filip Ekstrom Kelvinius, Andreas Svensson, and Thomas B. Schon (Uppsala University, arXiv 2604.28163) surveys sequential, incremental, and streaming inference methods for Gaussian process (GP) models from a signal processing (SP) perspective. The authors argue that the rise of machine learning (ML) marks one of the strongest methodological shifts in SP's nearly 100-year history, and that adapting ML models often requires sequential inference, which differs from the standard ML paradigm that assumes independent and identically distributed data. The paper provides a self-contained overview of GPs, reviews recent methodological advances in sequential GP inference, and bridges them with modern ML developments. Applications covered include state-space modeling, sequential regression and prediction, time-series anomaly detection, sequential Bayesian optimization, adaptive and active sensing, and sequential detection and decision-making. The survey aims to give practitioners practical tools and a coherent roadmap for deploying sequential GP models in real-world systems.

Overview

Field: ML / Signal Processing Authors: Filip Ekstrom Kelvinius, Andreas Svensson, Thomas B. Schon Published: 2026-04-30 arXiv: 2604.28163

Abstract (original)

The proliferation of capable and efficient machine learning (ML) models marks one of the strongest methodological shifts in signal processing (SP) in its nearly 100-year history. ML models support the development of SP systems that represent complex, nonlinear relationships with high predictive accuracy. Adapting these models often requires sequential inference, which differs both theoretically and methodologically from the usual paradigm of ML, where data are often assumed independent and identically distributed.

Key points (translated summary)

Gaussian processes (GPs) provide a flexible and principled framework for stochastic function modeling, becoming increasingly relevant to SP as statistical and ML methods play a larger role.
The paper offers a self-contained, tutorial-style overview of GPs, with special focus on recent advances in sequential, incremental, or streaming inference.
Techniques are introduced from a signal processing perspective while bridging recent ML developments.
Many surveyed developments apply directly to:
State-space modeling
Sequential regression and prediction
Time-series anomaly detection
Sequential Bayesian optimization
Adaptive and active sensing
Sequential detection and decision-making
By organizing these advances from an SP perspective, the authors aim to provide practitioners with practical tools and a coherent roadmap for deploying sequential GP models in real-world systems.

---

*Auto-collected on 2026-05-02.*