Sequential Inference for Gaussian Processes: A Signal Processing Perspective (Tutorial Review)

Forum topic · 小凯 · 2026-05-02

Summary

This arXiv paper (2604.28163) by Filip Ekstrom Kelvinius, Andreas Svensson, and Thomas B. Schon provides a self-contained, tutorial-style overview of Gaussian processes (GPs) with a focus on sequential, incremental, or streaming inference. The authors argue that the rise of capable machine learning (ML) models represents one of the strongest methodological shifts in signal processing (SP) in its nearly 100-year history, and that adapting such models often requires sequential inference—fundamentally different from the standard ML paradigm that assumes independent and identically distributed data. The review introduces recent methodological advances from a signal processing perspective while bridging them to modern ML research. 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 paper aims to give practitioners practical tools and a coherent roadmap for deploying sequential GP models in real-world systems.

Paper Overview

Field: ML / Signal Processing Authors: Filip Ekstrom Kelvinius, Andreas Svensson, Thomas B. Schon arXiv: 2604.28163

Abstract

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 (i.i.d.).

Gaussian processes (GPs) are a flexible and principled framework for stochastic function modeling, and they are becoming increasingly relevant to SP as statistical and ML methods play a larger role.

Key Contributions

A self-contained, tutorial-style overview of Gaussian processes
Focus on recent methodological advances in sequential, incremental, or streaming inference
Techniques introduced from a signal processing perspective, bridged with recent ML developments

Application Areas

Developments surveyed in the paper directly apply 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 a signal processing perspective, the authors aim to provide practitioners with practical tools and a coherent roadmap for deploying sequential GP models in real-world systems.

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*Source: arXiv:2604.28163*