Sequential Inference for Gaussian Processes: A Signal Processing Perspective
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. Gaussian processes (GPs) are a flexible yet principled framework for modeling random functions, and they have become increasingly relevant to SP as statistical and ML methods assume a more prominent role. We provide a self-contained, tutorial-style overview of GPs, with a particular focus on recent methodological advances in sequential, incremental, or streaming inference. We introduce these techniques from a signal-processing perspective while bridging them to recent advances in ML. Many of the developments we survey have direct applications to state-space modeling, sequential regression and forecasting, anomaly detection in time series, sequential Bayesian optimization, adaptive and active sensing, and sequential detection and decision-making. By organizing these advances from a signal-processing perspective, we intend to equip practitioners with practical tools and a coherent roadmap for deploying sequential GP models in real-world systems.
Code (0)
등록된 구현이 없습니다.
Tasks
Gaussian ProcessesAnomaly DetectionSimilar Papers 제목 키워드 기반
Robust, Online, and Adaptive Decentralized Gaussian Processes
Gaussian processes (GPs) offer a flexible, uncertainty-aware framework for modeling complex signals, but scale cubically with data, assume static targets, and are brittle to outliers, limiting their applicability in larg…
Gaussian ProcessesSparse Algorithms for Markovian Gaussian Processes
Approximate Bayesian inference methods that scale to very large datasets are crucial in leveraging probabilistic models for real-world time series. Sparse Markovian Gaussian processes combine the use of inducing variable…
Bayesian InferenceGaussian ProcessesTime SeriesTime Series Analysis+1Gaussian Processes for Nonlinear Signal Processing
Gaussian processes (GPs) are versatile tools that have been successfully employed to solve nonlinear estimation problems in machine learning, but that are rarely used in signal processing. In this tutorial, we present GP…
BIG-bench Machine LearningGaussian ProcessesGeneral ClassificationregressionLearning about a changing state
A long-lived Bayesian agent observes costly signals of a time-varying state. He chooses the signals' precisions sequentially, balancing their costs and marginal informativeness. I compare the optimal myopic and forward-l…
Gaussian ProcessesInformativenessMemory-Based Dual Gaussian Processes for Sequential Learning
Sequential learning with Gaussian processes (GPs) is challenging when access to past data is limited, for example, in continual and active learning. In such cases, errors can accumulate over time due to inaccuracies in t…
Active LearningBayesian OptimizationContinual LearningGaussian Processes