Revisiting the Sample Complexity of Sparse Spectrum Approximation of Gaussian Processes

Abstract

We introduce a new scalable approximation for Gaussian processes with provable guarantees which hold simultaneously over its entire parameter space. Our approximation is obtained from an improved sample complexity analysis for sparse spectrum Gaussian processes (SSGPs). In particular, our analysis shows that under a certain data disentangling condition, an SSGP's prediction and model evidence (for training) can well-approximate those of a full GP with low sample complexity. We also develop a new auto-encoding algorithm that finds a latent space to disentangle latent input coordinates into well-separated clusters, which is amenable to our sample complexity analysis. We validate our proposed method on several benchmarks with promising results supporting our theoretical analysis.

References in corpus (4)

• Multi-Robot Informative Path Planning for Active Sensing of Environmental Phenomena: A Tale of Two Algorithms
• Decentralized Data Fusion and Active Sensing with Mobile Sensors for Modeling and Predicting Spatiotemporal Traffic Phenomena
• Decentralized High-Dimensional Bayesian Optimization with Factor Graphs
• GP-Localize: Persistent Mobile Robot Localization using Online Sparse Gaussian Process Observation Model

Cited by in corpus (1)

• Unpacking the Expressed Consequences of AI Research in Broader Impact Statements