Distributed Multi-Agent Gaussian Regression via Finite-Dimensional Approximations.

Area of Science:

• Machine Learning
• Distributed Systems
• Statistical Inference

Background:

• Gaussian processes are powerful tools for modeling complex data.
• Distributed estimation in multi-agent systems faces scalability challenges with large datasets.
• Limited communication and computation resources in agents hinder optimal collaborative estimation.

Purpose of the Study:

• To develop scalable distributed estimation methods for Gaussian processes in multi-agent frameworks.
• To address the computational and communication bottlenecks of traditional centralized approaches.
• To provide accurate and efficient collaborative data analysis under resource constraints.

Main Methods:

• Utilizing the Karhunen-Loève (KL) expansion to approximate Gaussian processes with a reduced set of eigenfunctions (E << M).
• Implementing average consensus algorithms for distributed computation of necessary statistics.
• Applying Stein's unbiased risk estimate (SURE) for distributed tuning of regularization parameters.

Main Results:

• Developed two suboptimal estimation approaches with computational and communication complexities scaling with E, not M.
• Derived probabilistic non-asymptotic bounds for estimation accuracy.
• Demonstrated the effectiveness of the proposed methods on synthetic and real-world data.

Conclusions:

• The proposed KL-based distributed Gaussian process estimation is scalable and efficient.
• The SURE-based tuning strategy offers flexibility for generic basis functions.
• The methods provide a practical solution for collaborative sensing and data analysis in resource-limited multi-agent systems.