Efficient Gaussian process regression for large datasets.

Area of Science:

• Machine Learning
• Statistical Modeling
• Nonparametric Statistics

Background:

• Gaussian processes are valuable for regression, classification, and spatiotemporal modeling.
• Their practical application is hindered by cubic computational complexity (O(n³)) and numerical instability with large datasets.
• Existing solutions like subset methods have limitations in data selection and fine-scale structure estimation.

Purpose of the Study:

• To address the computational bottlenecks of Gaussian processes for large datasets.
• To propose a novel approach that overcomes the limitations of existing subset-based methods.
• To enhance the scalability and numerical stability of Gaussian process modeling.

Main Methods:

• A novel approach inspired by compressive sensing is introduced.
• This method involves projecting all data points onto a lower-dimensional subspace.
• The technique is evaluated theoretically and empirically using simulated and real-world data.

Main Results:

• The proposed linear projection method demonstrates theoretical advantages over traditional approaches.
• Empirical results show superior performance compared to existing methods on simulated datasets.
• Real-world data analysis confirms the effectiveness and efficiency of the new technique.

Conclusions:

• Linear projection onto a lower-dimensional subspace offers a computationally efficient alternative for Gaussian processes.
• This approach mitigates the O(n³) complexity and improves numerical stability.
• The method provides a scalable solution for large-scale nonparametric regression and spatiotemporal modeling.