Konsep Inti
Kernel Multigrid enhances Back-fitting efficiency by incorporating sparse GPR.
Abstrak
The content discusses the challenges of training additive Gaussian Processes (GPs) and introduces Kernel Multigrid (KMG) as a solution. It covers the convergence rate of Back-fitting, the use of Kernel Packets (KPs), and the application of sparse Gaussian Process Regression (GPR). The article provides insights into efficient approximations for high-dimensional targets and addresses computational complexities in GP models.
Structure:
- Introduction to Additive GPs and Bayesian Back-fitting.
- Challenges in training additive GPs due to computational complexity.
- Introduction of Kernel Packets (KPs) and their impact on convergence rate.
- Proposal of Kernel Multigrid (KMG) algorithm for enhanced Back-fitting.
- Evaluation of KMG performance on synthetic and real-world datasets.
- Conclusion and future research directions.
Key Highlights:
- Additive GPs address high-dimensional generalized models effectively.
- Computational complexity hinders training additive GP models.
- Bayesian Back-fitting is commonly used but faces convergence rate challenges.
- Kernel Packets provide insights into the convergence rate limitations of Back-fitting.
- Kernel Multigrid algorithm reduces iterations required for convergence efficiently.
Statistik
By employing a sparse GPR with merely 10 inducing points, KMG can produce accurate approximations of high-dimensional targets within 5 iterations.