Summary of Kernel Multigrid: Accelerate Back-fitting Via Sparse Gaussian Process Regression, by Lu Zou and Liang Ding
Kernel Multigrid: Accelerate Back-fitting via Sparse Gaussian Process Regression
by Lu Zou, Liang Ding
First submitted to arxiv on: 20 Mar 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary Additive Gaussian Processes (GPs) are a popular approach for nonparametric feature selection. The traditional training method is Bayesian Back-fitting, but the convergence rate of this method for additive GPs remains an open problem. This paper proposes a novel technique called Kernel Packets (KP), which reveals that Back-fitting converges at a rate of no faster than (1-())^t, where n and t denote the data size and iteration number, respectively. The authors further develop an algorithm called Kernel Multigrid (KMG), which combines Back-fitting with sparse Gaussian Process Regression (GPR) to process residuals after each iteration. KMG is applicable to additive GPs with both structured and scattered data and reduces the required iterations to (n) while maintaining time and space complexities of (nn) and (n) per iteration, respectively. Numerical experiments demonstrate that KMG can produce accurate approximations of high-dimensional targets within 5 iterations using only 10 inducing points. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Gaussian Processes are a type of machine learning algorithm used for selecting important features from data. The problem is that the training process, called Back-fitting, takes too long to converge. This paper introduces a new method called Kernel Packets and uses it to solve this problem. They also develop an algorithm called Kernel Multigrid, which helps speed up the convergence process even more. This new approach can be used for both types of data: structured and scattered. The results show that their method is faster and works well for big datasets. |
Keywords
* Artificial intelligence * Feature selection * Machine learning * Regression
