Summary of Exploiting Hankel-toeplitz Structures For Fast Computation Of Kernel Precision Matrices, by Frida Viset et al.
Exploiting Hankel-Toeplitz Structures for Fast Computation of Kernel Precision Matrices
by Frida Viset, Anton Kullberg, Frederiek Wesel, Arno Solin
First submitted to arxiv on: 5 Aug 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Machine Learning (stat.ML)
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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 The Hilbert-space Gaussian Process (HGP) approach offers a hyperparameter-independent basis function approximation for speeding up Gaussian Process (GP) inference by projecting the GP onto M basis functions. This leads to a favorable data-independent computational complexity during hyperparameter optimization but requires a one-time precomputation of the precision matrix with high computational costs. The authors propose a novel approach that reduces this dominating computational complexity to O(NM), without introducing additional approximations, by exploiting the structure of the precision matrix. They also develop two theorems that provide sufficient conditions for the complexity reduction to hold for other approximate GP models, such as Variational Fourier Feature (VFF) approach. The authors’ contribution provides a pure speed-up of several existing widely used GP approximations without further approximations. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Gaussian Processes (GP) are powerful tools in machine learning, but they can be slow and expensive to compute. Researchers have developed ways to make them faster by using basis functions, but these methods require a lot of computation upfront. In this paper, scientists find a way to speed up the process even further without sacrificing accuracy. They do this by looking at the structure of the precision matrix, which is a key component in GP computations. By exploiting this structure, they reduce the computational complexity from O(NM^2) to O(NM), making GPs much faster and more practical to use. |
Keywords
» Artificial intelligence » Hyperparameter » Inference » Machine learning » Optimization » Precision
