Summary of Intrinsic Gaussian Process Regression Modeling For Manifold-valued Response Variable, by Zhanfeng Wang and Xinyu Li and Hao Ding and Jian Qing Shi
Intrinsic Gaussian Process Regression Modeling for Manifold-valued Response Variable
by Zhanfeng Wang, Xinyu Li, Hao Ding, Jian Qing Shi
First submitted to arxiv on: 28 Nov 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 The paper proposes a novel intrinsic Gaussian process regression model for manifold-valued data, which can be applied to complex data with response variables situated on manifolds without a natural ambient space. The method constructs a well-defined Gaussian process regression model by applying the parallel transport operator on Riemannian manifolds to propose an intrinsic covariance structure. Asymptotic properties of the proposed models are established, including information consistency and posterior consistency, and it is shown that the posterior distribution of the regression function is invariant to the choice of orthonormal frames for the coordinate representations of the covariance function. Numerical studies demonstrate the effectiveness of the proposed methods. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper develops a new way to study complex data with response variables that exist on curved spaces, called manifolds. They create a special type of mathematical model, called Gaussian process regression, that can handle this kind of data. The model is designed to work well even when there isn’t a natural “coordinate system” for the manifold. The authors show that their method works by testing it with simulated and real examples. |
Keywords
» Artificial intelligence » Regression
