Summary of Residual Deep Gaussian Processes on Manifolds, by Kacper Wyrwal et al.
Residual Deep Gaussian Processes on Manifolds
by Kacper Wyrwal, Andreas Krause, Viacheslav Borovitskiy
First submitted to arxiv on: 31 Oct 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 proposed deep Gaussian process models operate on Riemannian manifolds, inspired by residual neural networks. These models can handle manifold- and scalar-valued functions, as well as vector fields, with manifold-to-manifold hidden layers and an arbitrary last layer. The authors target data inherently supported on manifolds, which shallow Gaussian processes struggle to model, particularly in complex settings like low-altitude wind patterns. Their approach improves prediction quality and uncertainty calibration while remaining robust to overfitting, reverting to shallower models when unnecessary complexity arises. Additionally, the models are showcased for Bayesian optimisation problems on manifolds, achieving significant improvements in later stages. Furthermore, the authors suggest their models can accelerate inference for non-manifold data by mapping it to a proxy manifold effectively. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The researchers created new types of computer models that work better on curved surfaces (manifolds) than traditional methods. These models are like building blocks that can be used to create different functions and patterns, which is helpful when dealing with complex data that doesn’t fit neatly into simple categories. The models were tested on real-world problems like optimizing robot movements and predicting wind patterns at different altitudes. The results show that the new models do a much better job than traditional methods of making accurate predictions and reducing uncertainty. |
Keywords
* Artificial intelligence * Inference * Overfitting
