Summary of Error Bounds For Gaussian Process Regression Under Bounded Support Noise with Applications to Safety Certification, by Robert Reed et al.
Error Bounds For Gaussian Process Regression Under Bounded Support Noise With Applications To Safety Certification
by Robert Reed, Luca Laurenti, Morteza Lahijanian
First submitted to arxiv on: 16 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 This paper presents novel error bounds for Gaussian Process Regression (GPR) when dealing with noisy data in applications like safety-critical domains. Traditional error bounds are overly conservative and restrictive, but this work provides probabilistic and deterministic bounds based on concentration inequalities and the assumption of low complexity latent functions in reproducing kernel Hilbert spaces. The derived errors are tighter than existing state-of-the-art bounds, particularly for Deep Kernel Learning (DKL) with neural network kernels. Furthermore, the paper illustrates how these error bounds can be combined with stochastic barrier functions to quantify the safety probability of unknown dynamical systems from finite data. The results demonstrate that the proposed approach yields consistently smaller error bounds and improved safety probabilities. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This research improves a powerful machine learning method called Gaussian Process Regression (GPR). GPR helps us learn complex relationships from noisy data, which is important for applications like self-driving cars or medical devices. The current way of calculating errors for GPR can be too cautious and limit its usefulness. This paper introduces new methods to calculate these errors more accurately, especially when using a type of neural network-based kernel called Deep Kernel Learning (DKL). These improved error calculations can help us better understand the reliability of complex systems, like those used in self-driving cars. |
Keywords
* Artificial intelligence * Machine learning * Neural network * Probability * Regression
