R2-GP: Variance-Calibrated Priors for Additive Gaussian Processes
We develop R2-GP, an R2D2-type prior for Gaussian process (GP) generalised additive models (GAMs) that calibrates explained variance ($R^2$) for Matérn covariance kernels.
ProofPaper ↗
Key points
- The function variance for standard Matérn kernels depends jointly on the effect magnitude and length-scale.
- We do this by rescaling each component based on its length scale and observed inputs, and modelling each rescaled variance as a share of the function variance induced by a global $R^2$ prior.
- To also scale to large sample sizes, we extend R2-GP to Hilbert space approximation methods, a framework for kernels exploiting their spectral decompositions for fast and efficient inference.
- Our simulations and real-world case studies demonstrate superior generalisation and parameter recovery over independent variance priors.
Sources (1)
- [1]R2-GP: Variance-Calibrated Priors for Additive Gaussian ProcessesarXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 19, 01:58 PM
We develop R2-GP, an R2D2-type prior for Gaussian process (GP) generalised additive models (GAMs) that calibrates explained variance ($R^2$) for Matérn covariance kernels.
The function variance for standard Matérn kernels depends jointly on the effect magnitude and length-scale.
Extractive summary: sentences quoted from the sources.