Approximate cross-validation formula for Bayesian linear regression
This work addresses computational efficiency for researchers using Bayesian linear regression, but it is incremental as it focuses on a specific approximation method.
The authors tackled the high computational cost of cross-validation in Bayesian linear regression by developing an approximate formula to evaluate leave-one-out CV error without performing full CV, which was tested on a synthetic model and a real-world supernova dataset.
Cross-validation (CV) is a technique for evaluating the ability of statistical models/learning systems based on a given data set. Despite its wide applicability, the rather heavy computational cost can prevent its use as the system size grows. To resolve this difficulty in the case of Bayesian linear regression, we develop a formula for evaluating the leave-one-out CV error approximately without actually performing CV. The usefulness of the developed formula is tested by statistical mechanical analysis for a synthetic model. This is confirmed by application to a real-world supernova data set as well.