Sparsity by Default: The Theory and Practice of ARD in Gaussian Process Regression for Variable Selection
Automatic relevance determination (ARD) is the standard device for input selection in Gaussian process (GP) regression. By giving the covariance kernel a separate lengthscale for every input and learning those lengthscales by maximizing the marginal likelihood, ARD lets the data decide which coordinates matter: irrelevant inputs receive very large lengthscales and are effectively switched off. We trace this mechanism to the Bayesian Occam's razor embodied in the marginal likelihood, derive the gradient through which it prunes inputs, and emphasize that ARD delivers effective rather than exact sparsity. We review the algorithms used in practice and the rules that turn lengthscales into sel...
| Authors | Jia Cai |
|---|---|
| Primary category | stat.ML |
| Published | 27 September 2026 |
| Last updated at source | 27 September 2026 |
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