Efficient leave-one-out cross-validation for Gaussian processes #3098
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…-pytorch#3098) Summary: BoTorch currently supports a naive version of leave-one-out (LOO) cross-validation, which entails generating all folds directly and evaluating the model on all folds separately. However, for Gaussian processes, there is an efficient way to compute all LOO results (LOO predictive means and variances) with a single linear-algebraic formula with a O(n^3) complexity, whereas the naive approach takes O(n^3) per fold, so O(n^4) in total. This commit implements the effient LOO CV method for non-ensemble BoTorch models whose prior marginal distributions are a multi-variate Normals. Differential Revision: D88273413
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…-pytorch#3098) Summary: BoTorch currently supports a naive version of leave-one-out (LOO) cross-validation, which entails generating all folds directly and evaluating the model on all folds separately. However, for Gaussian processes, there is an efficient way to compute all LOO results (LOO predictive means and variances) with a single linear-algebraic formula with a O(n^3) complexity, whereas the naive approach takes O(n^3) per fold, so O(n^4) in total. This commit implements the effient LOO CV method for non-ensemble BoTorch models whose prior marginal distributions are a multi-variate Normals. Differential Revision: D88273413
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Summary:
BoTorch currently supports a naive version of leave-one-out (LOO) cross-validation, which entails generating all folds directly and evaluating the model on all folds separately.
However, for Gaussian processes, there is an efficient way to compute all LOO results (LOO predictive means and variances) with a single linear-algebraic formula with a O(n^3) complexity, whereas the naive approach takes O(n^3) per fold, so O(n^4) in total.
This commit implements the effient LOO CV method for non-ensemble BoTorch models whose prior marginal distributions are a multi-variate Normals.
Differential Revision: D88273413