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About this paper
Ryan Giordano, Michael I. Jordan, Tamara Broderick
The Higher-Order Infinitesimal Jackknife (HOIJ) approximates computationally intensive uncertainty quantification methods like cross-validation and bootstrap using higher-order Taylor series expansions. This approach provides finite-sample accuracy guarantees and enables scalable statistical inference for complex models by efficiently computing higher-order derivatives through forward-mode automatic differentiation.
Key insights
- Higher-order terms are essential for realizing the full benefits of bootstrap inference, as first-order approximations provide no inferential advantage over standard asymptotic theory regarding covariance estimation.
- The framework provides finite-sample accuracy bounds for the approximation error, offering concrete reliability guarantees rather than purely asymptotic results.
- Forward-mode automatic differentiation enables the efficient computation of higher-order derivatives by avoiding the storage of large tensors, making the method practical for high-dimensional problems.
Summary by alphaXiv.
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