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These methods are powerful in large part due to their model agnosticism but can be slow to run on modern, large data sets due to the need to repeatedly re-fit the model. In this work, we use a linear approximation to the dependence of the fitting procedure on the weights, producing results that can be faster than repeated re-fitting by an order of magnitude. This linear approximation is sometimes known as the \"infinitesimal jackknife\" in the statistics literature, where it is mostly used as a theoretical tool to prove asymptotic results. We provide explicit finite-sample error bounds for the infinitesimal jackknife in terms of a small number of simple, verifiable assumptions. Our results apply whether the weights and data are stochastic or deterministic, and so can be used as a tool for proving the accuracy of the infinitesimal jackknife on a wide variety of problems. As a corollary, we state mild regularity conditions under which our approximation consistently estimates true leave-$k$-out cross-validation for any fixed $k$. These theoretical results, together with modern automatic differentiation software, support the application of the infinitesimal jackknife to a wide variety of practical problems in machine learning, providing a \"Swiss Army infinitesimal jackknife\". We demonstrate the accuracy of our methods on a range of simulated and real datasets.","url_abs":"http://arxiv.org/abs/1806.00550v3","url_pdf":"http://arxiv.org/pdf/1806.00550v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"a-swiss-army-infinitesimal-jackknife","repo_url":"https://github.com/rgiordan/AISTATS2019SwissArmyIJ","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"a-swiss-army-infinitesimal-jackknife","repo_url":"https://github.com/rgiordan/paragami","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"Apache-2.0"}},{"paper_slug":"a-swiss-army-infinitesimal-jackknife","repo_url":"https://github.com/rgiordan/vittles","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"Apache-2.0"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1806.00550","atlas_url":"https://app.syntology.ai/?focus=1806.00550","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1806.00550"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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