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Paper · 1806.00550 · 2018

A Swiss Army Infinitesimal Jackknife

arXiv · PDF · Open in the Atlas

Code that ran

We lifted 13 functions out of this paper's own repositories and ran 3 of them in a sandbox. "Ran" means the function executed on a synthesized input and returned a value. It is not a reproduction of the paper's results.

RepositoryRoleRan
rgiordan/paragami pwc_unofficial 3 of 13
FunctionStatusWhere it lives
register_vcs_handler Ran rgiordan/paragami/paragami/_version.py
code served (permissive licence) · get_code("f12f4dabbeb242eb")
run_command Ran rgiordan/paragami/paragami/_version.py
code served (permissive licence) · get_code("86d4ff45d6295e29")
versions_from_parentdir Ran rgiordan/paragami/paragami/_version.py
code served (permissive licence) · get_code("b9a1535d27f2a9fb")
T Not yet run rgiordan/paragami/paragami/autograd_supplement_lib.py
code served (permissive licence) · get_code("c58078439679996f")
get_config_from_root Not yet run rgiordan/paragami/versioneer.py
code served (permissive licence) · get_code("2d084e1d0452b36f")
get_pattern_from_json Not yet run rgiordan/paragami/paragami/pattern_containers.py
code served (permissive licence) · get_code("ae47e6b0064263a5")
get_sym_matrix_inv_sqrt_funcs Not yet run rgiordan/paragami/paragami/sparse_preconditioners_lib.py
code served (permissive licence) · get_code("758f00f5f7bc6874")
inv_jvp Not yet run rgiordan/paragami/paragami/autograd_supplement_lib.py
code served (permissive licence) · get_code("2df8ad17b32e10de")
jvp_solve Not yet run rgiordan/paragami/paragami/autograd_supplement_lib.py
code served (permissive licence) · get_code("b0f4d1ec0ad52f5a")
load_folded Not yet run rgiordan/paragami/paragami/pattern_containers.py
code served (permissive licence) · get_code("55ce578a264c57f1")
logsumexp Not yet run rgiordan/paragami/paragami/simplex_patterns.py
code served (permissive licence) · get_code("39be29e5b164b2e7")
transform_eigenspace Not yet run rgiordan/paragami/paragami/optimization_lib.py
code served (permissive licence) · get_code("2bfef97b72b48af3")
truncate_eigenvalues Not yet run rgiordan/paragami/paragami/optimization_lib.py
code served (permissive licence) · get_code("a468a55007359300")

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Abstract

The error or variability of machine learning algorithms is often assessed by repeatedly re-fitting a model with different weighted versions of the observed data. The ubiquitous tools of cross-validation (CV) and the bootstrap are examples of this technique. 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.

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