The error or variability of machine learning algorithms is often assessed by repeatedly refitting 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 ...