Ensemble learning is widely used in applications to make predictions in
complex decision problems---for example, averaging models fitted to a sequence
of samples bootstrapped from the available training data. While such methods
offer more accurate, stable, and robust predictions and model estimates, much
less is known about how to perform valid, assumption-lean inference on the
output of these types of procedures. In this paper, we propose the
jackknife+-after-bootstrap (J+aB), a procedure for constructing a predictive
interval, which uses only the available bootstrapped samples and their
corresponding fitted models, and is therefore "free" in terms of the cost of
model fitting. The J+aB offers a predictive coverage guarantee that holds with
no assumptions on the distribution of the data, the nature of the fitted model,
or the way in which the ensemble of models are aggregated---at worst, the
failure rate of the predictive interval is inflated by a factor of 2. Our
numerical experiments verify the coverage and accuracy of the resulting
predictive intervals on real data.

提出了一种基于 Jackknife + 和 Bootstrap 的预测区间构建方法 (J+aB)，该方法只使用可用的 Bootstrap 样本及其对应的拟合模型，可以在不假设数据分布，拟合模型的性质或集成模型聚合方式的情况下提供保证，并可以免费进行模型拟合，实验结果验证了预测区间的覆盖率和准确性。