# Orthogonal Bootstrap: Efficient Simulation of Input Uncertainty

arXiv: https://arxiv.org/abs/2404.19145 · HTML: https://mlsanity.com/paper/2404.19145/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 63 references that are in the map.
- First posted on arXiv 29 Apr 2024.

## Builds on (most cited first, 18 of 18)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [An Investigation of Why Overparameterization Exacerbates Spurious Correlations](https://mlsanity.com/paper/2005.04345/) (2020)
- [Orthogonal Statistical Learning](https://mlsanity.com/paper/1901.09036/) (2019)
- [A Swiss Army Infinitesimal Jackknife](https://mlsanity.com/paper/1806.00550/) (2018)
- [Confidence Intervals for Random Forests: The Jackknife and the Infinitesimal Jackknife](https://mlsanity.com/paper/1311.4555/) (2013)
- [Discriminative Jackknife: Quantifying Uncertainty in Deep Learning via Higher-Order Influence Functions](https://mlsanity.com/paper/2007.13481/) (2020)
- [A Higher-Order Swiss Army Infinitesimal Jackknife](https://mlsanity.com/paper/1907.12116/) (2019)
- [Approximating Full Conformal Prediction at Scale via Influence Functions](https://mlsanity.com/paper/2202.01315/) (2022)
- [Subsampling to Enhance Efficiency in Input Uncertainty Quantification](https://mlsanity.com/paper/1811.04500/) (2018)
- [Influence Functions for Machine Learning: Nonparametric Estimators for Entropies, Divergences and Mutual Informations](https://mlsanity.com/paper/1411.4342/) (2014)
- [A subsampled double bootstrap for massive data](https://mlsanity.com/paper/1508.01126/) (2015)
- [A Cheap Bootstrap Method for Fast Inference](https://mlsanity.com/paper/2202.00090/) (2022)
- [Bias Correction with Jackknife, Bootstrap, and Taylor Series](https://mlsanity.com/paper/1709.06183/) (2017)
- [Debiasing Samples from Online Learning Using Bootstrap](https://mlsanity.com/paper/2108.00236/) (2021)
- [Constructing Prediction Intervals with Neural Networks: An Empirical Evaluation of Bootstrapping and Conformal Inference Methods](https://mlsanity.com/paper/2210.05354/) (2022)
- [Correcting Convexity Bias in Function and Functional Estimate](https://mlsanity.com/paper/2208.07996/) (2022)

## Abstract (arXiv)

Bootstrap is a popular methodology for simulating input uncertainty. However, it can be computationally expensive when the number of samples is large. We propose a new approach called Orthogonal Bootstrap that reduces the number of required Monte Carlo replications. We decomposes the target being simulated into two parts: the textitnon-orthogonal part which has a closed-form result known as Infinitesimal Jackknife and the textitorthogonal part which is easier to be simulated. We theoretically and numerically show that Orthogonal Bootstrap significantly reduces the computational cost of Bootstrap while improving empirical accuracy and maintaining the same width of the constructed interval.