# Centroid Approximation for Bootstrap: Improving Particle Quality at Inference

arXiv: https://arxiv.org/abs/2110.08720 · HTML: https://mlsanity.com/paper/2110.08720/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 32 of its 67 references that are in the map.
- First posted on arXiv 17 Oct 2021.

## Builds on (most cited first, 30 of 32)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Deep Reinforcement Learning with Double Q-learning](https://mlsanity.com/paper/1509.06461/) (2015)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Images](https://mlsanity.com/paper/1412.1897/) (2014)
- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [Deep Exploration via Bootstrapped DQN](https://mlsanity.com/paper/1602.04621/) (2016)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Snapshot Ensembles: Train 1, get M for free](https://mlsanity.com/paper/1704.00109/) (2017)
- [Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1402.4102/) (2014)
- [Deep Bayesian Bandits Showdown: An Empirical Comparison of Bayesian Deep Networks for Thompson Sampling](https://mlsanity.com/paper/1802.09127/) (2018)
- [Out-of-Distribution Detection Using an Ensemble of Self Supervised Leave-out Classifiers](https://mlsanity.com/paper/1809.03576/) (2018)
- [High-Quality Prediction Intervals for Deep Learning: A Distribution-Free, Ensembled Approach](https://mlsanity.com/paper/1802.07167/) (2018)
- [Masksembles for Uncertainty Estimation](https://mlsanity.com/paper/2012.08334/) (2020)
- [Adaptive, Distribution-Free Prediction Intervals for Deep Networks](https://mlsanity.com/paper/1905.10634/) (2019)
- [Predictive Inference Is Free with the Jackknife+-after-Bootstrap](https://mlsanity.com/paper/2002.09025/) (2020)
- [Stein Points](https://mlsanity.com/paper/1803.10161/) (2018)
- [Bootstrapping Upper Confidence Bound](https://mlsanity.com/paper/1906.05247/) (2019)
- [Sparse Variational Inference: Bayesian Coresets from Scratch](https://mlsanity.com/paper/1906.03329/) (2019)
- [Prediction Intervals: Split Normal Mixture from Quality-Driven Deep Ensembles](https://mlsanity.com/paper/2007.09670/) (2020)
- [Variational Gaussian Dropout is not Bayesian](https://mlsanity.com/paper/1711.02989/) (2017)
- [An Efficient Minibatch Acceptance Test for Metropolis-Hastings](https://mlsanity.com/paper/1610.06848/) (2016)
- [Wasserstein Measure Coresets](https://mlsanity.com/paper/1805.07412/) (2018)
- [Bayesian Bootstrap Spike-and-Slab LASSO](https://mlsanity.com/paper/2011.14279/) (2020)
- [Mini-batch Metropolis-Hastings MCMC with Reversible SGLD Proposal](https://mlsanity.com/paper/1908.02910/) (2019)

## Abstract (arXiv)

Bootstrap is a principled and powerful frequentist statistical tool for uncertainty quantification. Unfortunately, standard bootstrap methods are computationally intensive due to the need of drawing a large i.i.d. bootstrap sample to approximate the ideal bootstrap distribution; this largely hinders their application in large-scale machine learning, especially deep learning problems. In this work, we propose an efficient method to explicitly optimize a small set of high quality ``centroid'' points to better approximate the ideal bootstrap distribution. We achieve this by minimizing a simple objective function that is asymptotically equivalent to the Wasserstein distance to the ideal bootstrap distribution. This allows us to provide an accurate estimation of uncertainty with a small number of bootstrap centroids, outperforming the naive i.i.d. sampling approach. Empirically, we show that our method can boost the performance of bootstrap in a variety of applications.