# Normal-bundle Bootstrap

arXiv: https://arxiv.org/abs/2007.13869 · HTML: https://mlsanity.com/paper/2007.13869/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jul 2020.

## Built on by (most cited first, 2 of 2)

- [Gaussian Process Subspace Regression for Model Reduction](https://mlsanity.com/paper/2107.04668/) (2021)
- [Digital Twins and Civil Engineering Phases: Reorienting Adoption Strategies](https://mlsanity.com/paper/2403.02426/) (2024)

## Abstract (arXiv)

Probabilistic models of data sets often exhibit salient geometric structure. Such a phenomenon is summed up in the manifold distribution hypothesis, and can be exploited in probabilistic learning. Here we present normal-bundle bootstrap (NBB), a method that generates new data which preserve the geometric structure of a given data set. Inspired by algorithms for manifold learning and concepts in differential geometry, our method decomposes the underlying probability measure into a marginalized measure on a learned data manifold and conditional measures on the normal spaces. The algorithm estimates the data manifold as a density ridge, and constructs new data by bootstrapping projection vectors and adding them to the ridge. We apply our method to the inference of density ridge and related statistics, and data augmentation to reduce overfitting.