# A Flexible Approach for Normal Approximation of Geometric and Topological Statistics

arXiv: https://arxiv.org/abs/2210.10744 · HTML: https://mlsanity.com/paper/2210.10744/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 51 references that are in the map.
- First posted on arXiv 19 Oct 2022.

## Builds on (most cited first, 2 of 2)

- [Efficient multivariate entropy estimation via k-nearest neighbour distances](https://mlsanity.com/paper/1606.00304/) (2016)
- [Finite-Sample Analysis of Fixed-k Nearest Neighbor Density Functional Estimators](https://mlsanity.com/paper/1606.01554/) (2016)

## Built on by (most cited first, 1 of 1)

- [Graph Memory: Spectral Associative Memory via Dirichlet Energy](https://mlsanity.com/paper/2609.32365/) (2026)

## Abstract (arXiv)

We derive normal approximation results for a class of stabilizing functionals of binomial or Poisson point process, that are not necessarily expressible as sums of certain score functions. Our approach is based on a flexible notion of the add-one cost operator, which helps one to deal with the second-order cost operator via suitably appropriate first-order operators. We combine this flexible notion with the theory of strong stabilization to establish our results. We illustrate the applicability of our results by establishing normal approximation results for certain geometric and topological statistics arising frequently in practice. Several existing results also emerge as special cases of our approach.