# Online stochastic Newton methods for estimating the geometric median and applications

arXiv: https://arxiv.org/abs/2304.00770 · HTML: https://mlsanity.com/paper/2304.00770/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 22 references that are in the map.
- First posted on arXiv 3 Apr 2023.

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

- [Online estimation of the inverse of the Hessian for stochastic optimization with application to universal stochastic Newton algorithms](https://mlsanity.com/paper/2401.10923/) (2024)
- [A Full Adagrad algorithm with O(Nd) operations](https://mlsanity.com/paper/2405.01908/) (2024)

## Abstract (arXiv)

In the context of large samples, a small number of individuals might spoil basic statistical indicators like the mean. It is difficult to detect automatically these atypical individuals, and an alternative strategy is using robust approaches. This paper focuses on estimating the geometric median of a random variable, which is a robust indicator of central tendency. In order to deal with large samples of data arriving sequentially, online stochastic Newton algorithms for estimating the geometric median are introduced and we give their rates of convergence. Since estimates of the median and those of the Hessian matrix can be recursively updated, we also determine confidences intervals of the median in any designated direction and perform online statistical tests.