# Probability Tools for Sequential Random Projection

arXiv: https://arxiv.org/abs/2402.14026 · HTML: https://mlsanity.com/paper/2402.14026/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 20 references that are in the map.
- First posted on arXiv 16 Feb 2024.

## Builds on (most cited first, 3 of 3)

- [Sketching as a Tool for Numerical Linear Algebra](https://mlsanity.com/paper/1411.4357/) (2014)
- [Q-Star Meets Scalable Posterior Sampling: Bridging Theory and Practice via HyperAgent](https://mlsanity.com/paper/2402.10228/) (2024)
- [Simple, unified analysis of Johnson-Lindenstrauss with applications](https://mlsanity.com/paper/2402.10232/) (2024)

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

- [Improving statistical learning methods via features selection without replacement sampling and random projection](https://mlsanity.com/paper/2506.00053/) (2025)

## Abstract (arXiv)

We introduce the first probabilistic framework tailored for sequential random projection, an approach rooted in the challenges of sequential decision-making under uncertainty. The analysis is complicated by the sequential dependence and high-dimensional nature of random variables, a byproduct of the adaptive mechanisms inherent in sequential decision processes. Our work features a novel construction of a stopped process, facilitating the analysis of a sequence of concentration events that are interconnected in a sequential manner. By employing the method of mixtures within a self-normalized process, derived from the stopped process, we achieve a desired non-asymptotic probability bound. This bound represents a non-trivial martingale extension of the Johnson-Lindenstrauss (JL) lemma, marking a pioneering contribution to the literature on random projection and sequential analysis.