Probability Tools for Sequential Random Projection
<|reference_start|>Probability Tools for Sequential Random Projection: 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.<|reference_end|>
@article{li2024probability,
    title={Probability Tools for Sequential Random Projection},
    author={Yingru Li},
    journal={arXiv preprint arXiv:2402.14026},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.14026},
    primaryClass={math.ST cs.DS cs.IT cs.NA math.IT math.NA math.PR stat.ML stat.TH}
}