Simple Analysis of Johnson-Lindenstrauss Transform under Neuroscience Constraints [article]

Maciej Skorski
2020 arXiv   pre-print
The paper re-analyzes a version of the celebrated Johnson-Lindenstrauss Lemma, in which matrices are subjected to constraints that naturally emerge from neuroscience applications: a) sparsity and b) sign-consistency. This particular variant was studied first by Allen-Zhu, Gelashvili, Micali, Shavit and more recently by Jagadeesan (RANDOM'19). The contribution of this work is a novel proof, which in contrast to previous works a) uses the modern probability toolkit, particularly basics of
more » ... sian and sub-gamma estimates b) is self-contained, with no dependencies on subtle third-party results c) offers explicit constants. At the heart of our proof is a novel variant of Hanson-Wright Lemma (on concentration of quadratic forms). Of independent interest are also auxiliary facts on sub-gaussian random variables.
arXiv:2008.08857v1 fatcat:hfszf5b4tfdrhkadjetvq5cf3m