A product-CLT and its application in invariance principle of random projection

2021/06/28 by Duan, JunTao, Popescu, Ionel, Zhou, Fan
#FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2106.14825

Abstract

Johnson-Lindenstrauss lemma states random projections can be used as a topology preserving embedding technique for fixed vectors. In this paper, we try to understand how random projections affect probabilistic properties of random vectors. In particular we prove the distribution of inner product of two independent random vectors X, Z ∈ Rⁿ is preserved by random projection S:Rⁿ → R^m. More precisely, \[ sup_t | P(\frac1C_m,n X^TS^TSZ

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