Probability Tools for Sequential Random Projection
Keywords: Sequential random projection, Johnson-Lindenstrauss, Sequential decision-making, High-dimensional probability, Self-normalized Processes
TL;DR: Providing a non-trivial martingale extension of Johnson-Lindenstrauss and new insights into high-dimensional data processing.
Abstract: We introduce the first probabilistic framework 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. This analytical difficulty is resolved by a construction of a stopped process that interconnect a series of concentration events 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.
Student Paper: Yes
Submission Number: 15
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