Non-adaptive adaptive sampling on turnstile streams
Sepideh Mahabadi, Ilya Razenshteyn, David P. Woodruff, Samson Zhou · 2020
Adaptive sampling is a useful algorithmic tool for data summarization problems in the classical centralized setting, where the entire dataset is available to the single processor performing the computation. Adaptive sampling repeatedly selects rows of an underlying matrix A∈ℝ n× d , where n≫ d, with probabilities proportional to their distances to the subspace of the previously selected rows. Intuitively, adaptive sampling seems to be limited to trivial multi-pass algorithms in the streaming model of computation due to its inherently sequential nature of assigning sampling probabilities to each row only after the previous iteration is completed. Surprisingly, we show this is not the case by giving the first one-pass algorithms for adaptive sampling on turnstile streams and using space poly(d,k,logn), where k is the number of adaptive sampling rounds to be performed.