Published on Mon Mar 30 2020

On Biased Random Walks, Corrupted Intervals, and Learning Under Adversarial Design

Daniel Berend, Aryeh Kontorovich, Lev Reyzin, Thomas Robinson

We tackle some fundamental problems in probability theory on corrupted random processes on the integer line. We analyze when a biased random walk is expected to reach its bottommost point and when intervals of integer points can be detected under a natural model of noise.

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Abstract

We tackle some fundamental problems in probability theory on corrupted random processes on the integer line. We analyze when a biased random walk is expected to reach its bottommost point and when intervals of integer points can be detected under a natural model of noise. We apply these results to problems in learning thresholds and intervals under a new model for learning under adversarial design.