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Modern Streaming Data Analysis: Game-Theoretic Approach and Adaptive Change Detection
Abstract
The problem of sequential hypothesis testing is studied and the goal is to distinguish between the null hypothesis where the samples are generated sequentially according to a distribution p and the alternative hypothesis where the samples are generated sequentially according to a distribution q. The defender aims to distinguish the two hypotheses using as fewer samples as possible subject to false alarm constraints. The problem is studied under the adversarial setting, where the data generating distributions under the two hypotheses are manipulated by an adversary, whose goal is to deteriorate the performance of the defender, e.g., increasing the probability of error and expected sample sizes, with minimal cost. This problem is formulated as a non-zero-sum game between the defender and the adversary. A pair of strategies (the adversary’s strategy and the defender’s strategy) is proposed and proved to be a Nash equilibrium pair asymptotically. We also study the problem of quickest detection of an adversarial attack. Specifically, under the null hypothesis, the adversary picks p as the data generating distribution and it won’t change this distribution later. Under the alternative hypothesis, at some unknown time, an adversary changes the data-generating distribution from p to q. The goal of the defender is to detect the change as quickly as possible subject to false alarm constraint, while the goal of the adversary is to use the fewest cost to fool the defender. The problem is formulated as a non-zero-sum game between the adversary and the defender. A pair of strategies for the defender and the attacker is proposed and proved to be a Nash equilibrium pair for the non-zero-sum game asymptotically. Thirdly, we propose an adaptive top-r method to monitor large-scale data streams which can quickly detect the change under the circumstance that the number of changed data streams is unknown. In particular, our proposed method combines the Benjamin-Hochberg (BH) false discovery rate (FDR) control procedure and the CUSUM procedure for detecting the change efficiently, and it can be implemented easily.
Subject Area
Statistics
Recommended Citation
Cao, Shuchen, "Modern Streaming Data Analysis: Game-Theoretic Approach and Adaptive Change Detection" (2023). ETD collection for University of Nebraska-Lincoln. AAI30425221.
https://digitalcommons.unl.edu/dissertations/AAI30425221