Utility Change Point Detection in Online Social Media: A Revealed Preference Framework

This paper deals with change detection of utility maximization behavior given a dataset. In online social media, such changes occur due to the effect of marketing, advertising, or changes in ground truth. First, we use the revealed preference framework to detect the unknown time point (change point) at which the utility function changed. We derive necessary and sufficient conditions for detecting the change point. Second, in the presence of noisy measurements, we propose a method to detect the change point and construct a decision test. Also, an optimization criteria is provided to recover the linear perturbation coefficients. Finally, to reduce the computational cost, a dimensionality reduction algorithm using Johnson–Lindenstrauss transform is presented. The results developed are illustrated on two real datasets: Yahoo! Tech Buzz dataset and Youstatanalyzer dataset. By using the results developed in the paper, several useful insights can be gleaned from these datasets. First, the changes in ground truth affecting the utility of the agent can be detected by utility maximization behavior in online search. Second, the recovered utility functions satisfy the single crossing property indicating strategic substitute behavior in online search. Finally, due to the large number of videos in YouTube, the utility maximization behavior was verified through the dimensionality reduction algorithm.

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