Infer user preferences from aggregate measurements: A novel message passing algorithm for privacy attack

Social media platforms, such as Facebook and TikTok, have triggered debates on privacy. The recent transformation of social media into an increasingly centralized service, exemplified by TikTok, only exacerbates the matter. While aggregation has been deemed an effective way to combat privacy infringement, a high degree of centralization can make aggregation ineffective. We present a randomized article-push algorithm and a message-passing reconstruction algorithm that enable social media platforms to infer user preferences from only the publicly available aggregate data of article-reads, without storing any individual users’ actions. Its O(n) complexity allows the reconstruction algorithm to scale to a large population, as is typical of social media platforms. Moreover, the feasibility of the privacy attack depends on the algorithm using as few articles as possible. We determine the minimum number of articles needed for high probability inference. Given the proportion of users, 0<ϵ<1, who prefer a given topic, we design a push algorithm and a reconstruction algorithm that achieve an article-to-user ratio β=ϵ(1−ϵ), at which phase transition occurs. The analysis of the algorithm departs from the classic density evolution due to the lack of monotonicity in the per-iteration error probability, which makes it surprising that phase transition takes place. By formulating the inference problem as a compressed sensing problem, we show that our phase transition threshold ϵ(1−ϵ) is extremely close to that of compressed sensing, even when the latter algorithm is of a worst-case O(n³) complexity and uses a dense Gaussian measurement matrix.