Abstract 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 ( n 3 ) complexity and uses a dense Gaussian measurement matrix.

中文翻译：

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从聚合测量中推断用户偏好：一种用于隐私攻击的新型消息传递算法

摘要 Facebook 和 TikTok 等社交媒体平台引发了关于隐私的争论。最近社交媒体转变为日益集中的服务，以 TikTok 为例，只会加剧这一问题。虽然聚合被认为是打击侵犯隐私的有效方式，但高度集中可能会使聚合无效。我们提出了一种随机文章推送算法和一种消息传递重建算法，使社交媒体平台能够仅从公开可用的文章阅读汇总数据中推断出用户偏好，而无需存储任何个人用户的操作。它的 O ( n ) 复杂度允许重建算法扩展到大量人群，这是社交媒体平台的典型特征。而且，隐私攻击的可行性取决于使用尽可能少的文章的算法。我们确定高概率推理所需的最少文章数。给定喜欢给定主题的用户比例 0 ϵ 1 ，我们设计了一个推送算法和一个重构算法，以实现文章与用户的比率 β = ϵ ( 1 − ϵ ) ，在该比率发生相变。由于每次迭代错误概率缺乏单调性，算法的分析背离了经典的密度演化，这使得相变的发生令人惊讶。通过将推理问题表述为压缩感知问题，我们表明我们的相变阈值 ϵ ( 1 − ϵ ) 非常接近压缩感知，