随机列重复下的马尔可夫数据库匹配
Matching of Markov Databases Under Random Column Repetitions
摘要：
相关混洗数据库的匹配条目具有从隐私到生物学的实际应用。本文针对时间索引数据库抽样中的同步误差问题，研究了随机列重复和删除情况下的随机数据库匹配问题。假设对于数据库中的每个条目（行），属性（列）是相关的，这被建模为马尔可夫过程。提出了用列直方图作为置换不变特征来检测重复模式，并利用信息论工具证明了列直方图的渐近唯一性。重复检测，然后由一个基于典型性的行匹配方案。考虑到这一整体方案，成功匹配的数据库中的数据库增长率的充分条件。Fano不等式的一个修正版本导致了成功匹配的一个严格的必要条件，建立了列重复下的匹配能力。该容量等于擦除界限，其假设重复位置是先验已知的。总的来说，我们的研究结果提供了关于匿名时间索引数据的隐私保护发布的见解。
英文摘要：
Matching entries of correlated shuffled databases have practical applications ranging from privacy to biology. In this paper, motivated by synchronization errors in the sampling of time-indexed databases, matching of random databases under random column repetitions and deletions is investigated. It is assumed that for each entry (row) in the database, the attributes (columns) are correlated, which is modeled as a Markov process. Column histograms are proposed as a permutation-invariant feature to detect the repetition pattern, whose asymptotic-uniqueness is proved using information-theoretic tools. Repetition detection is then followed by a typicality-based row matching scheme. Considering this overall scheme, sufficient conditions for successful matching of databases in terms of the database growth rate are derived. A modified version of Fano's inequality leads to a tight necessary condition for successful matching, establishing the matching capacity under column repetitions. This capacity is equal to the erasure bound, which assumes the repetition locations are known a-priori. Overall, our results provide insights on privacy-preserving publication of anonymized time-indexed data.
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