多项式时间内近最优的节点隐私社区估计
Near-optimal node-private community estimation in polynomial-time
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中文总结 AI 辅助
研究解决Klopp和Zadik的开放问题，提出高概率多项式时间节点隐私算法，通过显式构造替代及接受-拒绝算法，在随机块模型中实现精确恢复，分析表明该算法在社区数量和隐私参数特定增长情况下能达极小极大率，匹配隐私成本下限。
中文摘要 AI 辅助
本文解决了Klopp和Zadik（2026）的一个开放问题，提供了一种高概率多项式时间的节点隐私算法，其在随机块模型中精确恢复方面的性能几乎与他们的指数时间节点隐私算法相匹配。结果涉及为惩罚似然函数显式构造的Lipschitz替代，以及精心设计的接受-拒绝算法，能在多项式时间内从相应指数机制中采样社区标签。还严格分析了算法的隐私、运行时和效用，表明即使社区数量K随节点数量n对数增长，隐私参数ε随log(n)增长时也能实现精确恢复的极小极大率，与该设置下隐私成本的已知下限相匹配。
英文摘要
In this paper, we resolve an open question of Klopp & Zadik (2026) by providing a high-probability polynomial-time, node-private algorithm which nearly matches the performance of their exponential-time node-private algorithm for exact recovery in stochastic block models. Our result involves an explicitly constructed Lipschitz surrogate for the penalized likelihood function, as well as a carefully devised accept-reject algorithm that samples community labels from the corresponding exponential mechanism in polynomial-time. We rigorously analyze the privacy, runtime, and utility of our proposed algorithm, showing that even when the number of communities K grows logarithmically with the number of nodes n, we can achieve the minimax rates for exact recovery with the privacy parameter epsilon growing as log(n), thus matching known lower bounds on the cost of privacy for this setting.
