Recovery thresholds in the sparse planted matching problem
Recovery thresholds in the sparse planted matching problem
复制标题
稀疏种植匹配问题中的恢复阈值
DOI：
10.1103/physreve.102.022304
复制
发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Lenka Zdeborov'a
中科院分区：
文献类型：
--
作者：
G. Semerjian;G. Sicuro;Lenka Zdeborov'a
通过利用种植匹配内部和外部边上权重的两种不同分布所产生的信息，我们考虑了恢复隐藏在加权随机图中的未知完美匹配的统计推断问题。最近的一项工作证明了在大尺寸极限下，对于完全连通图上特定形式的权重分布，存在完全恢复阶段和部分恢复阶段之间的相变。我们在两个方向上推广和推广了这一结果：我们利用分支随机游走过程的技术联系，得到了一般权重分布和可能的稀疏图的相变位置的判据，以及对相变周围的临界区域的更精确的定量描述。
We consider the statistical inference problem of recovering an unknown perfect matching, hidden in a weighted random graph, by exploiting the information arising from the use of two different distributions for the weights on the edges inside and outside the planted matching. A recent work has demonstrated the existence of a phase transition, in the large size limit, between a full and a partial-recovery phase for a specific form of the weights distribution on fully connected graphs. We generalize and extend this result in two directions: we obtain a criterion for the location of the phase transition for generic weights distributions and possibly sparse graphs, exploiting a technical connection with branching random walk processes, as well as a quantitatively more precise description of the critical regime around the phase transition.