推理的统计物理学：推理和算法
Statistical physics of inference: Thresholds and algorithms
摘要：
在今天的科学中，许多基本问题都可以被表述为推理问题：对一组变量进行部分或噪声观测，目标是根据测量中包含的间接信息恢复或推断变量的值。对于这样的问题，核心的科学问题是：在什么条件下，测量中包含的信息足以使令人满意的推断成为可能？对于这个任务，最有效的算法是什么？越来越多的工作表明，我们通常可以通过将这些基本障碍视为统计物理学意义上的相变来理解和定位它们。此外，事实证明，我们可以利用获得的物理洞察力来开发新的有前途的算法。推理和统计物理之间的连接目前正在见证一个令人印象深刻的复兴，我们在这里回顾目前的国家的最先进的，与教学重点的伊辛模型制定为一个推理问题，我们称之为种植自旋玻璃。在应用方面，我们审查两类问题：（一）推断的集群图和网络，社区检测作为一个特殊的情况下，（ii）估计信号从其嘈杂的线性测量，与压缩传感作为稀疏估计的情况下。我们的目标是为物理学和其他领域的研究人员提供一个教学评论，对这个迷人的话题感兴趣。
英文摘要：
Many questions of fundamental interest in todays science can be formulated as inference problems: Some partial, or noisy, observations are performed over a set of variables and the goal is to recover, or infer, the values of the variables based on the indirect information contained in the measurements. For such problems, the central scientific questions are: Under what conditions is the information contained in the measurements sufficient for a satisfactory inference to be possible? What are the most efficient algorithms for this task? A growing body of work has shown that often we can understand and locate these fundamental barriers by thinking of them as phase transitions in the sense of statistical physics. Moreover, it turned out that we can use the gained physical insight to develop new promising algorithms. Connection between inference and statistical physics is currently witnessing an impressive renaissance and we review here the current state-of-the-art, with a pedagogical focus on the Ising model which formulated as an inference problem we call the planted spin glass. In terms of applications we review two classes of problems: (i) inference of clusters on graphs and networks, with community detection as a special case and (ii) estimating a signal from its noisy linear measurements, with compressed sensing as a case of sparse estimation. Our goal is to provide a pedagogical review for researchers in physics and other fields interested in this fascinating topic.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
