ATD: Detection of Clusters in Distributed Systems of Information under Dependence

该提案的第一部分涉及检测相关性。一个特殊情况是检验多变量总体的协方差矩阵是否是单位矩阵的问题。研究人员将重新考虑这个经典问题，假设在另一种情况下，只有一小部分变量是相关的。第二部分的建议是集中在确定哪些相关结构是可能的伯努利随机变量。研究人员建议调查这种代数约束下的相关性之间的相关性伯努利随机变量的约束下的相关性结构所隐含的同质性（平稳性）和各向同性，在长期依赖的情况下。第三部分讨论了随机技术在时间序列和随机场变点分析中的应用。这在数据的潜在分布未知的检测情况下特别重要。最近推出的一种新的方法来引导时间序列，即线性过程引导，持有一定的承诺，似乎可扩展到random fields.The异常检测的任务是典型的监视设置的第一步是检测异常的存在。应用范围包括检测运输危险放射性或生物活性材料的车辆、目标跟踪、从卫星图像识别人造物体等。除了监视之外，类似的检测问题还出现在许多其他领域，例如卫星火灾的检测，城市地区的流感爆发或医学成像中的肿瘤检测。研究人员将专注于检测数据中不寻常的依赖关系，对这种依赖关系进行建模，并根据精心设计的模拟设计校准探测器的新方法。

The first part of the proposal deals with detecting correlations. A special case is the problem of testing whether the covariance matrix of a multivariate population is the identity matrix. The investigators will reconsider this classical problem assuming that, under the alternative, only a small fraction of the variables are correlated. The second part of the proposal is focused on determining which correlation structures are possible for Bernoulli random variables. The investigators propose to investigate such algebraic constraints on correlations between Bernoulli random variables under constraints on the correlation structure implied by homogeneity (stationarity) and isotropy, in the case of long range dependence. The third part is on applying resampling techniques to change point analysis of time series and random fields. This is particularly important in detection situations where the underlying distribution of the data is unknown. A recently introduced novel way to bootstrap time series, namely the linear process bootstrap, holds some promise and seems extendable to random fields.The task of anomaly detection is quintessential in surveillance settings where the first step is to detect the presence of an anomaly. Applications range from detecting vehicles that transport hazardous radioactive or bioactive materials, target tracking, man-made object recognition from satellite images, and more. Beyond surveillance, similar detection problems arise in many other areas, such as the detection of fires for satellites, flu outbreaks in an urban area, or the detection of tumors in medical imaging. The investigators will focus on detecting unusual dependencies in the data, on modeling such dependencies and on engineering new ways of calibrating detectors based on carefully designed simulations.