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

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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.