Detection of correlations with adaptive sensing

The problem of detecting correlations from samples of a high-dimensional Gaussian vector has recently received a lot of attention. In most existing work, detection procedures are provided with a full sample. However, following common wisdom in experimental design, the experimenter may have the capacity to make targeted measurements in an on-line and adaptive manner. In this paper, we investigate such adaptive sensing procedures for detecting positive correlations. It is shown that, using the same number of measurements, adaptive procedures are able to detect significantly weaker correlations than their nonadaptive counterparts. We also establish minimax lower bounds that show the limitations of any procedure. Keywords: Sequential testing; adaptive sensing; high-dimensional detection; highdimensional detection; sequential testing; sparse covariance matrices; sparse principal component analysi