Identifying correlated components in high-dimensional multivariate Gaussian models

Abstract

In this paper, the problem of identifying correlated components in a high-dimensional Gaussian vector is considered. In the setup considered, instead of having to take a full-vector observation at each time index, the observer is allowed to observe any subset or full set of components in the vector, and he has the freedom to design his sampling strategies over time. The observer aims to find an optimal sampling strategy and a decision rule to maximize the error exponent (per sample). We focus on sequential strategies, in which the sampling actions depend on the observations taken so far. We first derive performance bounds of any sequential sampling strategy. We then design a low complexity procedure called sequential diagonal procedure. We show that this low complexity sequential procedure substantially outperforms the optimal non-adaptive strategy when the strength of the signal is strong.