Detection of Correlations with Adaptive Sensing

TL;DR

This paper explores adaptive sensing methods for detecting correlations in high-dimensional Gaussian data, demonstrating that adaptive measurements can identify weaker correlations more efficiently than non-adaptive methods.

Contribution

It introduces adaptive sensing procedures for correlation detection and proves they outperform non-adaptive methods, along with establishing fundamental lower bounds.

Findings

Adaptive procedures detect weaker correlations with the same number of measurements.

Adaptive sensing significantly improves detection power over non-adaptive methods.

Minimax lower bounds reveal the fundamental limitations of correlation detection.

Abstract

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 work, we investigate such adaptive sensing procedures for detecting positive correlations. It it shown that, using the same number of measurements, adaptive procedures are able to detect significantly weaker correlations than their non-adaptive counterparts. We also establish minimax lower bounds that show the limitations of any procedure.