Functional renormalization group approach for signal detection

Abstract

This review paper utilizes renormalization group techniques for signal detection in nearly continuous positive spectra. We emphasize the universal aspects of the analogue field-theory approach. The primary objective is to present an extended self-consistent construction of the analogue effective field-theory framework for data, which can be interpreted as a maximum entropy model. In particular, we leverage universality arguments to justify the $\mathbb{Z}_2$ symmetry of the classical action, highlighting the existence of both a large-scale (local) regime and a small-scale (nonlocal) regime. Secondly, in relation to noise models, we observe the universal relationship between phase transitions and symmetry breaking near the detection threshold. Finally, we address the challenge of defining the covariance matrix for tensor-like data. Based on the cutting graph prescription, we note the superiority of definitions that rely on complete graphs of large size for data analysis.