Field theoretical approach for signal detection in nearly continuous positive spectra I: Matricial data

Abstract

Renormalization group techniques are widely used in modern physics to describe the low energy relevant aspects of systems involving a large number of degrees of freedom. Those techniques are thus expected to be a powerful tool to address open issues in data analysis when data sets are very larges. Signal detection and recognition for covariance matrix having a nearly continuous spectra is currently one of these opened issues. First investigations in this direction has been proposed in [Journal of Statistical Physics, 167, Issue 3-4, pp 462-475, (2017)] and [arXiv:2002.10574], from an analogy between coarse-graining and principal component analysis (PCA), regarding separation of sampling noise modes as a UV cut-off for small eigenvalues of the covariance matrix. The field theoretical framework proposed in this paper is a synthesis of these complementary point of views, aiming to be a general and operational framework, both for theoretical investigations and for experimental detection. Our investigations focus on signal detection, and exhibit experimental evidences in favor of a connection between symmetry breaking and the existence of an intrinsic detection threshold.

arXiv comment20 pages, 15 figures

References in corpus (32)

• Exact evolution equation for the effective potential
• Optimisation of the exact renormalisation group
• Regularity Properties and Pathologies of Position-Space Renormalization-Group Transformations
• An Introduction to the Nonperturbative Renormalization Group
• Mode-Coupling Approximations, Glass Theory and Disordered Systems
• Searching for collective behavior in a network of real neurons
• Optimization of the derivative expansion in the nonperturbative renormalization group
• Coarse--graining, fixed points, and scaling in a large population of neurons
• Convergence of Non-Perturbative Approximations to the Renormalization Group
• Derivative expansion and renormalisation group flows
• Non perturbative renormalisation group and momentum dependence of $n$-point functions (I)
• PCA meets RG
• Optimality and Sub-optimality of PCA I: Spiked Random Matrix Models
• Non perturbative renormalization group and momentum dependence of n-point functions (II)
• The Sherrington-Kirkpatrick model: an overview
• Classical-to-critical crossovers from field theory
• Information geometric approach to the renormalisation group
• Nonperturbative renormalization group beyond melonic sector: The Effective Vertex Expansion method for group fields theories
• Renormalization group analysis of the M-p-spin glass model with p=3 and M=3
• Ward identity violation for melonic $T^4$-truncation
• Truncation Effects in the Functional Renormalization Group Study of Spontaneous Symmetry Breaking
• Principal component analysis of the primordial tensor power spectrum
• Revisited functional renormalization group approach for random matrices in the large-$N$ limit
• Ward-constrained melonic renormalization group flow for the rank-four ${\varphi }^6$ tensorial group field theory
• Field theoretical approach for signal detection in nearly continuous positive spectra II: Tensorial data
• Exact Renormalization Groups as a form of Entropic Dynamics
• Pedagogical comments about nonperturbative Ward-constrained melonic renormalization group flow
• Reliability of the local truncations for the random tensor models renormalization group flow
• RG inspired Machine Learning for lattice field theory
• Inferring relevant features: from QFT to PCA
• Coarse-grained distinguishability of field interactions
• Statistical mechanics of stochastic growth phenomena

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