PreprintCC BY 4.0arXiv
Spectral theory of large data with power-law latent features
Abstract
Power-law eigenvalue spectra of covariance matrices estimated from data appear in diverse domains ranging from neural populations to proteins. We introduce a generative latent feature model for such data, optionally corrupted by measurement noise, and develop its spectral theory. We derive closed leading-order self-consistent equations for the Stieltjes transform of the covariance matrix from which the bulk eigenvalue density is obtained and provide a variational principle for the self-consistent equations. We also compute the positions and fluctuations of isolated top eigenvalues. The theory is validated in known algebraic limits and tested against simulations.
Related
- Spectral theory for dynamical large deviations in non-Markov self-interacting processes
- Efficient Spectral Broadening from 850 nm to 1150 nm in the Low-Peak-Power Regime Using a Single-Stage Bulk Multipass Cell
- High-sensitivity line-field spectral-domain OCT driven by a power-scaled gain-managed nonlinear fiber source
- Modelling Fourier filtering wavefront sensors for power spectral density-based methods: The AOPERA tool
- Understanding Latent-Dimension Scaling in Dynamical-System Learning through Spectral Reliability
BibTeX
@misc{fleig2026spectral,
title = {{Spectral theory of large data with power-law latent features}},
author = {Philipp Fleig},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39013},
eprint = {2610.39013},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39013},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Spectral theory of large data with power-law latent features
AU - Philipp Fleig
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.39013
UR - https://arxiv.org/abs/2610.39013
AB - Power-law eigenvalue spectra of covariance matrices estimated from data appear in diverse domains ranging from neural populations to proteins. We introduce a generative latent feature model for such data, optionally corrupted by measurement noise, and develop its spectral theory. We derive closed leading-order self-consistent equations for the Stieltjes transform of the covariance matrix from which the bulk eigenvalue density is obtained and provide a variational principle for the self-consistent equations. We also compute the positions and fluctuations of isolated top eigenvalues. The theory is validated in known algebraic limits and tested against simulations.
ER -