Year: 2022
Type: article
Abstract: Analytical understanding of how low-dimensional latent features reveal themselves in large-dimensional data is still lacking. We study this by defining a probabilistic linear latent features model with additive noise and by analytically and numerically computing the statistical distributions of pairwise correlations and eigenvalues of the data correlation matrix. This allows us to resolve the latent feature structure across a wide range of data regimes set by the number of recorded variables, observations, latent features, and the signal-to-noise ratio. We find a characteristic imprint of latent features in the distribution of correlations and eigenvalues and provide an analytic estimate for the boundary between signal and noise, even in the absence of a spectral gap.
Source: Physical review. E
Authors: Philipp Fleig, Ilya Nemenman
Institutions: University of Pennsylvania, Emory University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G2011061226, Modeling Sources of Variation in Interaction Networks Using a C. Elegans Microbiome Model, Dynamical Inference of Forces in Dusty Plasmas using Three-Dimensional Laser Sheet Tomography, CRCNS Research Proposal: Randomness and systematicity in neural codes for motor exploration, Programs on Critical Problems in Physics, Astrophysics and Biophysics at the Aspen Center for Physics, G8264086291
OpenAlex ID: W3214663881