Introduces a TAP-motivated framework and constructs explicit parameter-free spectral algorithms that achieve strong detection and weak recovery thresholds in three canonical correlated two-view models with matching lower bounds.
Better Together: Cross and Joint Covariances Enhance Signal Detectability in Undersampled Data
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
abstract
Many data-science applications involve detecting a shared signal between two high-dimensional variables. Using random matrix theory methods, we determine when such signal can be detected and reconstructed from sample correlations, despite the background of sampling noise induced correlations. We consider three different covariance matrices constructed from two high-dimensional variables: their individual self covariance, their cross covariance, and the self covariance of the concatenated (joint) variable, which incorporates the self and the cross correlation blocks. We observe the expected Baik, Ben Arous, and P\'ech\'e detectability phase transition in all these covariance matrices, and we show that joint and cross covariance matrices always reconstruct the shared signal earlier than the self covariances. Whether the joint or the cross approach is better depends on the mismatch of dimensionalities between the variables. We discuss what these observations mean for choosing the right method for detecting linear correlations in data and how these findings may generalize to nonlinear statistical dependencies.
years
2026 2verdicts
UNVERDICTED 2representative citing papers
DySIB recovers a two-dimensional representation matching the phase space of a physical pendulum from high-dimensional video data by maximizing predictive mutual information in latent space.
citing papers explorer
-
Optimal Spectral Algorithms for Correlated Two-view Models in High Dimensions
Introduces a TAP-motivated framework and constructs explicit parameter-free spectral algorithms that achieve strong detection and weak recovery thresholds in three canonical correlated two-view models with matching lower bounds.
-
Information bottleneck for learning the phase space of dynamics from high-dimensional experimental data
DySIB recovers a two-dimensional representation matching the phase space of a physical pendulum from high-dimensional video data by maximizing predictive mutual information in latent space.