Phase Transition of Eigenvalues of Covariances from the Spiked Mixture Model in High-dimensional Regimes
Year: 2026
Type: preprint
Abstract: The spiked mixture model (SMM) has been introduced as a probabilistic model that generalizes the single-spike (Wishart) model to a mixture model form. With applications ranging from imaging mass spectrometry in the life sciences to hyperspectral imaging in computer vision, it is crucial to understand under which circumstances its signals can be recovered from noisy measurements. The highly multiplexed nature of these measurement types furthermore necessitates such analysis to hold in highdimensional settings. In this paper, we prove that the extreme eigenvalues of the covariance matrix from the SMM exhibit a phase transition in high-dimensional regimes. We show that this phase transition, and thus signal recovery by extreme eigenvalues, depends on several interacting factors: the correlation between spikes (i.e., how similar in content underlying signals are), the energy parameters (i.e., the absolute strength of each underlying signal), and the mixture probabilities (i.e., how likely it is to encounter each underlying signal). This work provides sharp information-theoretic bounds on the parameters needed to detect one or more spikes from extreme eigenvalues of the SMM covariance matrix, and these guarantees could potentially impact any application of the SMM. Understanding this interplay could serve as a tool for driving experimental design in analytical chemistry and life sciences.
Source: arXiv (Cornell University)
Authors: Delacour, Paul-Louis, Van de Plas, Raf
Institution: Delft University of Technology
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funders: École Normale Supérieure, Institut national de recherche en informatique et en automatique (INRIA), National Institutes of Health, National Institute on Aging, National Eye Institute, National Cancer Institute, National Institute of Allergy and Infectious Diseases, National Institute of Diabetes and Digestive and Kidney Diseases, Common Fund
Awards: Vanderbilt University Biomolecular Multimodal Imaging Center for 3-Dimensional Tissue Mapping, Biomolecular Multimodal Imaging Center: 3-Dimensional Tissue Mapping of the Human Pancreas and Eye, Defining the impact of host factors on the molecular architecture and bacterial physiology of Staphylococcus aureus abscesses, G8873827080, A Multimodal 3D Atlas of Colorectal Cancer Across Ages of Onset, Vanderbilt University Biomolecular Multimodal Imaging Center for 3-Dimensional Mapping of the Human Kidney, Molecular mapping of microbial communities at the host-pathogen interface by multi-modal 3-dimensional imaging mass spectrometry, Elucidating Molecular Drivers of Aging and Alzheimer's Disease via Multimodal Imaging Mass Spectrometry, Multimodal Imaging Mass Spectrometry and Spatial Omics for the Human Kidney
OpenAlex ID: W7168362758