Related papers: Applications of Random Matrix Theory in Machine Le…

Estimating the eigenvalues of a population covariance matrix from a sample covariance matrix is a problem of fundamental importance in multivariate statistics; the eigenvalues of covariance matrices play a key role in many widely…

Functional magnetic resonance imaging (fMRI) aims to locate activated regions in human brains when specific tasks are performed. The conventional tool for analyzing fMRI data applies some variant of the linear model, which is restrictive in…

In this paper we study the problem of reconstruction of a low-rank matrix observed with additive Gaussian noise. First we show that under mild assumptions (about the prior distribution of the signal matrix) we can restrict our attention to…

Progress in natural language processing (NLP) models that estimate representations of word sequences has recently been leveraged to improve the understanding of language processing in the brain. However, these models have not been…

Large efforts are currently under way to systematically map functional connectivity between all pairs of millimeter-scale brain regions using big volumes of neuroimaging data. Functional magnetic resonance imaging (fMRI) can produce these…

Modern Machine Learning (ML) and Deep Neural Networks (DNNs) often operate on high-dimensional data and rely on overparameterized models, where classical low-dimensional intuitions break down. In particular, the proportional regime where…

Dimensional reduction of high dimensional data can be achieved by keeping only the relevant eigenmodes after principal component analysis. However, differentiating relevant eigenmodes from the random noise eigenmodes is problematic. A new…

Using random matrix technique we determine an exact relation between the eigenvalue spectrum of the covariance matrix and of its estimator. This relation can be used in practice to compute eigenvalue invariants of the covariance…

Functional connectivity (FC) analysis of resting-state fMRI data provides a framework for characterizing brain networks and their association with participant-level covariates. Due to the high dimensionality of neuroimaging data, standard…

Machine learning (ML) is rapidly transforming the way molecular dynamics simulations are performed and analyzed, from materials modeling to studies of protein folding and function. ML algorithms are often employed to learn low-dimensional…

Brain connectivity analysis is now at the foreground of neuroscience research. A connectivity network is characterized by a graph, where nodes represent neural elements such as neurons and brain regions, and links represent statistical…

Large language models and deep neural networks achieve strong performance but suffer from reliability issues and high computational cost. This thesis proposes a unified framework based on spectral geometry and random matrix theory to…

Reconstructing digital brain phantoms in the form of voxel-based, multi-channeled tissue probability maps for individual subjects is essential for capturing brain anatomical variability, understanding neurological diseases, as well as for…

Machine learning (ML) has revolutionized medical prognostics by integrating advanced algorithms with clinical data to enhance disease prediction, risk assessment, and patient outcome forecasting. This comprehensive review critically…

Accurate measurement of spatially variant noise in dynamic magnetic resonance (MR) images acquired using parallel imaging methods is problematic. We propose a new method based on the random matrix theory to accurately assess the noise…

Random matrix theory (RMT) provides a common mathematical formulation of distinct physical questions in three different areas: quantum chaos, the 1-d integrable model with the $1/r^2$ interaction (the Calogero-Sutherland-Moser system), and…

To measure the volume of specific image structures, a typical approach is to first segment those structures using a neural network trained on voxel-wise (strong) labels and subsequently compute the volume from the segmentation. A more…

There has been increasing interests in learning resting-state brain functional connectivity of autism disorders using functional magnetic resonance imaging (fMRI) data. The data in a standard brain template consist of over 200,000 voxel…

Brain-mapping techniques have proven to be vital in understanding the molecular, cellular, and functional mechanisms of the brain. Normal anatomical imaging can provide structural information on certain abnormalities in the brain. However…

The field of neuroimaging has truly become data rich, and novel analytical methods capable of gleaning meaningful information from large stores of imaging data are in high demand. Those methods that might also be applicable on the level of…