Related papers: Applications of Random Matrix Theory in Machine Le…
The main goal of machine learning (ML) is to study and improve mathematical models which can be trained with data provided by the environment to infer the future and to make decisions without necessarily having complete knowledge of all…
Functional Magnetic Resonance Imaging is a noninvasive tool for studying cerebral function. Many factors challenge activation detection, especially in low-signal scenarios that arise in the performance of high-level cognitive tasks. We…
Resting-state brain functional connectivity quantifies the synchrony between activity patterns of different brain regions. In functional magnetic resonance imaging (fMRI), each region comprises a set of spatially contiguous voxels at which…
We investigate the local spectral statistics of the loss surface Hessians of artificial neural networks, where we discover excellent agreement with Gaussian Orthogonal Ensemble statistics across several network architectures and datasets.…
Functional neuroimaging can measure the brain?s response to an external stimulus. It is used to perform brain mapping: identifying from these observations the brain regions involved. This problem can be cast into a linear supervised…
In this paper, we introduce a novel theoretical framework for multi-task regression, applying random matrix theory to provide precise performance estimations, under high-dimensional, non-Gaussian data distributions. We formulate a…
Brain structural networks are often represented as discrete adjacency matrices with elements summarizing the connectivity between pairs of regions of interest (ROIs). These ROIs are typically determined a-priori using a brain atlas. The…
Functional Magnetic Resonance Imaging (fMRI) is a primary modality for studying brain activity. Modeling spatial dependence of imaging data at different scales is one of the main challenges of contemporary neuroimaging, and it could allow…
Random feature maps are ubiquitous in modern statistical machine learning, where they generalize random projections by means of powerful, yet often difficult to analyze nonlinear operators. In this paper, we leverage the "concentration"…
The fine timing measurement (FTM) protocol is designed to determine precise ranging between Wi-Fi devices using round-trip time (RTT) measurements. However, the multipath propagation of radio waves generates inaccurate timing information,…
We use randomness as a measure to assess the impact of evoked pain on brain networks. Randomness is defined here as the intrinsic correlations that exist between different brain regions when the brain is in a task-free state. We use fMRI…
Diffusion Magnetic Resonance Imaging (MRI) exploits the anisotropic diffusion of water molecules in the brain to enable the estimation of the brain's anatomical fiber tracts at a relatively high resolution. In particular, tractographic…
Traditional dense volumetric representations for robotic mapping make simplifying assumptions about sensor noise characteristics due to computational constraints. We present a framework that, unlike conventional occupancy grid maps,…
This work analyzes singular-value spectra of weight matrices in pretrained transformer models to understand how information is stored at both ends of the spectrum. Using Random Matrix Theory (RMT) as a zero information hypothesis, we…
Machine Learning (ML) is increasingly being used for computer aided diagnosis of brain related disorders based on structural magnetic resonance imaging (MRI) data. Most of such work employs biologically and medically meaningful hand-crafted…
In this study, we consider the realm of covariance matrices in machine learning, particularly focusing on computing Fr\'echet means on the manifold of symmetric positive definite matrices, commonly referred to as Karcher or geometric means.…
Magnetic Resonance Imaging (MRI) is a principal diagnostic approach used in the field of radiology to create images of the anatomical and physiological structure of patients. MRI is the prevalent medical imaging practice to find…
Machine learning is a field of computer science that builds algorithms that learn. In many cases, machine learning algorithms are used to recreate a human ability like adding a caption to a photo, driving a car, or playing a game. While the…
Random matrix theory, which characterizes spectral distributions of infinitely large matrices, plays a central role across diverse fields, including high-dimensional data analysis, ecology, neuroscience, and machine learning. Among its key…
We study universal traits which emerge both in real-world complex datasets, as well as in artificially generated ones. Our approach is to analogize data to a physical system and employ tools from statistical physics and Random Matrix Theory…