Related papers: TPRM: Tensor partition regression models with appl…
The estimation of sparse hierarchical components reflecting patterns of the brain's functional connectivity from rsfMRI data can contribute to our understanding of the brain's functional organization, and can lead to biomarkers of diseases.…
This work presents a low-rank tensor model for multi-dimensional Markov chains. A common approach to simplify the dynamical behavior of a Markov chain is to impose low-rankness on the transition probability matrix. Inspired by the success…
Tiny Recursive Models (TRM) solve complex reasoning tasks with a fraction of the parameters of modern large language models (LLMs) by iteratively refining a latent state and final answer. While powerful, their deterministic recursion can…
The problem of partitioning a large and sparse tensor is considered, where the tensor consists of a sequence of adjacency matrices. Theory is developed that is a generalization of spectral graph partitioning. A best rank-$(2,2,\lambda)$…
Neurodegeneration as measured through magnetic resonance imaging (MRI) is recognized as a potential biomarker for diagnosing Alzheimer's disease (AD), but is generally considered less specific than amyloid or tau based biomarkers. Due to a…
Alzheimer's disease (AD) is a progressive neurodegenerative disorder characterized by cognitive decline, structural brain changes, and genetic predispositions. This study leverages machine-learning and statistical techniques to investigate…
Recommendation systems, social network analysis, medical imaging, and data mining often involve processing sparse high-dimensional data. Such high-dimensional data are naturally represented as tensors, and they cannot be efficiently…
The automatic diagnosis of Parkinson's disease is in high clinical demand due to its prevalence and the importance of targeted treatment. Current clinical practice often relies on diagnostic biomarkers in QSM and NM-MRI images. However, the…
Exploring the application of deep learning technologies in the field of medical diagnostics, Magnetic Resonance Imaging (MRI) provides a unique perspective for observing and diagnosing complex neurodegenerative diseases such as Alzheimer…
Recent works have shown that imposing tensor structures on the coefficient tensor in regression problems can lead to more reliable parameter estimation and lower sample complexity compared to vector-based methods. This work investigates a…
Statistical inference for tensors has emerged as a critical challenge in analyzing high-dimensional data in modern data science. This paper introduces a unified framework for inferring general and low-Tucker-rank linear functionals of…
Discovering components that are shared in multiple datasets, next to dataset-specific features, has great potential for studying the relationships between different subjects or tasks in functional Magnetic Resonance Imaging (fMRI) data.…
Numerous complex real-world systems, such as those in biological, ecological, and social networks, exhibit higher-order interactions that are often modeled using polynomial dynamical systems or homogeneous polynomial dynamical systems…
Tensor networks have in recent years emerged as the powerful tools for solving the large-scale optimization problems. One of the most popular tensor network is tensor train (TT) decomposition that acts as the building blocks for the…
Brain imaging has allowed neuroscientists to analyze brain morphology in genetic and neurodevelopmental disorders, such as Down syndrome, pinpointing regions of interest to unravel the neuroanatomical underpinnings of cognitive impairment…
Often, large, high dimensional datasets collected across multiple modalities can be organized as a higher order tensor. Low-rank tensor decomposition then arises as a powerful and widely used tool to discover simple low dimensional…
The medial temporal lobe (MTL) is a region impacted extensively and non-uniformly in early stages of Alzheimer's disease (AD). Regional MTL morphometric measures extracted from magnetic resonance imaging (MRI) are supportive features for…
Tensor-valued data arise naturally in multidimensional signal and imaging problems, such as biomedical imaging. When incorporated into generalized linear models (GLMs), naive vectorization can destroy their multi-way structure and lead to…
We construct efficient surrogate models for parametric forward operators arising in brain tumor growth simulations, governed by coupled semilinear parabolic reaction-diffusion systems on heterogeneous two- and three-dimensional domains. We…
Purpose: Conventional automated segmentation of the head anatomy in MRI distinguishes different brain and non-brain tissues based on image intensities and prior tissue probability maps (TPM). This works well for normal head anatomies, but…