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It is of great interest to quantify the contributions of genetic variation to brain structure and function, which are usually measured by high-dimensional imaging data (e.g., magnetic resonance imaging). In addition to the variance, the…

Statistical and mathematical modeling are crucial to describe, interpret, compare and predict the behavior of complex biological systems including the organization of hematopoietic stem and progenitor cells in the bone marrow environment.…

This paper proposes a physical-statistical modeling approach for spatio-temporal data arising from a class of stochastic convection-diffusion processes. Such processes are widely found in scientific and engineering applications where…

The statistical analysis of tree structured data is a new topic in statistics with wide application areas. Some Principal Component Analysis (PCA) ideas were previously developed for binary tree spaces. In this study, we extend these ideas…

Spatial transcriptomics is an emerging field that enables the identification of functional regions based on the spatial distribution of gene expression. Integrating this functional information present in transcriptomic data with structural…

As tensors become widespread in modern data analysis, Tucker low-rank Principal Component Analysis (PCA) has become essential for dimensionality reduction and structural discovery in tensor datasets. Motivated by the common scenario where…

Our understanding of the structure of the brain and its relationships with human traits is largely determined by how we represent the structural connectome. Standard practice divides the brain into regions of interest (ROIs) and represents…

In recent years, there has been increasing interest in developing models and tools to address the complex patterns of connectivity found in brain tissue. Specifically, this is due to a need to understand how emergent properties emerge from…

Deep learning has proven to successfully learn variations in tissue and cell morphology. Training of such models typically relies on expensive manual annotations. Here we conjecture that spatially resolved gene expression, e.i., the…

Functional magnetic resonance imaging (fMRI) data contain complex spatiotemporal dynamics, thus researchers have developed approaches that reduce the dimensionality of the signal while extracting relevant and interpretable dynamics. Models…

There has been increased interest in missing sensor data imputation, which is ubiquitous in the field of structural health monitoring (SHM) due to discontinuous sensing caused by sensor malfunction. To address this fundamental issue, this…

A powerful study design in the fields of genomics and metabolomics is the 'replicated time course experiment' where individual time series are observed for a sample of biological units, such as human patients, termed replicates. Standard…

Tensor train is a hierarchical tensor network structure that helps alleviate the curse of dimensionality by parameterizing large-scale multidimensional data via a set of network of low-rank tensors. Associated with such a construction is a…

Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…

Spatio-temporal feature encoding is essential for encoding facial expression dynamics in video sequences. At test time, most spatio-temporal encoding methods assume that a temporally segmented sequence is fed to a learned model, which could…

Cataloging the neuronal cell types that comprise circuitry of individual brain regions is a major goal of modern neuroscience and the BRAIN initiative. Single-cell RNA sequencing can now be used to measure the gene expression profiles of…

It is well established that temporal organization is critical to memory, and that the ability to temporally organize information is fundamental to many perceptual, cognitive, and motor processes. While our understanding of how the brain…

There is growing evidence in the epidemiologic literature of the relationship between air pollution and adverse health outcomes. Prediction of individual air pollution exposure in the Environmental Protection Agency (EPA) funded…

High-dimensional tensor-valued predictors arise in modern applications, increasingly as learned representations from neural networks. Existing tensor classification methods rely on sparsity or Tucker structures and often lack theoretical…

This paper proposes a probabilistic model of subspaces based on the probabilistic principal component analysis (PCA). Given a sample of vectors in the embedding space -- commonly known as a snapshot matrix -- this method uses quantities…