Related papers: Kronecker product linear exponent AR(1) correlatio…
Repeated measures analyses require proper choice of the correlation model to ensure accurate inference and optimal efficiency. The linear exponent autoregressive (LEAR) correlation model provides a flexible two-parameter correlation…
We propose an adjusted likelihood ratio test of two-factor separability (Kronecker product structure) for unbalanced multivariate repeated measures data. Here we address the particular case where the within subject correlation is believed…
This paper proposes methods for likelihood-based inference in multivariate linear regressions when the correlation matrix of the responses is separable; that is, it has a Kronecker product structure, but the variances are unrestricted. The…
We propose a Kronecker product model for correlation or covariance matrices in the large dimensional case. The number of parameters of the model increases logarithmically with the dimension of the matrix. We propose a minimum distance (MD)…
The matrix-variate normal distribution is a popular model for high-dimensional transposable data because it decomposes the dependence structure of the random matrix into the Kronecker product of two covariance matrices: one for each of the…
Kronecker PCA involves the use of a space vs. time Kronecker product decomposition to estimate spatio-temporal covariances. In this work the addition of a sparse correction factor is considered, which corresponds to a model of the…
Deep learning using neural networks is an effective technique for generating models of complex data. However, training such models can be expensive when networks have large model capacity resulting from a large number of layers and nodes.…
A growth curve model (GCM) aims to characterize how an outcome variable evolves, develops and grows as a function of time, along with other predictors. It provides a particularly useful framework to model growth trend in longitudinal data.…
We develop a higher order generalization of the LQ decomposition and show that this decomposition plays an important role in likelihood-based estimation and testing for separable, or Kronecker structured, covariance models, such as the…
Feed-forward neural networks can be understood as a combination of an intermediate representation and a linear hypothesis. While most previous works aim to diversify the representations, we explore the complementary direction by performing…
Starting from childhood, the human brain restructures and rewires throughout life. Characterizing such complex brain development requires effective analysis of longitudinal and multi-modal neuroimaging data. Here, we propose such an…
Several problems in neuroimaging and beyond require inference on the parameters of multi-task sparse hierarchical regression models. Examples include M/EEG inverse problems, neural encoding models for task-based fMRI analyses, and climate…
Our work addresses two important issues with recurrent neural networks: (1) they are over-parameterized, and (2) the recurrence matrix is ill-conditioned. The former increases the sample complexity of learning and the training time. The…
We propose nonparametric methods for functional linear regression which are designed for sparse longitudinal data, where both the predictor and response are functions of a covariate such as time. Predictor and response processes have smooth…
Large-scale neuroimaging studies have been collecting brain images of study individuals, which take the form of two-dimensional, three-dimensional, or higher dimensional arrays, also known as tensors. Addressing scientific questions arising…
This paper considers canonical correlation analysis for two longitudinal variables that are possibly sampled at different time resolutions with irregular grids. We modeled trajectories of the multivariate variables using random effects and…
Predicting whether a treatment leads to meaningful improvement is a central challenge in personalized medicine, particularly when disease progression manifests as subtle visual changes over time. While data-driven deep learning (DL) offers…
Neural encoding studies explore the relationships between measurements of neural activity and measurements of a behavior that is viewed as a response to that activity. The coupling between neural and behavioral measurements is typically…
Learning temporal patterns from multivariate longitudinal data is challenging especially in cases when data is sporadic, as often seen in, e.g., healthcare applications where the data can suffer from irregularity and asynchronicity as the…
Hypergraphs and tensors extend classic graph and matrix theory to account for multiway relationships, which are ubiquitous in engineering, biological, and social systems. While the Kronecker product is a potent tool for analyzing the…