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Characterizing Spatiotemporal Transcriptome of the Human Brain Via Low-Rank Tensor Decomposition
Spatiotemporal gene expression data of the human brain offer insights on the spatial and temporal patterns of gene regulation during brain...
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A Higher-Order Singular Value Decomposition Tensor Emulator for Spatiotemporal Simulators
We introduce methodology to construct an emulator for environmental and ecological spatiotemporal processes that uses the higher-order singular value...
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Change-point detection in a tensor regression model
In this paper, we consider an inference problem in a tensor regression model with one change-point. Specifically, we consider a general hypothesis...
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Finite mixture of hidden Markov models for tensor-variate time series data
The need to model data with higher dimensions, such as a tensor-variate framework where each observation is considered a three-dimensional object,...
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Rapid Detection of Hot-Spot by Tensor Decomposition with Application to Weekly Gonorrhea Data
In many bio-surveillance and healthcare applications, data sources are measured from many spatial locations repeatedly over time, say,...
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Tucker-3 decomposition with sparse core array using a penalty function based on Gini-index
Tucker-3 decomposition is a dimension reduction method for tensor data, similar to principal component analysis. One of the characteristics of...
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Bivariate densities in Bayes spaces: orthogonal decomposition and spline representation
A new orthogonal decomposition for bivariate probability densities embedded in Bayes Hilbert spaces is derived. It allows representing a density into...
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A multivariate Jacobi polynomials regression estimator associated with an ANOVA decomposition model
In this work, we construct a stable and fairly fast estimator for solving multidimensional non-parametric regression problems. The proposed estimator...
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The Tensor Derivative of Vector Functions
Taking the first-order partial derivative of a vector-valued function results in the Jacobian matrix, which contains all partial derivatives of each...
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Approximation and sampling of multivariate probability distributions in the tensor train decomposition
General multivariate distributions are notoriously expensive to sample from, particularly the high-dimensional posterior distributions in...
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A multigrid preconditioner for tensor product spline smoothing
Penalized spline smoothing is a well-established, nonparametric regression method that is efficient for one and two covariates. Its extension to more...
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A multi-way analysis of similarity patterns in longevity improvements
With the increasing availability of temporal data, a researcher often analyzes information saved into matrices, in which entries are replicated in...
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Block tensor train decomposition for missing data estimation
We propose a method for imputation of missing values in large scale matrix data based on a low-rank tensor approximation technique called the block...
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Space Decomposition and Estimation in Multivariate Linear Models
Linear models are important in statistical analysis. In many real situations, these models become more and more complex, as such the estimation of...
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A New Algorithm for the Partition of Pearson’s Chi-Squared Statistic for Multiway Contingency Table
Pearson’s chi-squared statistic is one of the most common statistical tools used to assess the association between two or more categorical variables...
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Modular regression - a Lego system for building structured additive distributional regression models with tensor product interactions
Semiparametric regression models offer considerable flexibility concerning the specification of additive regression predictors including effects as...
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Efficient and Accurate Evaluation Methods for Concordance Measures via Functional Tensor Characterizations of Copulas
There is now an increasingly large number of proposed concordance measures available to capture, measure and quantify different notions of dependence...
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Penalized function-on-function linear quantile regression
We introduce a novel function-on-function linear quantile regression model to characterize the entire conditional distribution of a functional...
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Multivariate Functional Singular Spectrum Analysis: A Nonparametric Approach for Analyzing Multivariate Functional Time Series
In this chapter, we develop multivariate functional singular spectrum analysis (MFSSA) over different dimensional domains with the goal of...
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Nonparametric matrix regression function estimation over symmetric positive definite matrices
Symmetric positive definite matrix data commonly appear in computer vision and medical imaging, such as diffusion tensor imaging. The aim of this...
