Related papers: Bayesian Nonlinear Tensor Regression with Function…

Regression models are used in a wide range of applications providing a powerful scientific tool for researchers from different fields. Linear, or simple parametric, models are often not sufficient to describe complex relationships between…

This article proposes a Bayesian approach to regression with a scalar response against vector and tensor covariates. Tensor covariates are commonly vectorized prior to analysis, failing to exploit the structure of the tensor, and resulting…

Nonparametric extension of tensor regression is proposed. Nonlinearity in a high-dimensional tensor space is broken into simple local functions by incorporating low-rank tensor decomposition. Compared to naive nonparametric approaches, our…

All neuroimaging modalities have their own strengths and limitations. A current trend is toward interdisciplinary approaches that use multiple imaging methods to overcome limitations of each method in isolation. At the same time…

In modern data science, dynamic tensor data is prevailing in numerous applications. An important task is to characterize the relationship between such dynamic tensor and external covariates. However, the tensor data is often only partially…

Tensor-valued data are becoming increasingly available in economics and this calls for suitable econometric tools. We propose a new dynamic linear model for tensor-valued response variables and covariates that encompasses some well-known…

Modeling with multidimensional arrays, or tensors, often presents a problem due to high dimensionality. In addition, these structures typically exhibit inherent sparsity, requiring the use of regularization methods to properly characterize…

We propose a Bayesian tensor regression model to accommodate the effect of multiple factors on phenotype prediction. We adopt a set of prior distributions that resolve identifiability issues that may arise between the parameters in the…

Methods for choosing a fixed set of knot locations in additive spline models are fairly well established in the statistical literature. While most of these methods are in principle directly extendable to non-additive surface models, they…

Tensor regression has attracted significant attention in statistical research. This study tackles the challenge of handling covariates with smooth varying structures. We introduce a novel framework, termed functional tensor regression,…

In many environmental applications involving spatially-referenced data, limitations on the number and locations of observations motivate the need for practical and efficient models for spatial interpolation, or kriging. A key component of…

Factor analysis models are widely utilized in social and behavioral sciences, such as psychology, education, and marketing, to measure unobservable latent traits. In this article, we introduce a nonlinear structured latent factor analysis…

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…

Tensors, also known as multidimensional arrays, are useful data structures in machine learning and statistics. In recent years, Bayesian methods have emerged as a popular direction for analyzing tensor-valued data since they provide a…

We develop a fully Bayesian framework for function-on-scalars regression with many predictors. The functional data response is modeled nonparametrically using unknown basis functions, which produces a flexible and data-adaptive functional…

To address the common problem of high dimensionality in tensor regressions, we introduce a generalized tensor random projection method that embeds high-dimensional tensor-valued covariates into low-dimensional subspaces with minimal loss of…

We propose a novel use of a broadcasting operation, which distributes univariate functions to all entries of the tensor covariate, to model the nonlinearity in tensor regression nonparametrically. A penalized estimation and the…

We provide a flexible framework for selecting among a class of additive partial linear models that allows both linear and nonlinear additive components. In practice, it is challenging to determine which additive components should be…

Classical regression methods treat covariates as a vector and estimate a corresponding vector of regression coefficients. Modern applications in medical imaging generate covariates of more complex form such as multidimensional arrays…

In recent years, image recognition method has been a research hotspot in various fields such as video surveillance, biometric identification, unmanned vehicles, human-computer interaction, and medical image recognition. Existing recognition…