Related papers: Parsimonious Tensor Response Regression
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…
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…
This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in…
Motivated by applications in neuroimaging analysis, we propose a new regression model, Sparse TensOr REsponse regression (STORE), with a tensor response and a vector predictor. STORE embeds two key sparse structures: element-wise sparsity…
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…
Dimension reduction provides a useful tool for analyzing high dimensional data. The recently developed \textit{Envelope} method is a parsimonious version of the classical multivariate regression model through identifying a minimal reducing…
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…
A major interest in longitudinal neuroimaging studies involves investigating voxel-level neuroplasticity due to treatment and other factors across visits. However, traditional voxel-wise methods are beset with several pitfalls, which can…
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…
The analysis of multidimensional data is becoming a more and more relevant topic in statistical and machine learning research. Given their complexity, such data objects are usually reshaped into matrices or vectors and then analysed.…
This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…
This paper proposes a new high dimensional regression method by merging Gaussian process regression into a variational autoencoder framework. In contrast to other regression methods, the proposed method focuses on the case where output…
Tomographic imaging is useful for revealing the internal structure of a 3D sample. Classical reconstruction methods treat the object of interest as a vector to estimate its value. Such an approach, however, can be inefficient in analyzing…
We propose a nonparametric factorization approach for sparsely observed tensors. The sparsity does not mean zero-valued entries are massive or dominated. Rather, it implies the observed entries are very few, and even fewer with the growth…
Envelope methods offer targeted dimension reduction for various models. The overarching goal is to improve efficiency in multivariate parameter estimation by projecting the data onto a lower-dimensional subspace known as the envelope.…
Delineating the associations between images and a vector of covariates is of central interest in medical imaging studies. To tackle this problem of image response regression, we propose a novel nonparametric approach in the framework of…
We propose new methods for multivariate linear regression when the regression coefficient matrix is sparse and the error covariance matrix is dense. We assume that the error covariance matrix has equicorrelation across the response…
The sparse modeling is an evident manifestation capturing the parsimony principle just described, and sparse models are widespread in statistics, physics, information sciences, neuroscience, computational mathematics, and so on. In…
Compressive Learning is an emerging topic that combines signal acquisition via compressive sensing and machine learning to perform inference tasks directly on a small number of measurements. Many data modalities naturally have a…
We propose dimension reduction methods for sparse, high-dimensional multivariate response regression models. Both the number of responses and that of the predictors may exceed the sample size. Sometimes viewed as complementary, predictor…