Related papers: Equivariant and scale-free Tucker decomposition mo…
Unrolled neural networks have enabled state-of-the-art reconstruction performance and fast inference times for the accelerated magnetic resonance imaging (MRI) reconstruction task. However, these approaches depend on fully-sampled scans as…
Low-rank approximation of a matrix by means of structured random sampling has been consistently efficient in its extensive empirical studies around the globe, but adequate formal support for this empirical phenomenon has been missing so…
A separable covariance model for a random matrix provides a parsimonious description of the covariances among the rows and among the columns of the matrix, and permits likelihood-based inference with a very small sample size. However, in…
Motivated by Tucker tensor decomposition, this paper imposes low-rank structures to the column and row spaces of coefficient matrices in a multivariate infinite-order vector autoregression (VAR), which leads to a supervised factor model…
Low-rank approximation is an effective model compression technique to not only reduce parameter storage requirements, but to also reduce computations. For convolutional neural networks (CNNs), however, well-known low-rank approximation…
We consider the problem of recovering low-rank matrices from random rank-one measurements, which spans numerous applications including covariance sketching, phase retrieval, quantum state tomography, and learning shallow polynomial neural…
There exist many high-dimensional data in real-world applications such as biology, computer vision, and social networks. Feature selection approaches are devised to confront with high-dimensional data challenges with the aim of efficient…
This paper introduces a novel variational Bayesian method that integrates Tucker decomposition for efficient high-dimensional inverse problem solving. The method reduces computational complexity by transforming variational inference from a…
In this paper, we study the estimation of partially linear models for spatial data distributed over complex domains. We use bivariate splines over triangulations to represent the nonparametric component on an irregular two-dimensional…
In high-dimensional multivariate regression problems, enforcing low rank in the coefficient matrix offers effective dimension reduction, which greatly facilitates parameter estimation and model interpretation. However, commonly-used…
This paper tackles the problem of robust covariance matrix estimation when the data is incomplete. Classical statistical estimation methodologies are usually built upon the Gaussian assumption, whereas existing robust estimation ones assume…
This paper studies the inference about linear functionals of high-dimensional low-rank matrices. While most existing inference methods would require consistent estimation of the true rank, our procedure is robust to rank misspecification,…
In this paper, we consider multivariate response regression models with high dimensional predictor variables. One way to model the correlation among the response variables is through the low rank decomposition of the coefficient matrix,…
In tensor completion tasks, the traditional low-rank tensor decomposition models suffer from the laborious model selection problem due to their high model sensitivity. In particular, for tensor ring (TR) decomposition, the number of model…
Higher-order tensors arise frequently in applications such as neuroimaging, recommendation system, social network analysis, and psychological studies. We consider the problem of low-rank tensor estimation from possibly incomplete,…
Existing models for high-dimensional time series are overwhelmingly developed within the finite-order vector autoregressive (VAR) framework. However, the more flexible vector autoregressive moving averages (VARMA) have been much less…
In the realm of tensor optimization, the low-rank Tucker decomposition is crucial for reducing the number of parameters and for saving storage. We explore the geometry of Tucker tensor varieties -- the set of tensors with bounded Tucker…
We propose and analyse a reduced-rank method for solving least-squares regression problems with infinite dimensional output. We derive learning bounds for our method, and study under which setting statistical performance is improved in…
Many applications in data science and scientific computing involve large-scale datasets that are expensive to store and compute with, but can be efficiently compressed and stored in an appropriate tensor format. In recent years, randomized…
The reduced-rank method exploits the distortion-variance tradeoff to yield superior solutions for classic problems in statistical signal processing such as parameter estimation and filtering. The central idea is to reduce the variance of…