Related papers: Statistical inference for large-dimensional tensor…
We introduce a temporal feature encoding architecture called Time Series Representation Model (TSRM) for multivariate time series forecasting and imputation. The architecture is structured around CNN-based representation layers, each…
This article establishes a new and comprehensive estimation and inference theory for principal component analysis (PCA) under the weak factor model that allow for cross-sectional dependent idiosyncratic components under the nearly minimal…
Recommendation systems, social network analysis, medical imaging, and data mining often involve processing sparse high-dimensional data. Such high-dimensional data are naturally represented as tensors, and they cannot be efficiently…
Tensor completion refers to the task of estimating the missing data from an incomplete measurement or observation, which is a core problem frequently arising from the areas of big data analysis, computer vision, and network engineering. Due…
Tensor decompositions have become essential tools for feature extraction and compression of multiway data. Recent advances in tensor operators have enabled desirable properties of standard matrix algebra to be retained for multilinear…
The CP decomposition for high dimensional non-orthogonal spiked tensors is an important problem with broad applications across many disciplines. However, previous works with theoretical guarantee typically assume restrictive incoherence…
We present an incremental, scalable and efficient dimension reduction technique for tensors that is based on sparse random linear coding. Data is stored in a compactified representation with fixed size, which makes memory requirements low…
This paper proposes a supervised dimension reduction methodology for tensor data which has two advantages over most image-based prognostic models. First, the model does not require tensor data to be complete which expands its application to…
This paper derives the CUR-type factorization for tensors in the Tucker format based on a new variant of the discrete empirical interpolation method known as L-DEIM. This novel sampling technique allows us to construct an efficient…
Tensor decomposition is a powerful computational tool for multiway data analysis. Many popular tensor decomposition approaches---such as the Tucker decomposition and CANDECOMP/PARAFAC (CP)---amount to multi-linear factorization. They are…
Multilinear Principal Component Analysis (MPCA) is a widely utilized method for the dimension reduction of tensor data. However, the integration of MPCA into federated learning remains unexplored in existing research. To tackle this gap,…
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…
Tucker decomposition is one of the most popular models for analyzing and compressing large-scale tensorial data. Existing Tucker decomposition algorithms usually rely on a single solver to compute the factor matrices and core tensor, and…
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 proposes a novel diffusion-index model for forecasting when predictors are high-dimensional matrix-valued time series. We apply an $\alpha$-PCA method to extract low-dimensional matrix factors and build a bilinear regression…
We study the low-rank phase retrieval problem, where the objective is to recover a sequence of signals (typically images) given the magnitude of linear measurements of those signals. Existing solutions involve recovering a matrix…
Given sparse multi-dimensional data (e.g., (user, movie, time; rating) for movie recommendations), how can we discover latent concepts/relations and predict missing values? Tucker factorization has been widely used to solve such problems…
We study the best low-rank Tucker decomposition of symmetric tensors. The motivating application is decomposing higher-order multivariate moments. Moment tensors have special structure and are important to various data science problems. We…
Large tensor (multi-dimensional array) data are now routinely collected in a wide range of applications, due to modern data collection capabilities. Often such observations are taken over time, forming tensor time series. In this paper we…
Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…