Related papers: Decomposable Sparse Tensor on Tensor Regression

In this paper, we propose a general framework for sparse and low-rank tensor estimation from cubic sketchings. A two-stage non-convex implementation is developed based on sparse tensor decomposition and thresholded gradient descent, which…

Tensor regression networks achieve high compression rate of neural networks while having slight impact on performances. They do so by imposing low tensor rank structure on the weight matrices of fully connected layers. In recent years,…

This paper is concerned with the problem of low rank plus sparse matrix decomposition for big data. Conventional algorithms for matrix decomposition use the entire data to extract the low-rank and sparse components, and are based on…

How can we accurately complete tensors by learning relationships of dimensions along each mode? Tensor completion, a widely studied problem, is to predict missing entries in incomplete tensors. Tensor decomposition methods, fundamental…

Tensor decomposition models play an increasingly important role in modern data science applications. One problem of particular interest is fitting a low-rank Canonical Polyadic (CP) tensor decomposition model when the tensor has sparse…

Tensor completion is an extension of matrix completion aimed at recovering a multiway data tensor by leveraging a given subset of its entries (observations) and the pattern of observation. The low-rank assumption is key in establishing a…

This work introduces a tensor-based method to perform supervised classification on spatiotemporal data processed in an echo state network. Typically when performing supervised classification tasks on data processed in an echo state network,…

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…

In this study, we consider the numerical solution of large systems of linear equations obtained from the stochastic Galerkin formulation of stochastic partial differential equations. We propose an iterative algorithm that exploits the…

The problem of finding the unique low dimensional decomposition of a given matrix has been a fundamental and recurrent problem in many areas. In this paper, we study the problem of seeking a unique decomposition of a low rank matrix $Y\in…

We discuss how recently discovered techniques and tools from compressed sensing can be used in tensor decompositions, with a view towards modeling signals from multiple arrays of multiple sensors. We show that with appropriate bounds on a…

Matrices can be decomposed via rank-one approximations: the best rank-one approximation is a singular vector pair, and the singular value decomposition writes a matrix as a sum of singular vector pairs. The singular vector tuples of a…

The reduced-rank vector autoregressive (VAR) model can be interpreted as a supervised factor model, where two factor modelings are simultaneously applied to response and predictor spaces. This article introduces a new model, called vector…

Producing large complex simulation datasets can often be a time and resource consuming task. Especially when these experiments are very expensive, it is becoming more reasonable to generate synthetic data for downstream tasks. Recently,…

Tensor classification has become increasingly crucial in statistics and machine learning, with applications spanning neuroimaging, computer vision, and recommendation systems. However, the high dimensionality of tensors presents significant…

In autoregressive modeling for tensor-valued time series, Tucker decomposition, when applied to the coefficient tensor, provides a clear interpretation of supervised factor modeling but loses its efficiency rapidly with increasing tensor…

Low-rank tensors appear to be prosperous in many applications. However, the sets of bounded-rank tensors are non-smooth and non-convex algebraic varieties, rendering the low-rank optimization problems to be challenging. To this end, we…

The current methods for learning representations with auto-encoders almost exclusively employ vectors as the latent representations. In this work, we propose to employ a tensor product structure for this purpose. This way, the obtained…

We proposed the tensor-input tree (TT) method for scalar-on-tensor and tensor-on-tensor regression problems. We first address scalar-on-tensor problem by proposing scalar-output regression tree models whose input variable are tensors (i.e.,…

Many problems in high-dimensional statistics appear to have a statistical-computational gap: a range of values of the signal-to-noise ratio where inference is information-theoretically possible, but (conjecturally) computationally…