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The nuclear norm (NN) has been widely explored in matrix recovery problems, such as Robust PCA and matrix completion, leveraging the inherent global low-rank structure of the data. In this study, we introduce a new modified nuclear norm…
In this paper, we propose a coupled tensor norm regularization that could enable the model output feature and the data input to lie in a low-dimensional manifold, which helps us to reduce overfitting. We show this regularization term is…
To enable DNNs on edge devices like mobile phones, low-rank approximation has been widely adopted because of its solid theoretical rationale and efficient implementations. Several previous works attempted to directly approximate a…
This study aims to solve the over-reliance on the rank estimation strategy in the standard tensor factorization-based tensor recovery and the problem of a large computational cost in the standard t-SVD-based tensor recovery. To this end, we…
We propose a new numerical algorithm for computing the tensor rank decomposition or canonical polyadic decomposition of higher-order tensors subject to a rank and genericity constraint. Reformulating this computational problem as a system…
Over the past years Robust PCA has been established as a standard tool for reliable low-rank approximation of matrices in the presence of outliers. Recently, the Robust PCA approach via nuclear norm minimization has been extended to…
Low-rank regularization (LRR) has been widely applied in various machine learning tasks, but the associated optimization is challenging. Directly optimizing the rank function under constraints is NP-hard in general. To overcome this…
Higher-order low-rank tensor arises in many data processing applications and has attracted great interests. Inspired by low-rank approximation theory, researchers have proposed a series of effective tensor completion methods. However, most…
Inspired by ideas taken from the machine learning literature, new regularization techniques have been recently introduced in linear system identification. In particular, all the adopted estimators solve a regularized least squares problem,…
The goal of this paper is to find a low-rank approximation for a given tensor. Specifically, we give a computable strategy on calculating the rank of a given tensor, based on approximating the solution to an NP-hard problem. In this paper,…
In many applications, high-dimensional data points can be well represented by low-dimensional subspaces. To identify the subspaces, it is important to capture a global and local structure of the data which is achieved by imposing low-rank…
Low-rank matrix regression is a fundamental problem in data science with various applications in systems and control. Nuclear norm regularization has been widely applied to solve this problem due to its convexity. However, it suffers from…
The canonical polyadic decomposition (CPD) of a low rank tensor plays a major role in data analysis and signal processing by allowing for unique recovery of underlying factors. However, it is well known that the low rank CPD approximation…
In this paper, we consider the estimation of a low Tucker rank tensor from a number of noisy linear measurements. The general problem covers many specific examples arising from applications, including tensor regression, tensor completion,…
In this paper, we investigate the sample size requirement for a general class of nuclear norm minimization methods for higher order tensor completion. We introduce a class of tensor norms by allowing for different levels of coherence, which…
Low-Rank Tensor Completion, a method which exploits the inherent structure of tensors, has been studied extensively as an effective approach to tensor completion. Whilst such methods attained great success, none have systematically…
This paper studies the issues about tensors. Three typical kinds of tensor decomposition are mentioned. Among these decompositions, the t-SVD is proposed in this decade. Different definitions of rank derive from tensor decompositions. Based…
Probabilistic Circuits (PCs) are a class of generative models that allow exact and tractable inference for a wide range of queries. While recent developments have enabled the learning of deep and expressive PCs, this increased capacity can…
Recovery of low-rank matrices from a small number of linear measurements is now well-known to be possible under various model assumptions on the measurements. Such results demonstrate robustness and are backed with provable theoretical…
We define 2-indexed $(q,p)$-Schatten quasi-norms for any $q,p > 0$ on operators on a tensor product of Hilbert spaces, naturally extending the norms defined by Pisier's theory of operator-valued Schatten spaces. We establish several…