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Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…
We combine Recurrent Neural Networks with Tensor Product Representations to learn combinatorial representations of sequential data. This improves symbolic interpretation and systematic generalisation. Our architecture is trained end-to-end…
Modern NLP models rely heavily on engineered features, which often combine word and contextual information into complex lexical features. Such combination results in large numbers of features, which can lead to over-fitting. We present a…
Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. These methods exploit the tensor structure of function spaces and apply…
One of the key problems in tensor completion is the number of uniformly random sample entries required for recovery guarantee. The main aim of this paper is to study $n_1 \times n_2 \times n_3$ third-order tensor completion based on…
Tensor decomposition is a mathematically supported technique for data compression. It consists of applying some kind of a Low Rank Decomposition technique on the tensors or matrices in order to reduce the redundancy of the data. However, it…
We introduce a tensor-based model of shared representation for meta-learning from a diverse set of tasks. Prior works on learning linear representations for meta-learning assume that there is a common shared representation across different…
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 set of convex low rank inducing norms for a coupled matrices and tensors (hereafter coupled tensors), which shares information between matrices and tensors through common modes. More specifically, we propose a mixture of the…
In the present paper we propose two new algorithms of tensor completion for three-order tensors. The proposed methods consist in minimizing the average rank of the underlying tensor using its approximate function namely the tensor nuclear…
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…
The low-tubal-rank tensor model has been recently proposed for real-world multidimensional data. In this paper, we study the low-tubal-rank tensor completion problem, i.e., to recover a third-order tensor by observing a subset of its…
The advancement of sensing technology has driven the widespread application of high-dimensional data. However, issues such as missing entries during acquisition and transmission negatively impact the accuracy of subsequent tasks. Tensor…
In recent years, low-rank based tensor completion, which is a higher-order extension of matrix completion, has received considerable attention. However, the low-rank assumption is not sufficient for the recovery of visual data, such as…
The problem of incomplete data is common in signal processing and machine learning. Tensor completion algorithms aim to recover the incomplete data from its partially observed entries. In this paper, taking advantages of high…
We consider the problem of sparse coding, where each sample consists of a sparse linear combination of a set of dictionary atoms, and the task is to learn both the dictionary elements and the mixing coefficients. Alternating minimization is…
We consider a novel algorithm, for the completion of partially observed low-rank tensors, as a generalization of matrix completion. The proposed low-rank tensor completion (TC) method builds on the conventional nuclear norm (NN)…
Recently, the \textit{Tensor Nuclear Norm~(TNN)} regularization based on t-SVD has been widely used in various low tubal-rank tensor recovery tasks. However, these models usually require smooth change of data along the third dimension to…
In this paper we propose new techniques to sample arbitrary third-order tensors, with an objective of speeding up tensor algorithms that have recently gained popularity in machine learning. Our main contribution is a new way to select, in a…
Tensor completion is a fundamental tool for incomplete data analysis, where the goal is to predict missing entries from partial observations. However, existing methods often make the explicit or implicit assumption that the observed entries…