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Tucker tensor decomposition offers a more effective representation for multiway data compared to the widely used PARAFAC model. However, its flexibility brings the challenge of selecting the appropriate latent multi-rank. To overcome the…

We propose a modular framework for multi-relational learning via tensor decomposition. In our learning setting, the training data contains multiple types of relationships among a set of objects, which we represent by a sparse three-mode…

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…

In numerous settings, it is increasingly common to deal with longitudinal data organized as high-dimensional multi-dimensional arrays, also known as tensors. Within this framework, the time-continuous property of longitudinal data often…

This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable…

Tensor time series data appears naturally in a lot of fields, including finance and economics. As a major dimension reduction tool, similar to its factor model counterpart, the idiosyncratic components of a tensor time series factor model…

We undertake Bayesian learning of the high-dimensional functional relationship between a system parameter vector and an observable, that is in general tensor-valued. The ultimate aim is Bayesian inverse prediction of the system parameters,…

With the advances in data acquisition technology, tensor objects are collected in a variety of applications including multimedia, medical and hyperspectral imaging. As the dimensionality of tensor objects is usually very high,…

Random Fourier features provide a way to tackle large-scale machine learning problems with kernel methods. Their slow Monte Carlo convergence rate has motivated the research of deterministic Fourier features whose approximation error can…

Tensor decomposition is a popular technique for tensor completion, However most of the existing methods are based on linear or shallow model, when the data tensor becomes large and the observation data is very small, it is prone to over…

Tensor train (TT) decomposition is a powerful representation for high-order tensors, which has been successfully applied to various machine learning tasks in recent years. However, since the tensor product is not commutative, permutation of…

Graphs are a commonly used construct for representing relationships between elements in complex high dimensional datasets. Many real-world phenomenon are dynamic in nature, meaning that any graph used to represent them is inherently…

Non-negative matrix factorization (NMF) is a recently developed technique for finding parts-based, linear representations of non-negative data. Although it has successfully been applied in several applications, it does not always result in…

This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in…

Directed networks are pervasive both in nature and engineered systems, often underlying the complex behavior observed in biological systems, microblogs and social interactions over the web, as well as global financial markets. Since their…

The Gaussian process (GP) is a nonparametric prior distribution over functions indexed by time, space, or other high-dimensional index set. The GP is a flexible model yet its limitation is given by its very nature: it can only model…

We propose a flexible nonparametric Bayesian modelling framework for multivariate time series of count data based on tensor factorisations. Our models can be viewed as infinite state space Markov chains of known maximal order with…

In this paper, we consider the nonstationary matrix-valued time series with common stochastic trends. Unlike the traditional factor analysis which flattens matrix observations into vectors, we adopt a matrix factor model in order to fully…

Recently, introducing Tensor Decomposition (TD) techniques into unsupervised feature selection (UFS) has been an emerging research topic. A tensor structure is beneficial for mining the relations between different modes and helps relieve…

Tensor completion is crucial in many scientific domains with missing data problems. Traditional low-rank tensor models, including CP, Tucker, and Tensor-Train, exploit low-dimensional structures to recover missing data. However, these…