Related papers: Time integration of tree tensor networks
New algorithms are proposed for the Tucker approximation of a 3-tensor, that access it using only the tensor-by-vector-by-vector multiplication subroutine. In the matrix case, Krylov methods are methods of choice to approximate the dominant…
Dynamic trees are mixtures of tree structured belief networks. They solve some of the problems of fixed tree networks at the cost of making exact inference intractable. For this reason approximate methods such as sampling or mean field…
We introduce tensor numerical techniques for solving optimal control problems constrained by elliptic operators in $\mathbb{R}^d$, $d=2,3$, with variable coefficients, which can be represented in a low rank separable form. We construct a…
For any linear system with unreduced dynamics governed by invertible propagators, we derive a closed, time-delayed, linear system for a reduced-dimensional quantity of interest. This method does not target dimensionality reduction: rather,…
A central aim in computational neuroscience is to relate the activity of large populations of neurons to an underlying dynamical system. Models of these neural dynamics should ideally be both interpretable and fit the observed data well.…
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…
Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model which represents data as an ordered network of…
Dynamic programming on tree decompositions is a frequently used approach to solve otherwise intractable problems on instances of small treewidth. In recent work by Bodlaender et al., it was shown that for many connectivity problems, there…
Recovery of internet network traffic data from incomplete observed data is an important issue in internet network engineering and management. In this paper, by fully combining the temporal stability and periodicity features in internet…
This paper is concerned with the low Tucker-rank tensor completion problem, which is about reconstructing a tensor $ T \in\mathbb{R}^{n\times n \times n}$ of low multilinear rank from partially observed entries. Riemannian optimization…
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…
Missing value problem in spatiotemporal traffic data has long been a challenging topic, in particular for large-scale and high-dimensional data with complex missing mechanisms and diverse degrees of missingness. Recent studies based on…
We present a sequential version of the multilinear Nystr\"om algorithm which is suitable for the low-rank Tucker approximation of tensors given in a streaming format. Accessing the tensor $\mathcal{A}$ exclusively through random sketches of…
Recently, Tensor Ring Networks (TRNs) have been applied in deep networks, achieving remarkable successes in compression ratio and accuracy. Although highly related to the performance of TRNs, rank selection is seldom studied in previous…
The tensor-train (TT) format is a data-sparse tensor representation commonly used in high dimensional data approximations. In order to represent data with interpretability in data science, researchers develop data-centric skeletonized low…
Neural networks have been able to achieve groundbreaking accuracy at tasks conventionally considered only doable by humans. Using stochastic gradient descent, optimization in many dimensions is made possible, albeit at a relatively high…
In this paper, we propose three approaches for the estimation of the Tucker decomposition of multi-way arrays (tensors) from partial observations. All approaches are formulated as convex minimization problems. Therefore, the minimum is…
Many problems encountered in plasma physics require a description by kinetic equations, which are posed in an up to six-dimensional phase space. A direct discretization of this phase space, often called the Eulerian approach, has many…
Low-rank tensor decomposition generalizes low-rank matrix approximation and is a powerful technique for discovering low-dimensional structure in high-dimensional data. In this paper, we study Tucker decompositions and use tools from…
The main aim of this paper is to develop a new algorithm for computing nonnegative low rank tensor approximation for nonnegative tensors that arise in many multi-dimensional imaging applications. Nonnegativity is one of the important…