Related papers: Tensor cross interpolation for global discrete opt…

A genetic algorithm procedure is demonstrated that refines the selection of interpolation points of the discrete empirical interpolation method (DEIM) when used for constructing reduced order models for time dependent and/or parametrized…

Tensor completion is a natural higher-order generalization of matrix completion where the goal is to recover a low-rank tensor from sparse observations of its entries. Existing algorithms are either heuristic without provable guarantees,…

Many problems can be formulated as recovering a low-rank tensor. Although an increasingly common task, tensor recovery remains a challenging problem because of the delicacy associated with the decomposition of higher order tensors. To…

This paper considers the decentralized convex optimization problem, which has a wide range of applications in large-scale machine learning, sensor networks, and control theory. We propose novel algorithms that achieve optimal computation…

Causal Bayesian networks are widely used tools for summarising the dependencies between variables and elucidating their putative causal relationships. By restricting the search to trees, for example, learning the optimum from data is…

The development of efficient machine learning models for molecular systems representation is becoming crucial in scientific research. We introduce TensorNet, an innovative O(3)-equivariant message-passing neural network architecture that…

Bayesian learning is a powerful learning framework which combines the external information of the data (background information) with the internal information (training data) in a logically consistent way in inference and prediction. By…

Tensor network methods are a conceptually elegant framework for encoding complicated datasets, where high-order tensors are approximated as networks of low-order tensors. In practice, however, the numeric implementation of tensor network…

Tensors are a natural way to express correlations among many physical variables, but storing tensors in a computer naively requires memory which scales exponentially in the rank of the tensor. This is not optimal, as the required memory is…

Tensor networks have in recent years emerged as the powerful tools for solving the large-scale optimization problems. One of the most popular tensor network is tensor train (TT) decomposition that acts as the building blocks for the…

In this work, we introduce an interior-point method that employs tensor decompositions to efficiently represent and manipulate the variables and constraints of semidefinite programs, targeting problems where the solutions may not be…

We propose a Bayesian tensor-on-tensor regression approach to predict a multidimensional array (tensor) of arbitrary dimensions from another tensor of arbitrary dimensions, building upon the Tucker decomposition of the regression…

Tensor ring (TR) decomposition is a simple but effective tensor network for analyzing and interpreting latent patterns of tensors. In this work, we propose a doubly randomized optimization framework for computing TR decomposition. It can be…

The convergence of many numerical optimization techniques is highly dependent on the initial guess given to the solver. To address this issue, we propose a novel approach that utilizes tensor methods to initialize existing optimization…

The reconstruction of missing information in epidemic spreading on contact networks can be essential in the prevention and containment strategies. The identification and warning of infectious but asymptomatic individuals (i.e., contact…

We propose a parallel version of the cross interpolation algorithm and apply it to calculate high-dimensional integrals motivated by Ising model in quantum physics. In contrast to mainstream approaches, such as Monte Carlo and quasi Monte…

The rapid growth of earth observation systems calls for a scalable approach to interpolate remote-sensing observations. These methods in principle, should acquire more information about the observed field as data grows. Gaussian processes…

Inverse protein folding -- the task of predicting a protein sequence from its backbone atom coordinates -- has surfaced as an important problem in the "top down", de novo design of proteins. Contemporary approaches have cast this problem as…

Influence maximization is the problem of finding the set of nodes of a network that maximizes the size of the outbreak of a spreading process occurring on the network. Solutions to this problem are important for strategic decisions in…

It is a significant challenge to predict the network topology from a small amount of dynamical observations. Different from the usual framework of the node-based reconstruction, two optimization approaches (i.e., the global and partitioned…