Related papers: Composition and tensor train structure in polynomi…
Tensor train (TT) format is a common approach for computationally efficient work with multidimensional arrays, vectors, matrices, and discretized functions in a wide range of applications, including computational mathematics and machine…
We study the problem of causal structure learning from data using optimal transport (OT). Specifically, we first provide a constraint-based method which builds upon lower-triangular monotone parametric transport maps to design conditional…
This paper discusses a method enabling optimal control of nonlinear systems that are subject to parametric uncertainty. A stochastic optimal tracking problem is formulated that can be expressed in function of the first two stochastic…
Tensor networks are a compressed format for multi-dimensional data. One-dimensional tensor networks -- often referred to as tensor trains (TT) or matrix product states (MPS) -- are increasingly being used as a numerical ansatz for continuum…
We present a flexible method for computing Bayesian optimal experimental designs (BOEDs) for inverse problems with intractable posteriors. The approach is applicable to a wide range of BOED problems and can accommodate various optimality…
We propose an algorithm for optimizations in which the gradients contain stochastic noise. This arises, for example, in structural optimizations when computations of forces and stresses rely on methods involving Monte Carlo sampling, such…
Global polynomial optimization is an important tool across applied mathematics, with many applications in operations research, engineering, and physical sciences. In various settings, the polynomials depend on external parameters that may…
We investigate questions related to the set $\mathcal{SEP}_d$ consisting of the linear maps $\rho$ acting on $\mathbb{C}^d\otimes \mathbb{C}^d$ that can be written as a convex combination of rank one matrices of the form $xx^*\otimes yy^*$.…
In this paper, we aim at the problem of tensor data completion. Tensor-train decomposition is adopted because of its powerful representation ability and linear scalability to tensor order. We propose an algorithm named Sparse Tensor-train…
Tensor networks provide a powerful framework for compressing multi-dimensional data. The optimal tensor network structure for a given data tensor depends on both data characteristics and specific optimality criteria, making tensor network…
An increasing amount of collected data are high-dimensional multi-way arrays (tensors), and it is crucial for efficient learning algorithms to exploit this tensorial structure as much as possible. The ever-present curse of dimensionality…
Tensor networks provide compact and scalable representations of high-dimensional data, enabling efficient computation in fields such as quantum physics, numerical partial differential equations (PDEs), and machine learning. This paper…
Well-designed queuing systems form the backbone of modern communications, distributed computing, and content delivery architectures. Designs balancing infrastructure costs and user experience indices require tools from teletraffic theory…
We consider the problem of decomposing a higher-order tensor with binary entries. Such data problems arise frequently in applications such as neuroimaging, recommendation system, topic modeling, and sensor network localization. We propose a…
The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…
The tensor train (TT) rank has received increasing attention in tensor completion due to its ability to capture the global correlation of high-order tensors ($\textrm{order} >3$). For third order visual data, direct TT rank minimization has…
We introduce a novel representation of structured polynomial ideals, which we refer to as chordal networks. The sparsity structure of a polynomial system is often described by a graph that captures the interactions among the variables.…
Tensor train decomposition is widely used in machine learning and quantum physics due to its concise representation of high-dimensional tensors, overcoming the curse of dimensionality. Cross approximation-originally developed for…
Tensor completion is an extension of matrix completion aimed at recovering a multiway data tensor by leveraging a given subset of its entries (observations) and the pattern of observation. The low-rank assumption is key in establishing a…
The moment-sum-of-squares (moment-SOS) hierarchy is one of the most celebrated and widely applied methods for approximating the minimum of an n-variate polynomial over a feasible region defined by polynomial (in)equalities. A key feature of…