Related papers: Tensor Completion via Gaussian Process Based Initi…

Combination of low-tensor rank techniques and the Fast Fourier transform (FFT) based methods had turned out to be prominent in accelerating various statistical operations such as Kriging, computing conditional covariance, geostatistical…

This paper proposes a supervised dimension reduction methodology for tensor data which has two advantages over most image-based prognostic models. First, the model does not require tensor data to be complete which expands its application to…

We propose a tensor generalized approximate message passing (TeG-AMP) algorithm for low-rank tensor inference, which can be used to solve tensor completion and decomposition problems. We derive TeG-AMP algorithm as an approximation of the…

The tensor-train (TT) decomposition expresses a tensor in a data-sparse format used in molecular simulations, high-order correlation functions, and optimization. In this paper, we propose four parallelizable algorithms that compute the TT…

Many robotic tasks, such as inverse kinematics, motion planning, and optimal control, can be formulated as optimization problems. Solving these problems involves addressing nonlinear kinematics, complex contact dynamics, long-horizon…

In this paper, we explore the role of tensor algebra in balanced truncation (BT) based model reduction/identification for high-dimensional multilinear/linear time invariant systems. In particular, we employ tensor train decomposition (TTD),…

This paper is concerned with the approximation of tensors using tree-based tensor formats, which are tensor networks whose graphs are dimension partition trees. We consider Hilbert tensor spaces of multivariate functions defined on a…

Recently, a tensor factorization based method for a low tubal rank tensor completion problem of a third order tensor was proposed, which performed better than some existing methods. Tubal rank is only defined on one mode of third order…

In this work, a tensor completion problem is studied, which aims to perfectly recover the tensor from partial observations. The existing theoretical guarantee requires the involved transform to be orthogonal, which hinders its applications.…

Various tensor decomposition methods have been proposed for data compression. In real world applications of the tensor decomposition, selecting the tensor shape for the given data poses a challenge and the shape of the tensor may affect the…

In the noisy tensor completion problem we observe $m$ entries (whose location is chosen uniformly at random) from an unknown $n_1 \times n_2 \times n_3$ tensor $T$. We assume that $T$ is entry-wise close to being rank $r$. Our goal is to…

In this work, we perform Bayesian inference tasks for the chemical master equation in the tensor-train format. The tensor-train approximation has been proven to be very efficient in representing high dimensional data arising from the…

Estimation of probability density function from samples is one of the central problems in statistics and machine learning. Modern neural network-based models can learn high dimensional distributions but have problems with hyperparameter…

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…

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 network techniques, known for their low-rank approximation ability that breaks the curse of dimensionality, are emerging as a foundation of new mathematical methods for ultra-fast numerical solutions of high-dimensional Partial…

A key bottleneck in quantum machine learning is the computational cost of repeated quantum circuit evaluations during the inference phase. To address this, we present a framework for constructing fast, cheap, provably accurate classical…

While Bernoulli sampling is extensively studied in tensor completion, t-CUR sampling approximates low-tubal-rank tensors via lateral and horizontal subtensors. However, both methods lack sufficient flexibility for diverse practical…

We present two algorithms to initialize layers of tensorized neural networks and general tensor network algorithms using partial computations of their Frobenius norms and positive lineal entrywise sums, depending on the type of tensor…

In recent studies, the tensor ring (TR) rank has shown high effectiveness in tensor completion due to its ability of capturing the intrinsic structure within high-order tensors. A recently proposed TR rank minimization method is based on…