Related papers: Model-Free State Estimation Using Low-Rank Canonic…
Tensors, which provide a powerful and flexible model for representing multi-attribute data and multi-way interactions, play an indispensable role in modern data science across various fields in science and engineering. A fundamental task is…
This work introduces a tensor-based method to perform supervised classification on spatiotemporal data processed in an echo state network. Typically when performing supervised classification tasks on data processed in an echo state network,…
In this paper, we propose a general framework for sparse and low-rank tensor estimation from cubic sketchings. A two-stage non-convex implementation is developed based on sparse tensor decomposition and thresholded gradient descent, which…
Large-scale integration of distributed energy resources into residential distribution feeders necessitates careful control of their operation through power flow analysis. While the knowledge of the distribution system model is crucial for…
We apply a series of projection techniques on top of tensor networks to compute energies of ground state wave functions with higher accuracy than tensor networks alone with minimal additional cost. We consider both matrix product states as…
Limited measurement availability at the distribution grid presents challenges for state estimation and situational awareness. This paper combines the advantages of two sparsity-based state estimation approaches (matrix completion and…
We study the problem of low-rank tensor factorization in the presence of missing data. We ask the following question: how many sampled entries do we need, to efficiently and exactly reconstruct a tensor with a low-rank orthogonal…
Controllability and observability energy functions play a fundamental role in model order reduction and are inherently connected to optimal control problems. For linear dynamical systems the energy functions are known to be quadratic…
The recent introduction of synchrophasor technology into power distribution systems has given impetus to various monitoring, diagnostic, and control applications, such as system identification and event detection, which are crucial for…
In this paper, we consider the statistical inference for several low-rank tensor models. Specifically, in the Tucker low-rank tensor PCA or regression model, provided with any estimates achieving some attainable error rate, we develop the…
This paper provides a unified framework for analyzing tensor estimation problems that allow for nonlinear observations, heteroskedastic noise, and covariate information. We study a general class of high-dimensional models where each…
Our interest lies in the recoverability properties of compressed tensors under the \textit{canonical polyadic decomposition} (CPD) model. The considered problem is well-motivated in many applications, e.g., hyperspectral image and video…
We introduce a variational algorithm to simulate quantum many-body states based on a tree tensor network ansatz which releases the isometry constraint usually imposed by the real-space renormalization coarse-graining: This additional…
Obtaining a reliable estimate of the joint probability mass function (PMF) of a set of random variables from observed data is a significant objective in statistical signal processing and machine learning. Modelling the joint PMF as a tensor…
This paper develops new identification results for multidimensional continuous measurement-error models where all observed measurements are contaminated by potentially correlated errors and none provides an injective mapping of the latent…
Quantum state tomography (QST) is a fundamental technique for estimating the state of a quantum system from measured data and plays a crucial role in evaluating the performance of quantum devices. However, standard estimation methods become…
This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…
Tensor decomposition is an important technique for capturing the high-order interactions among multiway data. Multi-linear tensor composition methods, such as the Tucker decomposition and the CANDECOMP/PARAFAC (CP), assume that the complex…
We introduce a method for extracting meaningful entanglement measures of tensor network states in general dimensions. Current methods require the explicit reconstruction of the density matrix, which is highly demanding, or the contraction…
In this paper, a purely measurement-based method is proposed to estimate the dynamic system state matrix by applying the regression theorem of the multivariate Ornstein-Uhlenbeck process. The proposed method employs a recursive algorithm to…