Related papers: Hankel-Norm Approximation of Large-Scale Descripto…
We consider the characterization and computation of H-infinity norms for a class of time-delay systems. It is well known that in the finite dimensional case the H-infinity norm of a transfer function can be computed using the connections…
This paper is contributed to a fast algorithm for Hankel tensor-vector products. For this purpose, we first discuss a special class of Hankel tensors that can be diagonalized by the Fourier matrix, which is called \emph{anti-circulant}…
To accelerate kernel methods, we propose a near input sparsity time algorithm for sampling the high-dimensional feature space implicitly defined by a kernel transformation. Our main contribution is an importance sampling method for…
We address the problem of learning the parameters of a stable linear time invariant (LTI) system or linear dynamical system (LDS) with unknown latent space dimension, or order, from a single time--series of noisy input-output data. We focus…
Structured Low-Rank Approximation is a problem arising in a wide range of applications in Numerical Analysis and Engineering Sciences. Given an input matrix $M$, the goal is to compute a matrix $M'$ of given rank $r$ in a linear or affine…
This article introduces a tensor network subspace algorithm for the identification of specific polynomial state space models. The polynomial nonlinearity in the state space model is completely written in terms of a tensor network, thus…
In this paper we propose efficient randomized fixed-precision techniques for low tubal rank approximation of tensors. The proposed methods are faster and more efficient than the existing fixed-precision algorithms for approximating the…
Based on information theory, we present a method to determine an optimal Markov approximation for modelling and prediction from time series data. The method finds a balance between minimal modelling errors by taking as much as possible…
We present a novel method to approximate optimal feedback laws for nonlinear optimal control based on low-rank tensor train (TT) decompositions. The approach is based on the Dirac-Frenkel variational principle with the modification that the…
We propose a method for the approximation of high- or even infinite-dimensional feature vectors, which play an important role in supervised learning. The goal is to reduce the size of the training data, resulting in lower storage…
We consider T-optimal experiment design problems for discriminating multi-factor polynomial regression models where the design space is defined by polynomial inequalities and the regression parameters are constrained to given convex sets.…
Least squares approximation is a technique to find an approximate solution to a system of linear equations that has no exact solution. In a typical setting, one lets $n$ be the number of constraints and $d$ be the number of variables, with…
Sparsity finds applications in areas as diverse as statistics, machine learning, and signal processing. Computations over sparse structures are less complex compared to their dense counterparts, and their storage consumes less space. This…
This work is devoted to the development and analysis of a linearization algorithm for microscopic elliptic equations, with scaled degenerate production, posed in a perforated medium and constrained by the homogeneous Neumann-Dirichlet…
Modern applications require methods that are computationally feasible on large datasets but also preserve statistical efficiency. Frequently, these two concerns are seen as contradictory: approximation methods that enable computation are…
Method of moment estimators exhibit appealing statistical properties, such as asymptotic unbiasedness, for nonconvex problems. However, they typically require a large number of samples and are extremely sensitive to model misspecification.…
Functional linear regression is one of the fundamental and well-studied methods in functional data analysis. In this work, we investigate the functional linear regression model within the context of reproducing kernel Hilbert space by…
System identification in modern engineering systems faces emerging challenges from unanticipated adversarial attacks beyond existing detection mechanisms. In this work, we obtain a provably accurate estimate of the Markov parameter matrix…
We develop here a computationally effective approach for producing high-quality $\mathcal{H}_\infty$-approximations to large scale linear dynamical systems having multiple inputs and multiple outputs (MIMO). We extend an approach for…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…