Related papers: On model reduction by least squares moment matchin…
Parameter estimation by nonlinear least squares minimization is a common problem with an elegant geometric interpretation: the possible parameter values of a model induce a manifold in the space of data predictions. The minimization problem…
The Levenberg-Marquardt algorithm is one of the most popular algorithms for finding the solution of nonlinear least squares problems. Across different modified variations of the basic procedure, the algorithm enjoys global convergence, a…
In this work, we consider the matrix completion problem, where the objective is to reconstruct a low-rank matrix from a few observed entries. A commonly employed approach involves nuclear norm minimization. For this method to succeed, the…
The least squares solutions with the minimum norm of the matrix equations ${\rm {\bf A}}{\rm {\bf X}} = {\rm {\bf B}}$, ${\rm {\bf X}}{\rm {\bf A}} = {\rm {\bf B}}$ and ${\rm {\bf A}}{\rm {\bf X}}{\rm {\bf B}} ={\rm {\bf D}} $ are…
Models of complex systems often consist of multiple interconnected subsystem/component models that are developed by multi-disciplinary teams of engineers or scientists. To ensure that such interconnected models can be applied for the…
We present a technique for the approximation of a class of Hilbert space-valued maps which arise within the framework of Model Order Reduction for parametric partial differential equations, whose solution map has a meromorphic structure.…
This paper presents a low-dimensional observer design for stable, single-input single-output, continuous-time linear time-invariant (LTI) systems. Leveraging the model reduction by moment matching technique, we approximate the system with a…
A new closed-form solver is proposed minimizing the algebraic error optimally, in the least-squares sense, to estimate the relative planar motion of two calibrated cameras. The main objective is to solve the over-determined case, i.e., when…
Parallel transmission has been a very promising candidate technology to mitigate the inevitable radio-frequency field inhomogeneity in magnetic resonance imaging (MRI) at ultra-high field (UHF). For the first few years, pulse design…
We consider a linear minimum mean squared error (LMMSE) estimation framework with model mismatch where the assumed model order is smaller than that of the underlying linear system which generates the data used in the estimation process. By…
In this work we introduce a new and richer class of finite order Markov chain models and address the following model selection problem: find the Markov model with the minimal set of parameters (minimal Markov model) which is necessary to…
Spectral methods of moments provide a powerful tool for learning the parameters of latent variable models. Despite their theoretical appeal, the applicability of these methods to real data is still limited due to a lack of robustness to…
In this paper, we study the problem of finding the least square solutions of over-determined linear algebraic equations over networks in a distributed manner. Each node has access to one of the linear equations and holds a dynamic state. We…
The so-called constrained least mean-square algorithm is one of the most commonly used linear-equality-constrained adaptive filtering algorithms. Its main advantages are adaptability and relative simplicity. In order to gain analytical…
This book is meant to provide an introduction to linear models and the theories behind them. Our goal is to give a rigorous introduction to the readers with prior exposure to ordinary least squares. In machine learning, the output is…
To find the least squares solution of a very large and inconsistent system of equations, one can employ the extended Kaczmarz algorithm. This method simultaneously removes the error term, such that a consistent system is asymptotically…
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…
Subsampling methods have been recently proposed to speed up least squares estimation in large scale settings. However, these algorithms are typically not robust to outliers or corruptions in the observed covariates. The concept of influence…
Canonical work handling distribution shifts typically necessitates an entire target distribution that lands inside the training distribution. However, practical scenarios often involve only a handful of target samples, potentially lying…
A method for data-driven interpolatory model reduction is presented in this extended abstract. This framework enables the computation of the transfer function values at given interpolation points based on time-domain input-output data only,…