1,721,042 research outputs found
Results on the PASCAL challenge "Simple causal effects in time series"
No full textA solution to the PASCAL challenge "Simple causal effects in time series" (www.causality.inf.ethz.ch) is presented. The data is modeled as a sum of a constant-plus-sin term and a term that is a linear function of a small number of inputs. The problem of identifying such a model from the data is nonconvex in the frequency and phase parameters of the sin and is combinatorial in the number of inputs. The proposed method is suboptimal and exploits several heuristics. First, the problem is split into two phases: 1) identification of the autonomous part and 2) identification of the input dependent part. Second, local optimization method is used to solve the problem in the first phase. Third, l1 regularization is used in order to find a sparse solution in the second phase
Bibliography on total least squares and related methods
No full textThe class of total least squares methods has been growing since the basic total least squares method was proposed by Golub and Van Loan in the 70's. Efficient and robust computational algorithms were developed and properties of the resulting estimators were established in the errors-in-variables setting. At the same time the developed methods were applied in diverse areas, leading to broad literature on the subject. This paper collects the main references and guides the reader in finding details about the total least squares methods and their applications. In addition, the paper comments on similarities and differences between the total least squares and the singular spectrum analysis methods
Structured low-rank approximation and its applications
No full textFitting data by a bounded complexity linear model is equivalent to low-rank approximation of a matrix constructed from the data. The data matrix being Hankel structured is equivalent to the existence of a linear time-invariant system that fits the data and the rank constraint is related to a bound on the model complexity. In the special case of fitting by a static model, the data matrix and its low-rank approximation are unstructured. We outline applications in system theory (approximate realization, model reduction, output error and errors-in-variables identification), signal processing (harmonic retrieval, sum-of-damped exponentials and finite impulse response modeling), and computer algebra (approximate common divisor). Algorithms based on the variable projections and alternating projections methods are presented. Generalizations of the low-rank approximation problem result from different approximation criteria (e.g., weighted norm), constraints on the data matrix (e.g., nonnegativity), and data structures (e.g., kernel mapping). Related problems are rank minimization and structured pseudospectra
An algorithm for closed-loop data-driven simulation
No full textClosed-loop data-driven simulation refers to the problem of constructing trajectories of a closed-loop system directly from data of the plant and a representation of the controller. Conditions under which the problem has a solution are given and an algorithm for computing the solution is presented. The problem formulation and its solution are in the spirit of the deterministic identification algorithms, i.e., in the theoretical analysis of the method, the data is assumed exact (noise free)
How effective is the nuclear norm heuristic in solving data approximation problems?
Full text linkThe question in the title is answered empirically by solving instances of three classical problems: fitting a straight line to data, fitting a real exponent to data, and system identification in the errors-in-variables setting. The results show that the nuclear norm heuristic performs worse than alternative problem dependant methods---ordinary and total least squares, Kung's method, and subspace identification. In the line fitting and exponential fitting problems, the globally optimal solution is known analytically, so that the suboptimality of the heuristic methods is quantified
Low Rank Approximation: Algorithms, Implementation, Applications
No full textatrix low-rank approximation is intimately related to data modelling; a problem that arises frequently in many different fields. This book is a comprehensive exposition of the theory, algorithms, and applications of structured low-rank approximation. Local optimization methods and effective suboptimal convex relaxations for Toeplitz, Hankel, and Sylvester structured problems are presented. A major part of the text is devoted to application of the theory. Applications described include: - system and control theory: approximate realization, model reduction, output error, and errors-in-variables identification; - signal processing: harmonic retrieval, sum-of-damped exponentials, finite impulse response modeling, and array processing; - machine learning: multidimensional scaling and recommender system; - computer vision: algebraic curve fitting and fundamental matrix estimation; - bioinformatics for microarray data analysis; - chemometrics for multivariate calibration; - psychometrics for factor analysis; and - computer algebra for approximate common divisor computation; Special knowledge from the respective application fields is not required. The book is complemented by a software implementation of the methods presented, which makes the theory directly applicable in practice. In particular, all numerical examples in the book are included in demonstration files and can be reproduced by the reader. This gives hands-on experience with the theory and methods detailed. In addition, exercises and MATLAB examples will assist the reader quickly to assimilate the theory on a chapter-by-chapter basis
On the complex least squares problem with constrained phase
Full text linkThe problem of solving approximately in the least squares sense an overdetermined linear system of equations with complex valued coefficients is considered, where the elements of the solution vector are constrained to have the same phase. A direct solution to this problem is given in [Linear Algebra and Its Applications, Vol. 433, pp. 1719-1721]. An alternative direct solution that reduces the problem to a generalized eigenvalue problem is derived in this paper. The new solution is related to generalized low-rank matrix approximation and makes possible one to use existing robust and efficient algorithms
Applications of structured low-rank approximation
No full textA number of problems in system theory, signal processing, and computer algebra fit into a generic structured low-rank approximation problem. Several problems of this type are reviewed in this paper and efficient local optimization methods (linear computational complexity in the size of the given data) for solving them are outlined
Closed-loop data-driven simulation
Full text linkClosed-loop data-driven simulation refers to the problem of finding the set of all responses of a closed-loop system to a given reference signal directly from an input/output trajectory of the plant and a representation of the controller. Conditions under which the problem has a solution are given and an algorithm for computing the solution is presented. The problem formulation and its solution are in the spirit of the deterministic subspace identification algorithms, i.e., in the theoretical analysis of the method, the data is assumed exact (noise free). The results have applications in data-driven control, \eg, testing controller's performance directly from closed-loop data of the plant in feedback with possibly different controller
Structured Low-rank Approximation as a Rational Function Minimization
Full text linkMany problems of system identification, model reduction and signal processing can be posed and solved as a structured low-rank approximation problem (SLRA). In this paper a reformulation of SLRA as minimization of a multivariate rational function is considered. Using two different parametrizations, we show that the problem reduces to optimization over a compact manifold or to a set of optimization problems over bounded domains of Euclidean space. We make a review of methods of polynomial algebra for global optimization of the rational cost function
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