We establish a new oracle inequality for kernelbased, regularized least squares regression methods, which uses the eigenvalues of the associated integral operator as a complexity measure. We then use this oracle inequality to derive learning rates for these methods. Here, it turns out that these rates are independent of the exponent of the regularization term. Finally, we show that our learning...

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We discuss stability for a class of learning algorithms with respect to noisy labels. The algorithms we consider are for regression, and they involve the minimization of regularized risk functionals, such as L(f) := 1 N PN i=1(f(xi) yi)+ kfkH. We shall call the algorithm ‘stable’ if, when yi is a noisy version of f (xi) for some function f 2 H, the output of the algorithm converges to f as the ...

The paper continues the authors' work on adaptive Wynn algorithm in a nonlinear regression model. In present it is shown that if mean response function satisfies condition of `saturated identifiability', which was introduced by Pronzato \cite{Pronzato}, then least squares estimators are strongly consistent. states parameter identifiable under any saturated design, i.e., values at $p$ distinct d...

In this note a new high performance least squares parameter estimator is proposed. The main features of the are: (i) global exponential convergence guaranteed for all identifiable linear regression equations; (ii) it incorporates forgetting factor allowing to preserve alertness time-varying parameters; (iii) thanks addition mixing step relies on set scalar equations ensuring superior transient ...

We demonstrate that sparse regression and compressive sensing techniques are capable of accurately determining a set of functions governing a nonlinear dynamical system. We analyze a technique introduced by Brunton, Proctor, and Kutz, 2016 [1] that builds a sparse representation of a dynamical system by computing sequential least squares fittings of the data to identify the governing equations....

a University of North Carolina Wilmington, Cameron School of Business, 601 South College Road, Wilmington, NC 28403, United States b University of Nebraska at Omaha, The Peter Kiewit Institute, 1110 S 67th St., Omaha, NE 68182-0392, United States c University of North Texas, 1155 Union Circle #305219, Denton, TX 76203-5017, United States d Sam Houston State University, College of Business Admin...

Within the context of nonlinear system identification, different variants of LS-SVM are applied to the Silver Box dataset. Starting from the dual representation of the LS-SVM, and using Nyström techniques, it is possible to compute an approximation for the nonlinear mapping to be used in the primal space. In this way, primal space based techniques as Ordinary Least Squares (OLS), Ridge Regressi...

This paper addresses the use of temperature measurements to estimate product compositions in distillation columns. A simple linear multivariate calibration procedure based on steady-state data is used, which requires minimal modeling effort. It is found that these principal-component-regression (PCR) and partial-least-squares (PLS) estimators perform well, even for multicomponent mixtures, pres...