Robust Least Squares and Applications
نویسنده
چکیده
We consider least-squares problems where the coef-cient matrices A; b are unknown-but-bounded. We minimize the worst-case residual error using (convex) second-order cone programming (SOCP), yielding an algorithm with complexity similar to one singular value decomposition of A. The method can be interpreted as a Tikhonov regularization procedure, with the advantage that it provides an exact bound on the robustness of solution, and a rigorous way to compute the reg-ularization parameter. When the perturbation has a known (e.g., Toeplitz) structure, the same problem can be solved in polynomial-time using semideenite programming (SDP). We also consider the case when A; b are rational functions of an unknown-but-bounded perturbation vector. We show how to minimize (via SDP) upper bounds on the optimal worst-case residual. We provide numerical examples, including one from robust identiication and one from robust interpolation. Notation For a matrix X, kXk denotes the largest singular value, and kXk F the Frobenius norm; I denotes identity matrix , with size inferred from context.
منابع مشابه
A robust least squares fuzzy regression model based on kernel function
In this paper, a new approach is presented to fit arobust fuzzy regression model based on some fuzzy quantities. Inthis approach, we first introduce a new distance between two fuzzynumbers using the kernel function, and then, based on the leastsquares method, the parameters of fuzzy regression model isestimated. The proposed approach has a suitable performance to<b...
متن کاملSimultaneous robust estimation of multi-response surfaces in the presence of outliers
A robust approach should be considered when estimating regression coefficients in multi-response problems. Many models are derived from the least squares method. Because the presence of outlier data is unavoidable in most real cases and because the least squares method is sensitive to these types of points, robust regression approaches appear to be a more reliable and suitable method for addres...
متن کاملFuzzy Robust Regression Analysis with Fuzzy Response Variable and Fuzzy Parameters Based on the Ranking of Fuzzy Sets
Robust regression is an appropriate alternative for ordinal regression when outliers exist in a given data set. If we have fuzzy observations, using ordinal regression methods can't model them; In this case, using fuzzy regression is a good method. When observations are fuzzy and there are outliers in the data sets, using robust fuzzy regression methods are appropriate alternatives....
متن کاملThe analysis of residuals variation and outliers to obtain robust response surface
In this paper, the main idea is to compute the robust regression model, derived by experimentation, in order to achieve a model with minimum effects of outliers and fixed variation among different experimental runs. Both outliers and nonequality of residual variation can affect the response surface parameter estimation. The common way to estimate the regression model coefficients is the ordinar...
متن کاملRank based Least-squares Independent Component Analysis
In this paper, we propose a nonparametric rank-based alternative to the least-squares independent component analysis algorithm developed. The basic idea is to estimate the squared-loss mutual information, which used as the objective function of the algorithm, based on its copula density version. Therefore, no marginal densities have to be estimated. We provide empirical evaluation of th...
متن کاملLeast Squares Support Vector Machine for Constitutive Modeling of Clay
Constitutive modeling of clay is an important research in geotechnical engineering. It is difficult to use precise mathematical expressions to approximate stress-strain relationship of clay. Artificial neural network (ANN) and support vector machine (SVM) have been successfully used in constitutive modeling of clay. However, generalization ability of ANN has some limitations, and application of...
متن کامل