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To construct as adequate regression model one has to fulfill the set of measured features with their generated derivatives. Often the number of these features exceeds the number of the samples in the data set. After a feature generation process the problem of feature selection from a set of highly correlated features arises. The proposed algorithm uses an evidence maximization procedure to select a model as a subset of generated features. During the selection process it rejects multicollinear features. A problem of European option volatility modelling illustrates the algorithm. Its performance is compared with performance of similar well-known algorithms. [ABSTRACT FROM AUTHOR]

Desirability functions of Derringer and Suich, one of the widely used approaches in multiresponse optimization, have nondifferentiable points in their formulations as a drawback. To solve the optimization problem of the overall desirability function, one way is to modify the individual desirability functions by approximation approaches and then to use the gradient based methods. Another way is to use the optimization techniques that do not employ the derivative information. In this study, we propose a new approach which is easy to implement and does not need assumptions like convexity and smoothness. Our approach is based on writing the optimization problem of the overall desirability function as a mixed-integer nonlinear problem, and then putting a constraint on the integer variable to obtain a continuous formulation. The resulting problem is solved as a nonlinear model with discontinuous first order derivatives (DNLP) with Branch And Reduce Optimization Navigator (BARON), a new solver of the General Algebraic Modeling System (GAMS) for nonconvex optimization problems. The solutions obtained for two example problems are better than those of the others. [ABSTRACT FROM AUTHOR]

Generalized linear models are widely-used statistical techniques. As an extension, generalized partial linear models utilize semiparametric methods and augment the usual parametric terms by a single nonparametric component of a continuous covariate. In this paper, after a short introduction, we present our model in the generalized additive context with a focus on penalized maximum likelihood and on the penalized iteratively reweighted least squares (P-IRLS) problem based on B-splines which is attractive for nonparametric components. Then, we approach solving the P-IRLS problem using continuous optimization techniques. They become an important complementary technology and alternative to the penalty methods with the flexibility of choosing the penalty parameter adaptively. In particular, we model and treat the constrained P-IRLS problem by the elegant framework of conic quadratic programming. This paper is of a more theoretical nature and a preparation of real-world applications in future. [ABSTRACT FROM AUTHOR]