Reconstructing phylogenetic trees using the criterion of minimum evolution requires the use of a formula FT (d) that estimates the total length of a tree T given only the estimated distances d between the leaves of the tree. Let U(T ) be the collection of linear formulas FT (d) that correctly estimate the total length of T whenever d is an additive distance function on T . The current paper cha...

It is a well-known problem that obtaining a correct bandwidth in nonparametric regression is difficult in the presence of correlated errors. There exist a wide variety of methods coping with this problem, but they all critically depend on a tuning procedure which requires accurate information about the correlation structure. Since the errors cannot be observed, the latter is a hard goal to achi...

T HE introduction by Hoerl and Kennard (1970) of a ridge regression estimator to deal with the problem of multicollinearity in regression has been followed by a large number of papers in the statistical literature. In the area of econometrics, though, the method of ridge regression has received little attention. I One of the reasons for the lack of interest in ridge regression on the part of th...

In this paper we consider the problem of constructing measurements optimized to distinguish between a collection of possibly non-orthogonal quantum states. We consider a collection of pure states and seek a positive operator-valued measure (POVM) consisting of rank-one operators with measurement vectors closest in squared norm to the given states. We compare our results to previous measurements...

In this paper, a multi-class feature selection scheme based on recursive feature elimination (RFE) is proposed for texture classifications. The feature selection scheme is performed in the context of one-against-all least squares support vector machine classifiers (LSSVM). The margin difference between binary classifiers with and without an associated feature is used to characterize the discrim...

Motivated by the numerical treatment of parametric and stochastic PDEs, we analyze the least-squares method for polynomial approximation of multivariate functions based on random sampling according to a given probability measure. Recent work has shown that in the univariate case and for the uniform distribution, the least-squares method is optimal in expectation in [1] and in probability in [7]...

In this paper, an efficient computational approach is proposed to solve the discrete time nonlinear stochastic optimal control problem. For this purpose, a linear quadratic regulator model, which is a linear dynamical system with the quadratic criterion cost function, is employed. In our approach, the model-based optimal control problem is reformulated into the input-output equations. In this w...

Many different methods have been proposed to construct a smooth regression function, including local polynomial estimators, kernel estimators, smoothing splines and LS-SVM estimators. Each of these estimators use hyperparameters. In this paper a robust version for general cost functions based on the Akaike information criterion is proposed.

An automatic and local fairing algorithm for bicubic Bspline surfaces is proposed. A local fairness criterion selects the knot, where the spline surface has to be faired. A fairing step is than applied, which locally modi es the control net by a constrained least-squares approximation. It consists of increasing locally the smoothness of the surface from C to C. Some extensions of this method ar...

Due to its simplicity, the completion-of-squares technique is quite popular in linear optimal control. However, this simple technique is limited to linear quadratic Gaussian systems. In this note, by interpreting the completion-ofsquares from a new angle, we extend this technique to performance optimization of general Markov systems with the long run average criterion, leading to a new approach...