An algorithm is presented for online learning of rotations. The proposed algorithm involves matrix exponentiated gradient updates and is motivated by the von Neumann divergence. The multiplicative updates are exponentiated skew-symmetric matrices which comprise the Lie algebra of the rotation group. The orthonormality and unit determinant of the matrix parameter are preserved using matrix logar...

We present the theoretical basis and sample Monte Carlo data for the YFS exponentiated calculation of ee → ZZ → f1f̄1 + f̄2f2 at and beyond LEP2 energies, where the left-handed part of fi is a component of an SU2L doublet, i = 1, 2. The calculation is performed for both SM couplings and for anomalous ZZV triple gauge boson couplings in the conventions of Hagiwara et al.. Our formulas, which are g...

This paper is concerned with the problem of finding a representative sample of Pareto-optimal points inmulti-objective optimization. The Normal Boundary Intersection algorithm is a scalarization scheme for generating a set of evenly spaced Efficient solutions. A drawback of this algorithm is that Pareto-optimality of solutions is not guaranteed. The contributions of this paper are two-fold. Fir...

The two main and contradicting criteria guiding sampling design are accuracy of estimators and sampling costs. In stratified random sampling, the sample size must be allocated to strata in order to optimize both objectives. In this note we address, following a biobjective methodology, this allocation problem. A two-phase method is proposed to describe the set of Pareto-optimal solutions of this...

In this paper we present a new interactive procedure for multiObjective optimization, which is based on the use of a set of value functions as a preference model built by an ordinal regression method. The procedure is composed of two alternating stages. In the first stage, a representative sample of solutions from the Pareto optimal set (or from its approximation) is generated. In the second st...

We consider the problem of identifying the Pareto front for multiple objectives from a finite set of operating points. Sampling an operating point gives a random vector where each coordinate corresponds to the value of one of the objectives. The Pareto front is the set of operating points that are not dominated by any other operating point in respect to all objectives (considering the mean of t...

Maximum likelihood and Bayes estimators of the parameters, survival function (SF) and hazard rate function (HRF) are obtained for the three-parameter exponentiated Burr type XII distribution when sample is available from type II censored scheme. Bayes estimators have been developed using the standard Bayes and MCMC methods under square error and LINEX loss functions, using informative type of p...

In this chapter, we present a new method for interactive multiobjective optimization, which is based on application of a logical preference model built using the Dominance-based Rough Set Approach (DRSA). The method is composed of two main stages that alternate in an interactive procedure. In the first stage, a sample of solutions from the Pareto optimal set (or from its approximation) is gener...

We define a new quantile regression model based on reparameterized exponentiated odd log-logistic Weibull distribution, and obtain some of its structural properties. It includes as sub-models known models that can be utilized in many areas. The maximum likelihood method is adopted to estimate the parameters, several simulations are performed study finite sample properties estimators. applicabil...

We present an adaptive variant of the exponentiated gradient algorithm. Leveraging the optimistic learning framework of Rakhlin & Sridharan (2012), we obtain regret bounds that in the learning from experts setting depend on the variance and path length of the best expert, improving on results by Hazan & Kale (2008) and Chiang et al. (2012), and resolving an open problem posed by Kale (2012). Ou...