According to Markowitz (1952) portfolio theory assumed that the investor has a concave utility function that expresses an attitude of risk aversion and managed to put portfolio selection based on two criteria, mean and variance. Other studies have improved this approach and following Basel II recommendations by using Value-at-Risk (VaR) as a standard risk measure in finance, Alexander & Baptist...

We present a new method for top-down induction of decision trees (TDIDT) with multivariate binary splits at the nodes. The primary contribution of this work is a new splitting criterion called soft entropy, which is continuous and differentiable with respect to the parameters of the splitting function. Using simple gradient descent to find multivariate splits and a novel pruning technique, our ...

A methodology is proposed to jointly model treatments with quantitative levels measured throughout time by combining the response surface and growth curve techniques. The model parameters, which measure the effect throughout time of the factors related to the second-order response surface model, are estimated. These estimates are made through a suitable transformation that allows to express the...

1098-4402= We have conducted a multiobjective computational optimization of a high brightness, high average current photoinjector under development at Cornell University. This injector employs a dc photoemission electron gun. Using evolutionary algorithms combined with parallel computing resources, the multivariate parameter space of the photoinjector was explored for optimal values. This power...

The purpose of this article is to find the settings of the factors which simultaneously optimize several mean responses in a multivariate generalized linear model (GLM) environment. The generalized distance approach, initially developed for the simultaneous optimization of several linear response surfacemodels, is adapted to this multivariate GLM situation. An application of the proposed method...

In this problem Z0 is a convex closed subset of a Banach spaceZ , and G and H are continuous operators from Z to the space of integrable random variables L1(Ω,F , P). The random variable Y plays the role of a benchmark outcome. For example, one may set Y = G(z̄), where z̄ ∈ Z0 is some reasonable value of the decision vector, which is currently employed in the system. The relation (2) is the stoch...

In this paper, we propose the problem of optimizing multivariate performance measures from multi-view data, and an effective method to solve it. This problem has two features: the data points are presented by multiple views, and the target of learning is to optimize complex multivariate performance measures. We propose to learn a linear discriminant functions for each view, and combine them to ...

Elementary particle physics experiments, searching for very rare processes, require the efficient analysis and selection algorithms able to separate signal from the overwhelming background. In the last years a number of learning machines have been developed. Three of such algorithms have been applied to identify τ leptons in the ATLAS experiment: Probability Density Estimator with Range Searche...

Normal Boundary Intersection (NBI) is traditionally used to generate equally spaced and uniformly spread Pareto Frontiers for multi-objective optimization programming (MOP). This method tends to fail, however, when correlated objective functions must be optimized using Robust Parameter Designs (RPD). In such multi-objective optimization programming, there can be reached impractical optima and n...

We consider a class of multicriteria stochastic optimization problems that features benchmarking constraints based on conditional value-at-risk and second-order stochastic dominance. We develop alternative mixedinteger programming formulations and solution methods for cut generation problems arising in optimization under such multivariate risk constraints. We give the complete linear descriptio...