A soft robust model for optimization under ambiguity

In this paper, we propose a framework for robust optimization that relaxes the standard notion of robustness by allowing the decision maker to vary the protection level in a smooth way across the uncertainty set. We apply our approach to the problem of maximizing the expected value of a payoff function when the underlying distribution is ambiguous and therefore robustness is relevant. Our primary objective is to develop this framework and relate it to the standard notion of robustness, which deals with only a single guarantee across one uncertainty set. First, we show that our approach connects closely to the theory of convex risk measures. We show that the complexity of this approach is equivalent to that of solving a small number of standard robust problems. We then investigate the conservatism benefits and downside probability guarantees implied by this approach and compare to the standard robust approach. Finally, we illustrate theme thodology on an asset allocation example consisting of historical market data over a 25-year investment horizon and find in every case we explore that relaxing standard robustness with soft robustness yields a seemingly favorable risk-return trade-off: each case results in a higher out-of-sample expected return for a relatively minor degradation of out-of-sample downside performance. © 2010 INFORMS.

Linear matrix inequality-based robust model predictive control for time-delayed systems

This work addresses the solution to the problem of robust model predictive control (MPC) of systems with model uncertainty. The case of zone control of multi-variable stable systems with multiple time delays is considered. The usual approach of dealing with this kind of problem is through the inclusion of non-linear cost constraint in the control problem. The control action is then obtained at each sampling time as the solution to a non-linear programming (NLP) problem that for high-order systems can be computationally expensive. Here, the robust MPC problem is formulated as a linear matrix inequality problem that can be solved in real time with a fraction of the computer effort. The proposed approach is compared with the conventional robust MPC and tested through the simulation of a reactor system of the process industry.

Robust nonlinear model identification methods using forward regression

In this correspondence new robust nonlinear model construction algorithms for a large class of linear-in-the-parameters models are introduced to enhance model robustness via combined parameter regularization and new robust structural selective criteria. In parallel to parameter regularization, we use two classes of robust model selection criteria based on either experimental design criteria that optimizes model adequacy, or the predicted residual sums of squares (PRESS) statistic that optimizes model generalization capability, respectively. Three robust identification algorithms are introduced, i.e., combined A- and D-optimality with regularized orthogonal least squares algorithm, respectively; and combined PRESS statistic with regularized orthogonal least squares algorithm. A common characteristic of these algorithms is that the inherent computation efficiency associated with the orthogonalization scheme in orthogonal least squares or regularized orthogonal least squares has been extended such that the new algorithms are computationally efficient. Numerical examples are included to demonstrate effectiveness of the algorithms.

Fast model based feature matching technique applied to airport lighting

The use of image processing techniques to assess the performance of airport landing lighting using images of it collected from an aircraft-mounted camera is documented. In order to assess the performance of the lighting, it is necessary to uniquely identify each luminaire within an image and then track the luminaires through the entire sequence and store the relevant information for each luminaire, that is, the total number of pixels that each luminaire covers and the total grey level of these pixels. This pixel grey level can then be used for performance assessment. The authors propose a robust model-based (MB) featurematching technique by which the performance is assessed. The development of this matching technique is the key to the automated performance assessment of airport lighting. The MB matching technique utilises projective geometry in addition to accurate template of the 3D model of a landing-lighting system. The template is projected onto the image data and an optimum match found, using nonlinear least-squares optimisation. The MB matching software is compared with standard feature extraction and tracking techniques known within the community, these being the Kanade–Lucus–Tomasi (KLT) and scaleinvariant feature transform (SIFT) techniques. The new MB matching technique compares favourably with the SIFT and KLT feature-tracking alternatives. As such, it provides a solid foundation to achieve the central aim of this research which is to automatically assess the performance of airport lighting.

Robust linear mixed models with normal/independent distributions and Bayesian MCMC implementation

Linear mixed effects models have been widely used in analysis of data where responses are clustered around some random effects, so it is not reasonable to assume independence between observations in the same cluster. In most biological applications, it is assumed that the distributions of the random effects and of the residuals are Gaussian. This makes inferences vulnerable to the presence of outliers. Here, linear mixed effects models with normal/independent residual distributions for robust inferences are described. Specific distributions examined include univariate and multivariate versions of the Student-t, the slash and the contaminated normal. A Bayesian framework is adopted and Markov chain Monte Carlo is used to carry out the posterior analysis. The procedures are illustrated using birth weight data on rats in a texicological experiment. Results from the Gaussian and robust models are contrasted, and it is shown how the implementation can be used for outlier detection. The thick-tailed distributions provide an appealing robust alternative to the Gaussian process in linear mixed models, and they are easily implemented using data augmentation and MCMC techniques.

Multivariate analyses of UV-Vis absorption spectral data from cachaca wood extracts: a model to classify aged Brazilian cachacas according to the wood species used

Multivariate analyses of UV-Vis spectral data from cachaca wood extracts provide a simple and robust model to classify aged Brazilian cachacas according to the wood species used in the maturation barrels. The model is based on inspection of 93 extracts of oak and different Brazilian wood species by a non-aged cachaca used as an extraction solvent. Application of PCA (Principal Components Analysis) and HCA (Hierarchical Cluster Analysis) leads to identification of 6 clusters of cachaca wood extracts (amburana, amendoim, balsamo, castanheira, jatoba, and oak). LDA (Linear Discriminant Analysis) affords classification of 10 different wood species used in the cachaca extracts (amburana, amendoim, balsamo, cabreuva-parda, canela-sassafras, castanheira, jatoba, jequitiba-rosa, louro-canela, and oak) with an accuracy ranging from 80% (amendoim and castanheira) to 100% (balsamo and jequitiba-rosa). The methodology provides a low-cost alternative to methods based on liquid chromatography and mass spectrometry to classify cachacas aged in barrels that are composed of different wood species.

The kinesin walk: a dynamic model with elastically coupled heads.

Recently individual two-headed kinesin molecules have been studied in in vitro motility assays revealing a number of their peculiar transport properties. In this paper we propose a simple and robust model for the kinesin stepping process with elastically coupled Brownian heads that show all of these properties. The analytic and numerical treatment of our model results in a very good fit to the experimental data and practically has no free parameters. Changing the values of the parameters in the restricted range allowed by the related experimental estimates has almost no effect on the shape of the curves and results mainly in a variation of the zero load velocity that can be directly fitted to the measured data. In addition, the model is consistent with the measured pathway of the kinesin ATPase.

Robust Solutions of MultiObjective Linear Semi-Infinite Programs under Constraint Data Uncertainty

The multiobjective optimization model studied in this paper deals with simultaneous minimization of finitely many linear functions subject to an arbitrary number of uncertain linear constraints. We first provide a radius of robust feasibility guaranteeing the feasibility of the robust counterpart under affine data parametrization. We then establish dual characterizations of robust solutions of our model that are immunized against data uncertainty by way of characterizing corresponding solutions of robust counterpart of the model. Consequently, we present robust duality theorems relating the value of the robust model with the corresponding value of its dual problem.

Vector quantization based Gaussian modeling for speaker verification

Gaussian mixture models (GMMs) have become an established means of modeling feature distributions in speaker recognition systems. It is useful for experimentation and practical implementation purposes to develop and test these models in an efficient manner particularly when computational resources are limited. A method of combining vector quantization (VQ) with single multi-dimensional Gaussians is proposed to rapidly generate a robust model approximation to the Gaussian mixture model. A fast method of testing these systems is also proposed and implemented. Results on the NIST 1996 Speaker Recognition Database suggest comparable and in some cases an improved verification performance to the traditional GMM based analysis scheme. In addition, previous research for the task of speaker identification indicated a similar system perfomance between the VQ Gaussian based technique and GMMs

A discussion of “Estimating the historical and future probabilities of large terrorist events'' by Aaron Clauset and Ryan Woodard

The terrorist attacks in the United States on September 11, 2001 appeared to be a harbinger of increased terrorism and violence in the 21st century, bringing terrorism and political violence to the forefront of public discussion. Questions about these events abound, and “Estimating the Historical and Future Probabilities of Large Scale Terrorist Event” [Clauset and Woodard (2013)] asks specifically, “how rare are large scale terrorist events?” and, in general, encourages discussion on the role of quantitative methods in terrorism research and policy and decision-making. Answering the primary question raises two challenges. The first is identify- ing terrorist events. The second is finding a simple yet robust model for rare events that has good explanatory and predictive capabilities. The challenges of identifying terrorist events is acknowledged and addressed by reviewing and using data from two well-known and reputable sources: the Memorial Institute for the Prevention of Terrorism-RAND database (MIPT-RAND) [Memorial Institute for the Prevention of Terrorism] and the Global Terror- ism Database (GTD) [National Consortium for the Study of Terrorism and Responses to Terrorism (START) (2012), LaFree and Dugan (2007)]. Clauset and Woodard (2013) provide a detailed discussion of the limitations of the data and the models used, in the context of the larger issues surrounding terrorism and policy.

Predictive motion planning for AUVs subject to strong time-varying currents and forecasting uncertainties

This paper presents a novel path planning method for minimizing the energy consumption of an autonomous underwater vehicle subjected to time varying ocean disturbances and forecast model uncertainty. The algorithm determines 4-Dimensional path candidates using Nonlinear Robust Model Predictive Control (NRMPC) and solutions optimised using A*-like algorithms. Vehicle performance limits are incorporated into the algorithm with disturbances represented as spatial and temporally varying ocean currents with a bounded uncertainty in their predictions. The proposed algorithm is demonstrated through simulations using a 4-Dimensional, spatially distributed time-series predictive ocean current model. Results show the combined NRMPC and A* approach is capable of generating energy-efficient paths which are resistant to both dynamic disturbances and ocean model uncertainty.