Munevver Mine Subasi

Uniform quasi-concavity in probabilistic constrained stochastic programming

A probabilistic constrained stochastic linear programming problem is considered, where the rows of the random technology matrix are independent and normally distributed. The quasi-concavity of the constraining function needed for the convexity of the problem is ensured if the factors of the function are uniformly quasi-concave. A necessary and sufficient condition is given for that property to hold. It is also shown, through numerical examples, that such a special problem still has practical application in optimal portfolio construction.

Logical analysis of multi-class data

Logical Analysis of Data (LAD) is a two-class learning algorithm which integrates principles of combinatorics, optimization, and the theory of Boolean functions. This paper proposes an algorithm based on mixed integer linear programming to extend the LAD methodology to solve multi-class classification problems, where One-vs-All (OvA) learning models are efficiently constructed to classify observations in predefined classes. The utility of the proposed approach is demonstrated through experiments on multi-class benchmark datasets.

Using a similarity measure for credible classification

This paper concerns classification by Boolean functions. We investigate the classification accuracy obtained by standard classification techniques on unseen points (elements of the domain, {0, 1}(n), for some n) that are similar, in particular senses, to the points that have been observed as training observations. Explicitly, we use a new measure of how similar a point x in {0, 1}(n) is to a set of such points to restrict the domain of points on which we offer a classification. For points sufficiently dissimilar, no classification is given. We report on experimental results which indicate that the classification accuracies obtained on the resulting restricted domains are better than those obtained without restriction. These experiments involve a number of standard data-sets and classification techniques. We also compare the classification accuracies with those obtained by restricting the domain on which classification is given by using the Hamming distance.

New bounds for the probability that at least k-out-of-n events occur with unimodal distributions☆

Abstract The contribution of the shape information of the underlying distribution in probability bounding problem is investigated and a linear programming based bounding methodology to obtain robust and efficiently computable bounds for the probability that at least k -out-of- n events occur is developed. The dual feasible basis structures of the relaxed versions of linear programs involved are fully described. The bounds for the probability that at least k -out-of- n events occur are obtained in the form of formulas and as the customized algorithmic solutions of the LP’s formulated. An application in finance is presented.

A Classification Model to Predict the Rate of Decline of Kidney Function

The African American Study of Kidney Disease and Hypertension (AASK), a randomized double-blinded treatment trial, was motivated by the high rate of hypertension-related renal disease in the African-American population and the scarcity of effective therapies. This study describes a pattern-based classification approach to predict the rate of decline of kidney function using surface-enhanced laser desorption ionization/time of flight proteomic data from rapid and slow progressors classified by rate of change in glomerular filtration rate. An accurate classification model consisting of 7 out of 5,751 serum proteomic features is constructed by applying the logical analysis of data (LAD) methodology. On cross-validation by 10-folding, the model was shown to have an accuracy of 80.6 ± 0.11%, sensitivity of 78.4 ± 0.17%, and specificity of 78.5 ± 0.16%. The LAD discriminant is used to identify the patients in different risk groups. The LAD risk scores assigned to 116 AASK patients generated a receiver operating curves curve with AUC 0.899 (CI 0.845–0.953) and outperforms the risk scores assigned by proteinuria, one of the best predictors of chronic kidney disease progression.

New sufficient conditions for strong unimodality of multivariate discrete distributions

Abstract New sufficient conditions that ensure the strong unimodality of multivariate discrete distributions are obtained by the use of a special simplicial subdivision of multidimensional space. Strong unimodality of multivariate Polya–Eggenberger distribution is shown.