Chance constrained uncertain classification via robust optimization

Novelty detection models aim to find the minimum volume set covering a given probability mass. This paper proposes a robust single-class support vector machine (SSVM) for novelty detection, which is mainly based on the worst case conditional value-at-risk minimization. By assuming that every input is subject to an uncertainty with a specified symmetric support, this robust formulation results in a maximization term that is similar to the regularization term in the classical SSVM. When the uncertainty set is l1 -norm, l∞ -norm or box, its training can be reformulated to a linear program; while the uncertainty set is l2 -norm or ellipsoidal, its training is a tractable second-order cone program. The proposed method has a nice consistent statistical property. As the training size goes to infinity, the estimated normal region converges to the true provided that the magnitude of the uncertainty set decreases in a systematic way. The experimental results on three data sets clearly demonstrate its superiority over three benchmark models.

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“…If α * solves problem (29), the threshold ρ can be recovered by exploiting the complementary slackness condition that for any α * j ∈ (0, 1/nν)…”

Section: Ssvmmentioning

confidence: 99%

Robust Novelty Detection via Worst Case CVaR Minimization

Wang

Dang

Wang

2015

IEEE Trans. Neural Netw. Learning Syst.

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“…Ben-Tal et al [63] employed Bernstein bounding schemes for the CCP relaxation and transformed the problem as a convex second order cone program with robust set constraints to guarantee the satisfaction of the chance constraints and can be solved efficiently using interior point solvers.…”

Section: Chance Constrained Svm Through Robust Optimizationmentioning

confidence: 99%

“…Robust optimization is also used when the constraint is a chance constraint which is to ensure the small probability of misclassification for the uncertain data. The chance constraints are transformed by different bounding inequalities, for example multivariate Chebyshev inequality [61,62] and Bernstein bounding schemes [63].…”

Section: Introductionmentioning

confidence: 99%

A Survey of Support Vector Machines with Uncertainties

Wang

Pardalos

2014

Ann. Data. Sci.

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Support Vector Machines (SVM) is one of the well known supervised classes of learning algorithms. SVM have wide applications to many fields in recent years and also many algorithmic and modeling variations. Basic SVM models are dealing with the situation where the exact values of the data points are known. This paper presents a survey of SVM when the data points are uncertain. When a direct model cannot guarantee a generally good performance on the uncertainty set, robust optimization is introduced to deal with the worst case scenario and still guarantee an optimal performance. The data uncertainty could be an additive noise which is bounded by norm, where some efficient linear programming models are presented under certain conditions; or could be intervals with support and extremum values; or a more general case of polyhedral uncertainties with formulations presented. Another field of the uncertainty analysis is chance constrained SVM which is used to ensure the small probability of misclassification for the uncertain data. The multivariate Chebyshev inequality and Bernstein bounding schemes have been used to transform the chance constraints through robust optimization. The Chebyshev based model employs moment information of the uncertain training points. The Bernstein bounds can be less conservative than the Chebyshev bounds since it employs both support and moment information, but it also makes a strong assumption that all the elements in the data set are independent.

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“…More recently in [92] they further refine these methods by including a method that incorporates both "support (bounds on uncertainty of the true data point) and second order moments (mean and variance) of the uncertain training data points" to formulate a robust optimisation problem that is less conservative than when these are considered in isolation and tolerates errors in the estimation of both the support and second order moments.…”

Section: Optimisation Under Uncertaintymentioning

confidence: 99%

Optimisation of Storage for Concentrated Solar Power Plants

et al. 2014

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The proliferation of non-scheduled generation from renewable electrical energy sources such concentrated solar power (CSP) presents a need for enabling scheduled generation by incorporating energy storage; either via directly coupled Thermal Energy Storage (TES) or Electrical Storage Systems (ESS) distributed within the electrical network or grid. The challenges for 100% renewable energy generation are: to minimise capitalisation cost and to maximise energy dispatch capacity. The aims of this review article are twofold: to review storage technologies and to survey the most appropriate optimisation techniques to determine optimal operation and size of storage of a system to operate in the Australian National Energy Market (NEM). Storage technologies are reviewed to establish indicative characterisations of energy density, conversion efficiency, charge/discharge rates and costings. A partitioning of optimisation techniques based on methods most appropriate for various time scales is performed: from "whole of year", seasonal, monthly, weekly and daily averaging to those best suited matching the NEM bid timing of five minute dispatch bidding, averaged on the half hour as the trading settlement spot price. Finally, a selection of the most promising research directions and methods to determine the optimal operation and sizing of storage for renewables in the grid is presented.

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Chance constrained uncertain classification via robust optimization

Cited by 53 publications

References 11 publications

Robust Novelty Detection via Worst Case CVaR Minimization

Robust Novelty Detection via Worst Case CVaR Minimization

A Survey of Support Vector Machines with Uncertainties

Optimisation of Storage for Concentrated Solar Power Plants

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