Related papers: Wasserstein Distributionally Robust Multiclass Sup…
This paper studies a class of multiagent stochastic optimization problems where the objective is to minimize the expected value of a function which depends on a random variable. The probability distribution of the random variable is unknown…
This paper presents a review on methods for class-imbalanced learning with the Support Vector Machine (SVM) and its variants. We first explain the structure of SVM and its variants and discuss their inefficiency in learning with…
Support Vector Machine (SVM) is a powerful tool in binary classification, known to attain excellent misclassification rates. On the other hand, many realworld classification problems, such as those found in medical diagnosis, churn or fraud…
This paper proposes a novel non-parametric multidimensional convex regression estimator which is designed to be robust to adversarial perturbations in the empirical measure. We minimize over convex functions the maximum (over Wasserstein…
We propose a distributionally robust approach to risk-sensitive estimation of an unknown signal x from an observed signal y. The unknown signal and observation are modeled as random vectors whose joint probability distribution is unknown,…
Wasserstein distributionally robust optimization estimators are obtained as solutions of min-max problems in which the statistician selects a parameter minimizing the worst-case loss among all probability models within a certain distance…
Standard stochastic control methods assume that the probability distribution of uncertain variables is available. Unfortunately, in practice, obtaining accurate distribution information is a challenging task. To resolve this issue, we…
This paper presents a novel Wasserstein distributionally robust control and state estimation algorithm for partially observable linear stochastic systems, where the probability distributions of disturbances and measurement noises are…
We address the challenge of sequential data-driven decision-making under context distributional uncertainty. This problem arises in numerous real-world scenarios where the learner optimizes black-box objective functions in the presence of…
Support Vector Machine (SVM) stands out as a prominent machine learning technique widely applied in practical pattern recognition tasks. It achieves binary classification by maximizing the "margin", which represents the minimum distance…
In this paper, we introduce novel Twin Parametric Margin Support Vector Machine (TPMSVM) models designed to address multiclass classification tasks under feature uncertainty. To handle data perturbations, we construct bounded-by-norm…
This monograph develops a comprehensive statistical learning framework that is robust to (distributional) perturbations in the data using Distributionally Robust Optimization (DRO) under the Wasserstein metric. Beginning with fundamental…
Multiclass extensions of the support vector machine (SVM) have been formulated in a variety of ways. A recent empirical comparison of nine such formulations [Do\v{g}an et al. 2016] recommends the variant proposed by Weston and Watkins (WW),…
A new procedure for learning cost-sensitive SVM(CS-SVM) classifiers is proposed. The SVM hinge loss is extended to the cost sensitive setting, and the CS-SVM is derived as the minimizer of the associated risk. The extension of the hinge…
We consider sensitivity of a generic stochastic optimization problem to model uncertainty. We take a non-parametric approach and capture model uncertainty using Wasserstein balls around the postulated model. We provide explicit formulae for…
We study distributionally robust optimization (DRO) problems with uncertainty sets consisting of high-dimensional random vectors that are close in the multivariate Wasserstein distance to a reference random vector. We give conditions when…
The classical hinge-loss support vector machines (SVMs) model is sensitive to outlier observations due to the unboundedness of its loss function. To circumvent this issue, recent studies have focused on non-convex loss functions, such as…
A wide array of machine learning problems are formulated as the minimization of the expectation of a convex loss function on some parameter space. Since the probability distribution of the data of interest is usually unknown, it is is often…
We consider the problem of analyzing the probabilistic performance of first-order methods when solving convex optimization problems drawn from an unknown distribution only accessible through samples. By combining performance estimation…
We present a novel data-driven distributionally robust Model Predictive Control formulation for unknown discrete-time linear time-invariant systems affected by unknown and possibly unbounded additive uncertainties. We use off-line collected…