相关论文: Safe Sample Screening for Robust Support Vector Ma…

The support vector machines (SVM) is one of the most widely used and practical optimization based classification models in machine learning because of its interpretability and flexibility to produce high quality results. However, the big…

In the problem of high-dimensional convexity testing, there is an unknown set $S \subseteq \mathbb{R}^n$ which is promised to be either convex or $\varepsilon$-far from every convex body with respect to the standard multivariate normal…

Recent work has exposed the vulnerability of computer vision models to vector field attacks. Due to the widespread usage of such models in safety-critical applications, it is crucial to quantify their robustness against such spatial…

As a computationally fast and working efficient tool, sure independence screening has received much attention in solving ultrahigh dimensional problems. This paper contributes two robust sure screening approaches that simultaneously take…

In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…

A wide variety of machine learning algorithms such as support vector machine (SVM), minimax probability machine (MPM), and Fisher discriminant analysis (FDA), exist for binary classification. The purpose of this paper is to provide a…

In this paper we propose a linear variable screening method for computer experiments when the number of input variables is larger than the number of runs. This method uses a linear model to model the nonlinear data, and screens the…

The kernel support vector machine (SVM) is one of the most widely used classification methods; however, the amount of computation required becomes the bottleneck when facing millions of samples. In this paper, we propose and analyze a novel…

Many physical systems have underlying safety considerations that require that the policy employed ensures the satisfaction of a set of constraints. The analytical formulation usually takes the form of a Constrained Markov Decision Process…

Support vector regression (SVR) is one of the most popular machine learning algorithms aiming to generate the optimal regression curve through maximizing the minimal margin of selected training samples, i.e., support vectors. Recent…

We study statistical properties of the optimal value and optimal solutions of the Sample Average Approximation of risk averse stochastic problems. Central Limit Theorem type results are derived for the optimal value and optimal solutions…

As the number of samples and dimensionality of optimization problems related to statistics an machine learning explode, block coordinate descent algorithms have gained popularity since they reduce the original problem to several smaller…

Control Barrier Functions (CBFs) have been demonstrated to be a powerful tool for safety-critical controller design for nonlinear systems. Existing design paradigms do not address the gap between theory (controller design with continuous…

We study randomized algorithms for constrained optimization, in abstract frameworks that include, in strictly increasing generality: convex programming; LP-type problems; violator spaces; and a setting we introduce, consistent spaces. Such…

One of the limiting factors of using support vector machines (SVMs) in large scale applications are their super-linear computational requirements in terms of the number of training samples. To address this issue, several approaches that…

A computationally efficient method to solve non-convex programming problems with linear equality constraints is presented. The proposed method is based on a recursively feasible and descending sequential convex programming procedure proven…

This paper proposes a robust classification model, based on support vector machine (SVM), which simultaneously deals with outliers detection and feature selection. The classifier is built considering the ramp loss margin error and it…

The selection of Gaussian kernel parameters plays an important role in the applications of support vector classification (SVC). A commonly used method is the k-fold cross validation with grid search (CV), which is extremely time-consuming…

Chance-constrained programs (CCP) represent a trade-off between conservatism and robustness in optimization. In many CCPs, one optimizes an objective under a probabilistic constraint continuously parameterized by a random vector $\xi$. In…

Convolutional neural networks (CNNs) have become an established part of numerous safety-critical computer vision applications, including human robot interactions and automated driving. Real-world implementations will need to guarantee their…