Related papers: Qualitative Robustness of Support Vector Machines
We study the problem of robust performance of quantum systems under structured uncertainties. A specific feature of closed (Hamiltonian) quantum systems is that their poles lie on the imaginary axis and that neither a coherent controller…
We introduce a novel kind of robustness in linear programming. A solution x* is called robust optimal if for all realizations of objective functions coefficients and constraint matrix entries from given interval domains there are…
In nonparametric classification and regression problems, regularized kernel methods, in particular support vector machines, attract much attention in theoretical and in applied statistics. In an abstract sense, regularized kernel methods…
In the past five years, deep learning methods have become state-of-the-art in solving various inverse problems. Before such approaches can find application in safety-critical fields, a verification of their reliability appears mandatory.…
Machine learning methods may have the potential to significantly accelerate drug discovery. However, the increasing rate of new methodological approaches being published in the literature raises the fundamental question of how models should…
In this paper, we consider asymptotic properties of the support vector machine (SVM) in high-dimension, low-sample-size (HDLSS) settings. We show that the hard-margin linear SVM holds a consistency property in which misclassification rates…
A vision foundation model outputs an embedding vector for an image, which can be affected by common editing operations (e.g., JPEG compression, brightness, contrast adjustments). These common perturbations alter embedding vectors and may…
The combination of machine learning with control offers many opportunities, in particular for robust control. However, due to strong safety and reliability requirements in many real-world applications, providing rigorous statistical and…
Modern technologies are producing datasets with complex intrinsic structures, and they can be naturally represented as matrices instead of vectors. To preserve the latent data structures during processing, modern regression approaches…
We have made initial studies of the potential of support vector machines (SVM) for providing statistical models of nuclear systematics with demonstrable predictive power. Using SVM regression and classification procedures, we have created…
The support vector machine (SVM) algorithm is well known to the computer learning community for its very good practical results. The goal of the present paper is to study this algorithm from a statistical perspective, using tools of…
In this paper, to cope with the shortage of sufficient theoretical support resulted from the fast-growing quantitative financial modeling, we investigate two classes of generalized stochastic volatility models, establish their…
We introduce Harmonic Robustness, a powerful and intuitive method to test the robustness of any machine-learning model either during training or in black-box real-time inference monitoring without ground-truth labels. It is based on…
The existence of adversarial examples has led to considerable uncertainty regarding the trust one can justifiably put in predictions produced by automated systems. This uncertainty has, in turn, lead to considerable research effort in…
We show how, using linear-algebraic tools developed to prove Tverberg's theorem in combinatorial geometry, we can design new models of multi-class support vector machines (SVMs). These supervised learning protocols require fewer conditions…
In most papers establishing consistency for learning algorithms it is assumed that the observations used for training are realizations of an i.i.d. process. In this paper we go far beyond this classical framework by showing that support…
Convolutional and Recurrent, deep neural networks have been successful in machine learning systems for computer vision, reinforcement learning, and other allied fields. However, the robustness of such neural networks is seldom apprised,…
This paper develops a robust dynamic mode decomposition (RDMD) method endowed with statistical and numerical robustness. Statistical robustness ensures estimation efficiency at the Gaussian and non-Gaussian probability distributions,…
We provide a new computationally-efficient class of estimators for risk minimization. We show that these estimators are robust for general statistical models: in the classical Huber epsilon-contamination model and in heavy-tailed settings.…
Data-driven models, especially deep learning classifiers often demonstrate great success on clean datasets. Yet, they remain vulnerable to common data distortions such as adversarial and common corruption perturbations. These perturbations…