Related papers: Robustness and Regularization of Support Vector Ma…
The support vector machine (SVM) is one of the most successful learning methods for solving classification problems. Despite its popularity, SVM has a serious drawback, that is sensitivity to outliers in training samples. The penalty on…
The massive amount of available data potentially used to discover patters in machine learning is a challenge for kernel based algorithms with respect to runtime and storage capacities. Local approaches might help to relieve these issues.…
In this discussion paper, we survey recent research surrounding robustness of machine learning models. As learning algorithms become increasingly more popular in data-driven control systems, their robustness to data uncertainty must be…
In this work we study binary classification problems where we assume that our training data is subject to uncertainty, i.e. the precise data points are not known. To tackle this issue in the field of robust machine learning the aim is to…
Regularized kernel-based methods such as support vector machines (SVMs) typically depend on the underlying probability measure $\mathrm{P}$ (respectively an empirical measure $\mathrm{D}_n$ in applications) as well as on the regularization…
Recent advances in healthcare technologies have led to the availability of large amounts of biological samples across several techniques and applications. In particular, in the last few years, Raman spectroscopy analysis of biological…
The problem of adversarial examples has highlighted the need for a theory of regularisation that is general enough to apply to exotic function classes, such as universal approximators. In response, we give a very general equality result…
The support vector machine (SVM) is a well-established classification method whose name refers to the particular training examples, called support vectors, that determine the maximum margin separating hyperplane. The SVM classifier is known…
Scientific machine learning (SciML) is a field of increasing interest in several different application fields. In an optimization context, SciML-based tools have enabled the development of more efficient optimization methods. However,…
Support Vector Machines (SVMs) are among the most fundamental tools for binary classification. In its simplest formulation, an SVM produces a hyperplane separating two classes of data using the largest possible margin to the data. The focus…
This study introduces a novel formulation to enhance Support Vector Machines (SVMs) in handling class imbalance and noise. Unlike the conventional Soft Margin SVM, which penalizes the magnitude of constraint violations, the proposed model…
Using methods of Statistical Physics, we investigate the generalization performance of support vector machines (SVMs), which have been recently introduced as a general alternative to neural networks. For nonlinear classification rules, the…
Design of reliable systems must guarantee stability against input perturbations. In machine learning, such guarantee entails preventing overfitting and ensuring robustness of models against corruption of input data. In order to maximize…
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…
Several decades ago, Support Vector Machines (SVMs) were introduced for performing binary classification tasks, under a supervised framework. Nowadays, they often outperform other supervised methods and remain one of the most popular…
We derive generalization bounds for learning algorithms based on their robustness: the property that if a testing sample is "similar" to a training sample, then the testing error is close to the training error. This provides a novel…
We review the concept of support vector machines (SVMs) and discuss examples of their use. One of the benefits of SVM algorithms, compared with neural networks and decision trees is that they can be less susceptible to over fitting than…
Support vector machine (SVM) is one of the most studied paradigms in the realm of machine learning for classification and regression problems. It relies on vectorized input data. However, a significant portion of the real-world data exists…
Deep learning requires regularization mechanisms to reduce overfitting and improve generalization. We address this problem by a new regularization method based on distributional robust optimization. The key idea is to modify the…
Kernel-based regularized risk minimizers, also called support vector machines (SVMs), are known to possess many desirable properties but suffer from their super-linear computational requirements when dealing with large data sets. This…