Related papers: Support vector machines with a reject option
Neural networks are usually not the tool of choice for nonparametric high-dimensional problems where the number of input features is much larger than the number of observations. Though neural networks can approximate complex multivariate…
This paper considers the problem of recovering either a low rank matrix or a sparse vector from observations of linear combinations of the vector or matrix elements. Recent methods replace the non-convex regularization with $\ell_1$ or…
Support vector machines (SVMs) appeared in the early nineties as optimal margin classifiers in the context of Vapnik's statistical learning theory. Since then SVMs have been successfully applied to real-world data analysis problems, often…
The choice of the parameter value for regularized inverse problems is critical to the results and remains a topic of interest. This article explores a criterion for selecting a good parameter value by maximizing the probability of the data,…
We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…
We propose to learn non-convex regularizers with a prescribed upper bound on their weak-convexity modulus. Such regularizers give rise to variational denoisers that minimize a convex energy. They rely on few parameters (less than 15,000)…
Sparsity inducing regularization is an important part for learning over-complete visual representations. Despite the popularity of $\ell_1$ regularization, in this paper, we investigate the usage of non-convex regularizations in this…
In this thesis we discuss machine learning methods performing automated variable selection for learning sparse predictive models. There are multiple reasons for promoting sparsity in the predictive models. By relying on a limited set of…
In many real applications of statistical learning, a decision made from misclassification can be too costly to afford; in this case, a reject option, which defers the decision until further investigation is conducted, is often preferred. In…
We demonstrate that the primal-dual witness proof method may be used to establish variable selection consistency and $\ell_\infty$-bounds for sparse regression problems, even when the loss function and/or regularizer are nonconvex. Using…
Regularization is used in many different areas of optimization when solutions are sought which not only minimize a given function, but also possess a certain degree of regularity. Popular applications are image denoising, sparse regression…
We consider a composite convex minimization problem associated with regularized empirical risk minimization, which often arises in machine learning. We propose two new stochastic gradient methods that are based on stochastic dual averaging…
We consider the minimization of non-convex functions that typically arise in machine learning. Specifically, we focus our attention on a variant of trust region methods known as cubic regularization. This approach is particularly attractive…
The goal of classification with rejection is to avoid risky misclassification in error-critical applications such as medical diagnosis and product inspection. In this paper, based on the relationship between classification with rejection…
Machine learning based decision making systems applied in safety critical areas require reliable high certainty predictions. For this purpose, the system can be extended by an reject option which allows the system to reject inputs where…
We consider a deep neural network estimator based on empirical risk minimization with l_1-regularization. We derive a general bound for its excess risk in regression and classification (including multiclass), and prove that it is adaptively…
Feature selection is one of the most decisive tools in understanding data and machine learning models. Among other methods, sparsity induced by $L^{1}$ penalty is one of the simplest and best studied approaches to this problem. Although…
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…
We propose a method for support vector machine classification using indefinite kernels. Instead of directly minimizing or stabilizing a nonconvex loss function, our algorithm simultaneously computes support vectors and a proxy kernel matrix…
We consider regularized support vector machines (SVMs) and show that they are precisely equivalent to a new robust optimization formulation. We show that this equivalence of robust optimization and regularization has implications for both…