Related papers: Support vector machines with a reject option

This work considers the problem of binary classification: given training data $x_1, \dots, x_n$ from a certain population, together with associated labels $y_1,\dots, y_n \in \left\{0,1 \right\}$, determine the best label for an element $x$…

We consider the problem of binary classification where one can, for a particular cost, choose not to classify an observation. We present a simple proof for the oracle inequality for the excess risk of structural risk minimizers using a…

The regularization approach for variable selection was well developed for a completely observed data set in the past two decades. In the presence of missing values, this approach needs to be tailored to different missing data mechanisms. In…

The standard approach for dealing with the ill-posedness of the training problem in machine learning and/or the reconstruction of a signal from a limited number of measurements is regularization. The method is applicable whenever the…

Convex regularizers are often used for sparse learning. They are easy to optimize, but can lead to inferior prediction performance. The difference of $\ell_1$ and $\ell_2$ ($\ell_{1-2}$) regularizer has been recently proposed as a nonconvex…

We investigate implicit regularization schemes for gradient descent methods applied to unpenalized least squares regression to solve the problem of reconstructing a sparse signal from an underdetermined system of linear measurements under…

Two important goals of high-dimensional modeling are prediction and variable selection. In this article, we consider regularization with combined $L_1$ and concave penalties, and study the sampling properties of the global optimum of the…

We present a new method for minimizing the sum of a differentiable convex function and an $\ell_1$-norm regularizer. The main features of the new method include: $(i)$ an evolving set of indices corresponding to variables that are predicted…

Feature selection has evolved to be an important step in several machine learning paradigms. In domains like bio-informatics and text classification which involve data of high dimensions, feature selection can help in drastically reducing…

Regularized empirical risk minimization including support vector machines plays an important role in machine learning theory. In this paper regularized pairwise learning (RPL) methods based on kernels will be investigated. One example is…

In this paper, we study the effect of different regularizers and their implications in high dimensional image classification and sparse linear unmixing. Although kernelization or sparse methods are globally accepted solutions for processing…

In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric…

Prior knowledge and symbolic rules in machine learning are often expressed in the form of label constraints, especially in structured prediction problems. In this work, we compare two common strategies for encoding label constraints in a…

Classification models are very sensitive to data uncertainty, and finding robust classifiers that are less sensitive to data uncertainty has raised great interest in the machine learning literature. This paper aims to construct robust…

In logistic regression, it is often desirable to utilize regularization to promote sparse solutions, particularly for problems with a large number of features compared to available labels. In this paper, we present screening rules that…

Regularization techniques are widely employed in optimization-based approaches for solving ill-posed inverse problems in data analysis and scientific computing. These methods are based on augmenting the objective with a penalty function,…

Inverse reinforcement learning (IRL) usually assumes the reward function model is pre-specified as a weighted sum of features and estimates the weighting parameters only. However, how to select features and determine a proper reward model…

Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…

In real-world applications, one often encounters ambiguously labeled data, where different annotators assign conflicting class labels. Partial-label learning allows training classifiers in this weakly supervised setting, where…

For the problem of high-dimensional sparse linear regression, it is known that an $\ell_0$-based estimator can achieve a $1/n$ "fast" rate on the prediction error without any conditions on the design matrix, whereas in absence of…