Related papers: Large margin classifier with graph-based adaptive …
While large margin classifiers are originally an outcome of an optimization framework, support vectors (SVs) can be obtained from geometric approaches. This article presents advances in the use of Gabriel graphs (GGs) in binary and…
We present algorithms for efficiently learning regularizers that improve generalization. Our approach is based on the insight that regularizers can be viewed as upper bounds on the generalization gap, and that reducing the slack in the…
Modern machine learning systems such as deep neural networks are often highly over-parameterized so that they can fit the noisy training data exactly, yet they can still achieve small test errors in practice. In this paper, we study this…
Margin-based classifiers have been popular in both machine learning and statistics for classification problems. Since a large number of classifiers are available, one natural question is which type of classifiers should be used given a…
This paper investigates the phenomenon of benign overfitting in binary classification problems with heavy-tailed input distributions, extending the analysis of maximum margin classifiers to $\alpha$ sub-exponential distributions ($\alpha…
We propose thresholding as an approach to deal with class imbalance. We define the concept of thresholding as a process of determining a decision boundary in the presence of a tunable parameter. The threshold is the maximum value of this…
In this article, we study rates of convergence of the generalization error of multi-class margin classifiers. In particular, we develop an upper bound theory quantifying the generalization error of various large margin classifiers. The…
In machine learning, classifiers are typically susceptible to noise in the training data. In this work, we aim at reducing intra-class noise with the help of graph filtering to improve the classification performance. Considered graphs are…
Regularized linear regression is a promising approach for binary classification problems in which the training set has noisy labels since the regularization term can help to avoid interpolating the mislabeled data points. In this paper we…
Many binary classification problems minimize misclassification above (or below) a threshold. We show that instances of ranking problems, accuracy at the top or hypothesis testing may be written in this form. We propose a general framework…
Maximum margin binary classification is one of the most fundamental algorithms in machine learning, yet the role of featurization maps and the high-dimensional asymptotics of the misclassification error for non-Gaussian features are still…
We propose an adaptive refinement algorithm to solve total variation regularized measure optimization problems. The method iteratively constructs dyadic partitions of the unit cube based on i) the resolution of discretized dual problems and…
Adversarial robustness has become an important research topic given empirical demonstrations on the lack of robustness of deep neural networks. Unfortunately, recent theoretical results suggest that adversarial training induces a strict…
Real-world object classes appear in imbalanced ratios. This poses a significant challenge for classifiers which get biased towards frequent classes. We hypothesize that improving the generalization capability of a classifier should improve…
Deep neural networks often exhibit substantial disparities in class-wise accuracy, even when trained on class-balanced data, posing concerns for reliable deployment. While prior efforts have explored empirical remedies, a theoretical…
Modern machine learning classifiers often exhibit vanishing classification error on the training set. They achieve this by learning nonlinear representations of the inputs that maps the data into linearly separable classes. Motivated by…
The practical success of deep learning has led to the discovery of several surprising phenomena. One of these phenomena, that has spurred intense theoretical research, is ``benign overfitting'': deep neural networks seem to generalize well…
Variational regularization is commonly used to solve linear inverse problems, and involves augmenting a data fidelity by a regularizer. The regularizer is used to promote a priori information and is weighted by a regularization parameter.…
Learning classifiers that are robust to adversarial examples has received a great deal of recent attention. A major drawback of the standard robust learning framework is there is an artificial robustness radius $r$ that applies to all…
In the (special) smoothing spline problem one considers a variational problem with a quadratic data fidelity penalty and Laplacian regularisation. Higher order regularity can be obtained via replacing the Laplacian regulariser with a…