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For the binary classification problem, a novel nonlinear kernel-free quadratic hyper-surface support vector machine with 0-1 loss function (QSSVM$_{0/1}$) is proposed. Specifically, the task of QSSVM$_{0/1}$ is to seek a quadratic…
Classifiers and rating scores are prone to implicitly codifying biases, which may be present in the training data, against protected classes (i.e., age, gender, or race). So it is important to understand how to design classifiers and scores…
We introduce the anti-profile Support Vector Machine (apSVM) as a novel algorithm to address the anomaly classification problem, an extension of anomaly detection where the goal is to distinguish data samples from a number of anomalous and…
We introduce a new nearest-prototype classifier, the prototype vector machine (PVM). It arises from a combinatorial optimization problem which we cast as a variant of the set cover problem. We propose two algorithms for approximating its…
Support vector machines (SVMs) are an important tool in modern data analysis. Traditionally, support vector machines have been fitted via quadratic programming, either using purpose-built or off-the-shelf algorithms. We present an…
Support Vector Machines (SVM) with $\ell_1$ penalty became a standard tool in analysis of highdimensional classification problems with sparsity constraints in many applications including bioinformatics and signal processing. Although SVM…
We investigate the relation of two fundamental tools in machine learning and signal processing, that is the support vector machine (SVM) for classification, and the Lasso technique used in regression. We show that the resulting optimization…
Kernel-based machine learning algorithms are based on mapping data from the original input feature space to a kernel feature space of higher dimensionality to solve a linear problem in that space. Over the last decade, kernel based…
In conventional prediction tasks, a machine learning algorithm outputs a single best model that globally optimizes its objective function, which typically is accuracy. Therefore, users cannot access the other models explicitly. In contrast…
Support vector machine (SVM) has been one of the most popular learning algorithms, with the central idea of maximizing the minimum margin, i.e., the smallest distance from the instances to the classification boundary. Recent theoretical…
Dimension reduction techniques, such as Sufficient Dimension Reduction (SDR), are indispensable for analyzing high-dimensional datasets. This paper introduces a novel SDR method named Principal Square Response Forward Regression (PSRFR) for…
Machine learning is capable of discriminating phases of matter, and finding associated phase transitions, directly from large data sets of raw state configurations. In the context of condensed matter physics, most progress in the field of…
Advances in statistical learning theory present the opportunity to develop statistical models of quantum many-body systems exhibiting remarkable predictive power. The potential of such ``theory-thin'' approaches is illustrated with the…
The Support Vector Machine (SVM) has been used in a wide variety of classification problems. The original SVM uses the hinge loss function, which is non-differentiable and makes the problem difficult to solve in particular for regularized…
Nonlinear regression methods, such as local optimization algorithms, are widely used in the extraction of nanostructure profile parameters in optical scatterometry. The success of local optimization algorithms heavily relies on the…
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 this paper, we introduce principal asymmetric least squares (PALS) as a unified framework for linear and nonlinear sufficient dimension reduction. Classical methods such as sliced inverse regression (Li, 1991) and principal support…
Support Vector Machine (SVM) stands out as a prominent machine learning technique widely applied in practical pattern recognition tasks. It achieves binary classification by maximizing the "margin", which represents the minimum distance…
Based on the tensor-based large margin distribution and the nonparallel support tensor machine, we establish a novel classifier for binary classification problem in this paper, termed the Large Margin Distribution based NonParallel Support…
This paper presents a kernel-based discriminative learning framework on probability measures. Rather than relying on large collections of vectorial training examples, our framework learns using a collection of probability distributions that…