Related papers: Feature Selection for Linear SVM with Provable Gua…
Support vector machines (SVMs) are well-studied supervised learning models for binary classification. In many applications, large amounts of samples can be cheaply and easily obtained. What is often a costly and error-prone process is to…
Support Vector Machines (SVMs) based on hinge loss have been extensively discussed and applied to various binary classification tasks. These SVMs achieve a balance between margin maximization and the minimization of slack due to outliers.…
In this work, we propose the marginal structured SVM (MSSVM) for structured prediction with hidden variables. MSSVM properly accounts for the uncertainty of hidden variables, and can significantly outperform the previously proposed latent…
We study the problem of selecting limited features to observe such that models trained on them can perform well simultaneously across multiple subpopulations. This problem has applications in settings where collecting each feature is…
The Support Vector Machine (SVM) of Vapnik (1998) has become widely established as one of the leading approaches to pattern recognition and machine learning. It expresses predictions in terms of a linear combination of kernel functions…
The support vector machine (SVM) has an asymptotic behavior that parallels that of the quasi-maximum likelihood estimator (QMLE) for binary outcomes generated by a binary choice model (BCM), although it is not a QMLE. We show that, under…
In this paper, we study several important geometric optimization problems arising in machine learning. First, we revisit the Minimum Enclosing Ball (MEB) problem in Euclidean space $\mathbb{R}^d$. The problem has been extensively studied…
The surroundings of a cancerous tumor impact how it grows and develops in humans. New data from early breast cancer patients contains information on the collagen fibers surrounding the tumorous tissue -- offering hope of finding additional…
Recently, there has been considerable progress on designing algorithms with provable guarantees -- typically using linear algebraic methods -- for parameter learning in latent variable models. But designing provable algorithms for inference…
Learning structured models using maximum margin techniques has become an indispensable tool for com- puter vision researchers, as many computer vision applications can be cast naturally as an image labeling problem. Pixel-based or…
Support Vector Machines (SVMs) with various kernels have played dominant role in machine learning for many years, finding numerous applications. Although they have many attractive features interpretation of their solutions is quite…
Support vector machine (SVM) training is an active research area since the dawn of the method. In recent years there has been increasing interest in specialized solvers for the important case of linear models. The algorithm presented by…
Due to the rise of cardinality minimization in optimization, sparse support vector machines (SSVMs) have attracted much attention lately and show certain empirical advantages over convex SVMs. A common way to derive an SSVM is to add a…
We study convex empirical risk minimization for high-dimensional inference in binary models. Our first result sharply predicts the statistical performance of such estimators in the linear asymptotic regime under isotropic Gaussian features.…
We propose a method for the approximation of high- or even infinite-dimensional feature vectors, which play an important role in supervised learning. The goal is to reduce the size of the training data, resulting in lower storage…
In this article, we propose a new algorithm for supervised learning methods, by which one can both capture the non-linearity in data and also find the best subset model. To produce an enhanced subset of the original variables, an ideal…
Let $(Y,X_1,...,X_m)$ be a random vector. It is desired to predict $Y$ based on $(X_1,...,X_m)$. Examples of prediction methods are regression, classification using logistic regression or separating hyperplanes, and so on. We consider the…
This paper explores the following question: what kind of statistical guarantees can be given when doing variable selection in high-dimensional models? In particular, we look at the error rates and power of some multi-stage regression…
Linear optimization problems are investigated whose parameters are uncertain. We apply coherent distortion risk measures to capture the possible violation of a restriction. Each risk constraint induces an uncertainty set of coefficients,…
Support vector machine (SVM) is a well-known statistical technique for classification problems in machine learning and other fields. An important question for SVM is the selection of covariates (or features) for the model. Many studies have…