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Within the statistical and machine learning literature, regularization techniques are often used to construct sparse (predictive) models. Most regularization strategies only work for data where all predictors are treated identically, such…
Subgradient algorithms for training support vector machines have been quite successful for solving large-scale and online learning problems. However, they have been restricted to linear kernels and strongly convex formulations. This paper…
The elastic-net is among the most widely used types of regularization algorithms, commonly associated with the problem of supervised generalized linear model estimation via penalized maximum likelihood. Its nice properties originate from a…
This paper aims at refined error analysis for binary classification using support vector machine (SVM) with Gaussian kernel and convex loss. Our first result shows that for some loss functions such as the truncated quadratic loss and…
Linear regression is a popular machine learning approach to learn and predict real valued outputs or dependent variables from independent variables or features. In many real world problems, its beneficial to perform sparse linear regression…
In representation learning (RL), how to make the learned representations easy to interpret and less overfitted to training data are two important but challenging issues. To address these problems, we study a new type of regulariza- tion…
In this paper, we extend the methodology developed for Support Vector Machines (SVM) using $\ell_2$-norm ($\ell_2$-SVM) to the more general case of $\ell_p$-norms with $p\ge 1$ ($\ell_p$-SVM). The resulting primal and dual problems are…
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…
We consider the empirical risk minimization problem for linear supervised learning, with regularization by structured sparsity-inducing norms. These are defined as sums of Euclidean norms on certain subsets of variables, extending the usual…
Support Vector Machines (SVM), a popular machine learning technique, has been applied to a wide range of domains such as science, finance, and social networks for supervised learning. Whether it is identifying high-risk patients by…
This chapter describes componentwise Least Squares Support Vector Machines (LS-SVMs) for the estimation of additive models consisting of a sum of nonlinear components. The primal-dual derivations characterizing LS-SVMs for the estimation of…
Data augmentation is one of the most popular techniques for improving the robustness of neural networks. In addition to directly training the model with original samples and augmented samples, a torrent of methods regularizing the distance…
Quadratic programming is a ubiquitous prototype in convex programming. Many machine learning problems can be formulated as quadratic programming, including the famous Support Vector Machines (SVMs). Linear and kernel SVMs have been among…
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…
Growing evidence indicates that only a sparse subset from a pool of sensory neurons is active for the encoding of visual stimuli at any instant in time. Traditionally, to replicate such biological sparsity, generative models have been using…
Advances in artificial intelligence (AI) and deep learning have raised concerns about its increasing energy consumption, while demand for deploying AI in mobile devices and machines at the edge is growing. Binary neural networks (BNNs) have…
Support vector machine (SVM) is a powerful classification method that has achieved great success in many fields. Since its performance can be seriously impaired by redundant covariates, model selection techniques are widely used for SVM…
Despite the success of the popular kernelized support vector machines, they have two major limitations: they are restricted to Positive Semi-Definite (PSD) kernels, and their training complexity scales at least quadratically with the size…
This paper addresses a quadratic problem with assignment constraints, an NP-hard combinatorial optimization problem arisen from facility location, multiple-input multiple-output detection, and maximum mean discrepancy calculation et al. The…
This paper develops a convex approach for sparse one-dimensional deconvolution that improves upon L1-norm regularization, the standard convex approach. We propose a sparsity-inducing non-separable non-convex bivariate penalty function for…