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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…

The support vector machine (SVM) is a supervised learning algorithm that finds a maximum-margin linear classifier, often after mapping the data to a high-dimensional feature space via the kernel trick. Recent work has demonstrated that in…

This paper studies the sparse identification problem of unknown sparse parameter vectors in stochastic dynamic systems. Firstly, a novel sparse identification algorithm is proposed, which can generate sparse estimates based on least squares…

Several decades ago, Support Vector Machines (SVMs) were introduced for performing binary classification tasks, under a supervised framework. Nowadays, they often outperform other supervised methods and remain one of the most popular…

Marginalising over families of Gaussian Process kernels produces flexible model classes with well-calibrated uncertainty estimates. Existing approaches require likelihood evaluations of many kernels, rendering them prohibitively expensive…

Sparsity inducing regularization is an important part for learning over-complete visual representations. Despite the popularity of $\ell_1$ regularization, in this paper, we investigate the usage of non-convex regularizations in this…

We present the framework of slowly varying regression under sparsity, allowing sparse regression models to exhibit slow and sparse variations. The problem of parameter estimation is formulated as a mixed-integer optimization problem. We…

We consider the problem of learning a high-dimensional graphical model in which certain hub nodes are highly-connected to many other nodes. Many authors have studied the use of an l1 penalty in order to learn a sparse graph in…

Support vector machines (SVMs) are successful modeling and prediction tools with a variety of applications. Previous work has demonstrated the superiority of the SVMs in dealing with the high dimensional, low sample size problems. However,…

Gaussian processes (GPs) stand as crucial tools in machine learning and signal processing, with their effectiveness hinging on kernel design and hyper-parameter optimization. This paper presents a novel GP linear multiple kernel (LMK) and a…

Machine learning and quantum computing are two technologies each with the potential for altering how computation is performed to address previously untenable problems. Kernel methods for machine learning are ubiquitous for pattern…

Kernel logistic regression (KLR) is a widely used supervised learning method for binary and multi-class classification, which provides estimates of the conditional probabilities of class membership for the data points. Unlike other kernel…

We establish a general form of explicit, input-dependent, measure-valued warpings for learning nonstationary kernels. While stationary kernels are ubiquitous and simple to use, they struggle to adapt to functions that vary in smoothness…

Kernel methods are applied to many problems in pattern recognition, including subspace clustering (SC). That way, nonlinear problems in the input data space become linear in mapped high-dimensional feature space. Thereby, computationally…

The Nystr\"om methods have been popular techniques for scalable kernel based learning. They approximate explicit, low-dimensional feature mappings for kernel functions from the pairwise comparisons with the training data. However, Nystr\"om…

Using a support vector machine requires to set two types of hyperparameters: the soft margin parameter C and the parameters of the kernel. To perform this model selection task, the method of choice is cross-validation. Its leave-one-out…

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…

Modern deep neural networks require a tremendous amount of data to train, often needing hundreds or thousands of labeled examples to learn an effective representation. For these networks to work with less data, more structure must be built…

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…

Machine learning and quantum computing are being progressively explored to shed light on possible computational approaches to deal with hitherto unsolvable problems. Classical methods for machine learning are ubiquitous in pattern…