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Deep learning has enjoyed tremendous success in a variety of applications but its application to quantile regressions remains scarce. A major advantage of the deep learning approach is its flexibility to model complex data in a more…
Regularized kernel methods such as, e.g., support vector machines and least-squares support vector regression constitute an important class of standard learning algorithms in machine learning. Theoretical investigations concerning…
Research in modern data-driven dynamical systems is typically focused on the three key challenges of high dimensionality, unknown dynamics, and nonlinearity. The dynamic mode decomposition (DMD) has emerged as a cornerstone for modeling…
Most metric learning algorithms, as well as Fisher's Discriminant Analysis (FDA), optimize some cost function of different measures of within-and between-class distances. On the other hand, Support Vector Machines(SVMs) and several Multiple…
Sparse learning is ubiquitous in many machine learning tasks. It aims to regularize the goodness-of-fit objective by adding a penalty term to encode structural constraints on the model parameters. In this paper, we develop a flexible sparse…
This article is an overview of supervised machine learning problems for regression and classification. Topics include: kernel methods, training by stochastic gradient descent, deep learning architecture, losses for classification,…
Many standard estimators, when applied to adaptively collected data, fail to be asymptotically normal, thereby complicating the construction of confidence intervals. We address this challenge in a semi-parametric context: estimating the…
Support vector machine (SVM) is a particularly powerful and flexible supervised learning model that analyzes data for both classification and regression, whose usual algorithm complexity scales polynomially with the dimension of data space…
Although various distributed machine learning schemes have been proposed recently for pure linear models and fully nonparametric models, little attention has been paid on distributed optimization for semi-paramemetric models with…
We propose a method for support vector machine classification using indefinite kernels. Instead of directly minimizing or stabilizing a nonconvex loss function, our algorithm simultaneously computes support vectors and a proxy kernel matrix…
Penalized regression methods, most notably the lasso, are a popular approach to analyzing high-dimensional data. An attractive property of the lasso is that it naturally performs variable selection. An important area of concern, however, is…
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…
We introduce a semi-supervised learning estimator which tends to the first kernel principal component as the number of labelled points vanishes. Our approach is based on the notion of optimal target vector, which is defined as follows.…
Spectral methods have greatly advanced the estimation of latent variable models, generating a sequence of novel and efficient algorithms with strong theoretical guarantees. However, current spectral algorithms are largely restricted to…
In this paper, we investigate a semiparametric regression model under the context of treatment effects via a localized neural network (LNN) approach. Due to a vast number of parameters involved, we reduce the number of effective parameters…
We investigate structured sparsity methods for variable selection in regression problems where the target depends nonlinearly on the inputs. We focus on general nonlinear functions not limiting a priori the function space to additive…
The support vector machine (SVM) is a popular machine learning classification method which produces a nonlinear decision boundary in a feature space by constructing linear boundaries in a transformed Hilbert space. It is well known that…
We analyze the computational complexity of Quantum Sparse Support Vector Machine, a linear classifier that minimizes the hinge loss and the $L_1$ norm of the feature weights vector and relies on a quantum linear programming solver instead…
In high-dimensional model selection problems, penalized simple least-square approaches have been extensively used. This paper addresses the question of both robustness and efficiency of penalized model selection methods, and proposes a…
Kernel-free quadratic surface support vector machines (QSVM) have recently gained traction due to their flexibility in modeling nonlinear decision boundaries without relying on kernel functions. However, the introduction of a full quadratic…