Related papers: Learning a powerful SVM using piece-wise linear lo…
Quantum algorithms can enhance machine learning in different aspects. Here, we study quantum-enhanced least-square support vector machine (LS-SVM). Firstly, a novel quantum algorithm that uses continuous variable to assist matrix inversion…
Supervised machine learning approaches require the formulation of a loss functional to be minimized in the training phase. Sequential data are ubiquitous across many fields of research, and are often treated with Euclidean distance-based…
We distinguish two kinds of piecewise linear functions and provide an interesting representation for a piecewise linear function between two normed spaces. Based on such a representation, we study a fully piecewise linear vector…
Support Vector Machine (SVM) is an efficient classification approach, which finds a hyperplane to separate data from different classes. This hyperplane is determined by support vectors. In existing SVM formulations, the objective function…
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…
In this paper, we present new optimization models for Support Vector Machine (SVM), with the aim of separating data points in two or more classes. The classification task is handled by means of nonlinear classifiers induced by kernel…
This paper studies loss functions for finite sets. For a given finite set $S$, we give sum-of-square type loss functions of minimum degree. When $S$ is the vertex set of a standard simplex, we show such loss functions have no spurious…
The Support Vector Machine (SVM) is one of the most widely used classification methods. In this paper, we consider the soft-margin SVM used on data points with independent features, where the sample size $n$ and the feature dimension $p$…
We present a fast and memory efficient algorithm for the estimation of generalized linear models with an additive separable k-way error component. The brute force approach uses dummy variables to account for the unobserved heterogeneity,…
Over the past decades, numerous loss functions have been been proposed for a variety of supervised learning tasks, including regression, classification, ranking, and more generally structured prediction. Understanding the core principles…
This paper focuses on a semiparametric regression model in which the response variable is explained by the sum of two components. One of them is parametric (linear), the corresponding explanatory variable is measured with additive error and…
Value function learning plays a central role in many state-of-the-art reinforcement-learning algorithms. Many popular algorithms like Q-learning do not optimize any objective function, but are fixed-point iterations of some variant of…
Learning vector autoregressive models from multivariate time series is conventionally approached through least squares or maximum likelihood estimation. These methods typically assume a fully connected model which provides no direct insight…
It is shown that bootstrap approximations of support vector machines (SVMs) based on a general convex and smooth loss function and on a general kernel are consistent. This result is useful to approximate the unknown finite sample…
Variable selection, also known as feature selection in machine learning, plays an important role in modeling high dimensional data and is key to data-driven scientific discoveries. We consider here the problem of detecting influential…
This study combines two different learning paradigms, k-nearest neighbor (k-NN) rule, as memory-based learning paradigm and relevance vector machines (RVM), as statistical learning paradigm. This combination is performed in kernel space and…
Any applied mathematical model contains parameters. The paper proposes to use kernel learning for the parametric analysis of the model. The approach consists in setting a distribution on the parameter space, obtaining a finite training…
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 paper we consider learning in passive setting but with a slight modification. We assume that the target expected loss, also referred to as target risk, is provided in advance for learner as prior knowledge. Unlike most studies in…
The capacity of a learning machine is measured by its Vapnik-Chervonenkis dimension, and learning machines with a low VC dimension generalize better. It is well known that the VC dimension of SVMs can be very large or unbounded, even though…