Related papers: Conjugate Gradients for Kernel Machines
Most machine learning methods require tuning of hyper-parameters. For kernel ridge regression with the Gaussian kernel, the hyper-parameter is the bandwidth. The bandwidth specifies the length scale of the kernel and has to be carefully…
The aim of this paper is to develop novel quantum algorithms for Gaussian process quadrature methods. Gaussian process quadratures are numerical integration methods where Gaussian processes are used as functional priors for the integrands…
This paper shows that gradient boosting based on symmetric decision trees can be equivalently reformulated as a kernel method that converges to the solution of a certain Kernel Ridge Regression problem. Thus, we obtain the convergence to a…
This article derives an accurate, explicit, and numerically stable approximation to the kernel quadrature weights in one dimension and on tensor product grids when the kernel and integration measure are Gaussian. The approximation is based…
Gaussian process regression generally does not scale to beyond a few thousands data points without applying some sort of kernel approximation method. Most approximations focus on the high eigenvalue part of the spectrum of the kernel…
The robustness of the kernel recursive least square (KRLS) algorithm has recently been improved by combining them with more robust information-theoretic learning criteria, such as minimum error entropy (MEE) and generalized MEE (GMEE),…
We consider a Gaussian process formulation of the multiple kernel learning problem. The goal is to select the convex combination of kernel matrices that best explains the data and by doing so improve the generalisation on unseen data.…
Gaussian process regression (GPR) or kernel ridge regression is a widely used and powerful tool for nonlinear prediction. Therefore, active learning (AL) for GPR, which actively collects data labels to achieve an accurate prediction with…
Random Feature (RF) models are used as efficient parametric approximations of kernel methods. We investigate, by means of random matrix theory, the connection between Gaussian RF models and Kernel Ridge Regression (KRR). For a Gaussian RF…
In the multivariate regression, also referred to as multi-task learning in machine learning, the goal is to recover a vector-valued function based on noisy observations. The vector-valued function is often assumed to be of low rank.…
A stochastic conjugate gradient method for approximation of a function is proposed. The proposed method avoids computing and storing the covariance matrix in the normal equations for the least squares solution. In addition, the method…
Gaussian process regression is a widely-applied method for function approximation and uncertainty quantification. The technique has gained popularity recently in the machine learning community due to its robustness and interpretability. The…
Kernel ridge regression is used to approximate the kinetic energy of non-interacting fermions in a one-dimensional box as a functional of their density. The properties of different kernels and methods of cross-validation are explored, and…
Gaussian processes are powerful models for probabilistic machine learning, but are limited in application by their $O(N^3)$ inference complexity. We propose a method for deriving parametric families of kernel functions with compact spatial…
We present a theoretically grounded Gaussian process framework that leverages neural feature maps to construct expressive kernels. We show that the learned feature map can be interpreted as an optimal low-rank approximation to a Gram matrix…
Graph models are relevant in many fields, such as distributed computing, intelligent tutoring systems or social network analysis. In many cases, such models need to take changes in the graph structure into account, i.e. a varying number of…
Stochastic gradient descent (SGD) and its variants have established themselves as the go-to algorithms for large-scale machine learning problems with independent samples due to their generalization performance and intrinsic computational…
Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires $O(n^3)$ logic gates. We show that the quantum linear systems algorithm [Harrow et…
Low-rank tensor regression, a new model class that learns high-order correlation from data, has recently received considerable attention. At the same time, Gaussian processes (GP) are well-studied machine learning models for structure…
We present a novel approach to learn a kernel-based regression function. It is based on the useof conical combinations of data-based parameterized kernels and on a new stochastic convex optimization procedure of which we establish…