Related papers: Kernel-Matrix Determinant Estimates from stopped C…
Last decade witnesses significant methodological and theoretical advances in estimating large precision matrices. In particular, there are scientific applications such as longitudinal data, meteorology and spectroscopy in which the ordering…
The paper proposes a method for constructing a sparse estimator for the inverse covariance (concentration) matrix in high-dimensional settings. The estimator uses a penalized normal likelihood approach and forces sparsity by using a…
This paper highlights a formal connection between two families of widely used matrix factorization algorithms in numerical linear algebra. One family consists of the Jacobi eigenvalue algorithm and its variants for computing the Hermitian…
Natural gradients can improve convergence in stochastic variational inference significantly but inverting the Fisher information matrix is daunting in high dimensions. Moreover, in Gaussian variational approximation, natural gradient…
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…
Kernelization algorithms, usually a preprocessing step before other more traditional algorithms, are very special in the sense that they return (reduced) instances, instead of final results. This characteristic excludes the freedom of…
Transforming a matrix over a field to echelon form, or decomposing the matrix as a product of structured matrices that reveal the rank profile, is a fundamental building block of computational exact linear algebra. This paper surveys the…
We provide more technical details about the HLIBCov package, which is using parallel hierarchical ($\H$-) matrices to identify unknown parameters of the covariance function (variance, smoothness, and covariance length). These parameters are…
In spatial statistics and machine learning, the kernel matrix plays a pivotal role in prediction, classification, and maximum likelihood estimation. A thorough examination reveals that for large sample sizes, the kernel matrix becomes…
We derive the limiting matrix kernels for the the Gaussian Orthogonal and Symplectic ensembles scaled at the edge, with proofs of convergence in the operator norms that assure convergence of the determinants.
Reduced modeling in high-dimensional reproducing kernel Hilbert spaces offers the opportunity to approximate efficiently non-linear dynamics. In this work, we devise an algorithm based on low rank constraint optimization and kernel-based…
Gaussian Process Regression (GPR) is widely used for inferring functions from noisy data. GPR crucially relies on the choice of a kernel, which might be specified in terms of a collection of hyperparameters that must be chosen or learned.…
Algorithms come with multiple variants which are obtained by changing the mathematical approach from which the algorithm is derived. These variants offer a wide spectrum of performance when implemented on a multicore platform and we seek to…
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.…
Given a set of points $P\subset \mathbb{R}^{d}$ and a kernel $k$, the Kernel Density Estimate at a point $x\in\mathbb{R}^{d}$ is defined as $\mathrm{KDE}_{P}(x)=\frac{1}{|P|}\sum_{y\in P} k(x,y)$. We study the problem of designing a data…
Tucker decomposition is the cornerstone of modern machine learning on tensorial data analysis, which have attracted considerable attention for multiway feature extraction, compressive sensing, and tensor completion. The most challenging…
In this paper, we describe a new algorithm to build a few sparse principal components from a given data matrix. Our approach does not explicitly create the covariance matrix of the data and can be viewed as an extension of the Kogbetliantz…
A well-recognized limitation of kernel learning is the requirement to handle a kernel matrix, whose size is quadratic in the number of training examples. Many methods have been proposed to reduce this computational cost, mostly by using a…
Generalized linear mixed models (GLMMs) are a widely used tool in statistical analysis. The main bottleneck of many computational approaches lies in the inversion of the high dimensional precision matrices associated with the random…
Gaussian processes (GPs) are widely used in non-parametric Bayesian modeling, and play an important role in various statistical and machine learning applications. In a variety tasks of uncertainty quantification, generating random sample…