Related papers: Gauss quadrature for matrix inverse forms with app…

The condition-based complexity analysis framework is one of the gems of modern numerical algebraic geometry and theoretical computer science. Among the challenges that it poses is to expand the currently limited range of random polynomials…

We consider the solution of linear systems with tensor product structure using a GMRES algorithm. In order to cope with the computational complexity in large dimension both in terms of floating point operations and memory requirement, our…

This paper introduces an efficient algorithm for computing the general oscillatory matrix functions. These computations are crucial for solving second-order semi-linear initial value problems. The method is exploited using the scaling and…

We introduce a scalable Gaussian process (GP) framework with deep product kernels for data-driven learning of parametrized spatio-temporal fields over fixed or parameter-dependent domains. The proposed framework learns a continuous…

In this paper, we consider high-dimensional Gaussian graphical models where the true underlying graph is decomposable. A hierarchical $G$-Wishart prior is proposed to conduct a Bayesian inference for the precision matrix and its graph…

Matrix completion models are among the most common formulations of recommender systems. Recent works have showed a boost of performance of these techniques when introducing the pairwise relationships between users/items in the form of…

A fast forward feature selection algorithm is presented in this paper. It is based on a Gaussian mixture model (GMM) classifier. GMM are used for classifying hyperspectral images. The algorithm selects iteratively spectral features that…

The techniques for polynomial interpolation and Gaussian quadrature are generalized to matrix-valued functions. It is shown how the zeros and rootvectors of matrix orthonormal polynomials can be used to get a quadrature formula with the…

This paper introduces a computationally efficient algorithm in system theory for solving inverse problems governed by linear partial differential equations (PDEs). We model solutions of linear PDEs using Gaussian processes with priors…

We propose a sparse algebra for samplet compressed kernel matrices, to enable efficient scattered data analysis. We show the compression of kernel matrices by means of samplets produces optimally sparse matrices in a certain S-format. It…

We propose a generic algorithmic building block to accelerate training of machine learning models on heterogeneous compute systems. Our scheme allows to efficiently employ compute accelerators such as GPUs and FPGAs for the training of…

Highly oscillatory integrals of composite type arise in electronic engineering and their calculations is a challenging problem. In this paper, we propose two Gaussian quadrature rules for computing such integrals. The first one is…

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…

Nonlinear inverse problems have complicated landscapes. Hence the calculation with naive iterative schemes (e.g., Gauss-Newton or conjugate gradients) is trapped in local minima. The (first) Born approximation can avoid this trapping but…

The effectiveness of dimensionality reduction with quadratic manifolds hinges on the choice of a reduced basis and the associated quadratic correction terms. Existing approaches typically rely on subspaces spanned by the leading principal…

In the scope of "AI for Science", solving inverse problems is a longstanding challenge in materials and drug discovery, where the goal is to determine the hidden structures given a set of desirable properties. Deep generative models are…

The Grover search algorithm performs an unstructured search of a marked item in a database quadratically faster than classical algorithms and is shown to be optimal. Here, we show that if the search space is divided into two blocks with the…

Integral equation methods for the solution of partial differential equations, when coupled with suitable fast algorithms, yield geometrically flexible, asymptotically optimal and well-conditioned schemes in either interior or exterior…

Probabilistic machine learning models are distinguished by their ability to integrate prior knowledge of noise statistics, smoothness parameters, and training data uncertainty. A common approach involves modeling data with Gaussian…

Mixture models with Gamma and or inverse-Gamma distributed mixture components are useful for medical image tissue segmentation or as post-hoc models for regression coefficients obtained from linear regression within a Generalised Linear…