Related papers: Efficient parallel algorithm for estimating higher…
Maximum likelihood estimation is an important statistical technique for estimating missing data, for example in climate and environmental applications, which are usually large and feature data points that are irregularly spaced. In…
Diagrammatic expansions are a paradigmatic and powerful tool of quantum many-body theory. Their evaluation to high order, e.g., by the Diagrammatic Monte Carlo technique, can provide unbiased results in strongly correlated and challenging…
The works presented in this habilitation concern the algorithmics of polynomials. This is a central topic in computer algebra, with numerous applications both within and outside the field - cryptography, error-correcting codes, etc. For…
We implement a sample-efficient method for rapid and accurate emulation of semi-analytical galaxy formation models over a wide range of model outputs. We use ensembled deep learning algorithms to produce a fast emulator of an updated…
We present a numerically cheap approximation to super-sample covariance (SSC) of large scale structure cosmological probes, first in the case of angular power spectra. It necessitates no new elements besides those used for the prediction of…
We present estimates of the N-point galaxy, area-averaged, angular correlation functions $\bar{\omega}_{N}$($\theta$) for $N$ = 2,...,7 for galaxies from the fifth data release of the Sloan Digital Sky Survey. Our parent sample is selected…
A fast algorithm (linear in the degrees of freedom) for the solution of linear variable-coefficient rational-order fractional integral and differential equations is described. The approach is related to the ultraspherical method for…
Modeling the large-scale structure of the universe on nonlinear scales has the potential to substantially increase the science return of upcoming surveys by increasing the number of modes available for model comparisons. One way to achieve…
In this work we investigate the multivariate statistical description of the matter distribution in the nonlinear regime. We introduce the multivariate Edgeworth expansion of the lognormal distribution to model the cosmological matter field.…
Computationally efficient numerical methods for high-order approximations of convolution integrals involving weakly singular kernels find many practical applications including those in the development of fast quadrature methods for…
Sequential Monte Carlo samplers represent a compelling approach to posterior inference in Bayesian models, due to being parallelisable and providing an unbiased estimate of the posterior normalising constant. In this work, we significantly…
Pulsar Timing Array (PTA) searches for nHz gravitational-wave backgrounds (GWBs) typically model time-correlated noise by assuming a diagonal covariance in Fourier space, neglecting inter-frequency correlations introduced by the finite…
We consider the problem of clustering data points in high dimensions, i.e. when the number of data points may be much smaller than the number of dimensions. Specifically, we consider a Gaussian mixture model (GMM) with non-spherical…
Efficient sampling of many-dimensional and multimodal density functions is a task of great interest in many research fields. We describe an algorithm that allows parallelizing inherently serial Markov chain Monte Carlo (MCMC) sampling by…
Solving inverse problems and achieving statistical rigour in landscape evolution models requires running many model realizations. Parallel computation is necessary to achieve this in a reasonable time. However, no previous algorithm is…
We consider the problem of parameter estimation in a high-dimensional generalized linear model. Spectral methods obtained via the principal eigenvector of a suitable data-dependent matrix provide a simple yet surprisingly effective…
The graph Fourier transform (GFT) is in general dense and requires O(n^2) time to compute and O(n^2) memory space to store. In this paper, we pursue our previous work on the approximate fast graph Fourier transform (FGFT). The FGFT is…
We present a new efficient method for computing the non-linearity parameters of the higher order correlation functions of local type curvature perturbations in inflation models having a $\cal N$-component scalar field, focusing on the…
Finding effective ways to exploit parallel computing to accelerate Markov chain Monte Carlo methods is an important problem in Bayesian computation and related disciplines. In this paper, we consider the zeroth-order setting where the…
This paper presents an efficient parallel direct algorithm with near-optimal complexity for the compact fourth and sixth-order approximation of the three-dimensional Helmholtz equations [1] with the problem coefficient depending on only one…