Related papers: Supporting GENP with Random Multipliers

Inferring parameters and testing hypotheses from gravitational wave signals is a computationally intensive task central to modern astrophysics. Nested sampling, a Bayesian inference technique, has become an established standard for this in…

In this article, we discuss two specific classes of models - Gaussian Mixture Copula models and Mixture of Factor Analyzers - and the advantages of doing inference with gradient descent using automatic differentiation. Gaussian mixture…

Many developments in Mathematics involve the computation of higher order derivatives of Gaussian density functions. The analysis of univariate Gaussian random variables is a well-established field whereas the analysis of their multivariate…

Gaussian Process State Space Models (GP-SSMs) are a non-parametric model class suitable to represent nonlinear dynamics. They become increasingly popular in data-driven modeling approaches, i.e. when no first-order physics-based models are…

Bayesian inference of nanohertz gravitational-wave background models in pulsar timing array analyses often relies on Gaussian-process interpolators to avoid repeated, computationally expensive strain-spectrum calculations. However,…

This work represents a natural coalescence of two important lines of work: learning mixtures of Gaussians and algorithmic robust statistics. In particular we give the first provably robust algorithm for learning mixtures of any constant…

The residual cutting (RC) method has been proposed as an outer-inner loop iteration for efficiently solving large and sparse linear systems of equations arising in solving numerically problems of elliptic partial differential equations.…

We study multiply robust (MR) estimators of the longitudinal g-computation formula of Robins (1986). In the first part of this paper we review and extend the recently proposed parametric multiply robust estimators of Tchetgen-Tchetgen…

A machine-learnable variational scheme using Gaussian radial basis functions (GRBFs) is presented and used to approximate linear problems on bounded and unbounded domains. In contrast to standard mesh-free methods, which use GRBFs to…

We study the Nonparametric Maximum Likelihood Estimator (NPMLE) for estimating Gaussian location mixture densities in $d$-dimensions from independent observations. Unlike usual likelihood-based methods for fitting mixtures, NPMLEs are based…

Gaussian Boson Sampling (GBS) is a promising candidate for demonstrating quantum computational advantage and can be applied to solving graph-related problems. In this work, we propose Markov chain Monte Carlo-based algorithms to sample from…

We study a family of (multivariate-)Gaussian Hamiltonian Monte Carlo (GHMC) operators and prove that the family of Gaussian distributions and their mixtures are invariant under such operators. Furthermore, each such operator is a…

A symmetric random variable is called a Gaussian mixture if it has the same distribution as the product of two independent random variables, one being positive and the other a standard Gaussian random variable. Examples of Gaussian mixtures…

In this paper we introduce and analyse Langevin samplers that consist of perturbations of the standard underdamped Langevin dynamics. The perturbed dynamics is such that its invariant measure is the same as that of the unperturbed dynamics.…

Let $k$ be a field. Then Gaussian elimination over $k$ and the Euclidean division algorithm for the univariate polynomial ring $k[x]$ allow us to write any matrix in $SL_n(k)$ or $SL_n(k[x])$, $n\geq 2$, as a product of elementary matrices.…

In this paper, we focus on the analysis of the regularized Wasserstein barycenter problem. We provide uniqueness and a characterization of the barycenter for two important classes of probability measures: (i) Gaussian distributions and (ii)…

The asymptotic analysis of covariance parameter estimation of Gaussian processes has been subject to intensive investigation. However, this asymptotic analysis is very scarce for non-Gaussian processes. In this paper, we study a class of…

Nonparametric Bayesian approaches based on Gaussian processes have recently become popular in the empirical learning community. They encompass many classical methods of statistics, like Radial Basis Functions or various splines, and are…

Let $\orig{A}$ be any matrix and let $A$ be a slight random perturbation of $\orig{A}$. We prove that it is unlikely that $A$ has large condition number. Using this result, we prove it is unlikely that $A$ has large growth factor under…

Bayesian quantum estimation provides a robust framework for quantum technologies, especially in scenarios with limited data and minimal prior information. Yet, its application to continuous-variable Gaussian systems has remained limited and…