Related papers: Walk on spheres and Array-RQMC
Markov chain Monte Carlo (MCMC) simulations are modeled as driven by true random numbers. We consider variance bounding Markov chains driven by a deterministic sequence of numbers. The star-discrepancy provides a measure of efficiency of…
For training an encoder network to perform amortized variational inference, the Kullback-Leibler (KL) divergence from the exact posterior to its approximation, known as the inclusive or forward KL, is an increasingly popular choice of…
Statistical machine learning models should be evaluated and validated before putting to work. Conventional k-fold Monte Carlo Cross-Validation (MCCV) procedure uses a pseudo-random sequence to partition instances into k subsets, which…
Markov chain Monte Carlo methods such as Gibbs sampling and simple forms of the Metropolis algorithm typically move about the distribution being sampled via a random walk. For the complex, high-dimensional distributions commonly encountered…
In this paper we study the asymptotic behavior of the Random-Walk Metropolis algorithm on probability densities with two different `scales', where most of the probability mass is distributed along certain key directions with the…
Ollivier-Ricci curvature (ORC), defined via the Wasserstein distance that captures rich geometric information, has received growing attention in both theory and applications. However, the high computational cost of Wasserstein distance…
We introduce a method that uses the Cauchy-Crofton formula and a new curvature formula from integral geometry to reweight the sampling probabilities of Metropolis-within-Gibbs algorithms in order to increase their convergence speed. We…
In this article we review some of recent results on higher order quasi-Monte Carlo (HoQMC) methods. After a seminal work by Dick (2007, 2008) who originally introduced the concept of HoQMC, there have been significant theoretical progresses…
The Iterative Quasi-Monte Carlo (iQMC) method is a recently developed hybrid method for neutron transport simulations. iQMC replaces standard quadrature techniques used in deterministic linear solvers with Quasi-Monte Carlo simulation for…
The Diffusion Monte Carlo method is devoted to the computation of electronic ground-state energies of molecules. In this paper, we focus on implementations of this method which consist in exploring the configuration space with a {\bf fixed}…
Monte Carlo simulations are a powerful tool to investigate the thermodynamic properties of atomic systems. In practice however, sampling of the complete configuration space is often hindered by high energy barriers between different regions…
We consider the problem of estimating the density of a random variable $X$ that can be sampled exactly by Monte Carlo (MC). We investigate the effectiveness of replacing MC by randomized quasi Monte Carlo (RQMC) or by stratified sampling…
The famous Watts-Strogatz (WS) small-world network model does not approach the Erd\H{o}s-R\'enyi (ER) random graph model in the limit of total randomization which can lead to confusion and complicates certain analyses. In this paper we…
This paper proposes a new RWO-Sampling (Random Walk Over-Sampling) based on graphs for imbalanced datasets. In this method, two schemes based on under-sampling and over-sampling methods are introduced to keep the proximity information…
We show that for a uniformly irreducible random walk on a graph, with bounded range, there is a Floyd function for which the random walk converges to its corresponding Floyd boundary. Moreover if we add the assumptions, $p^{(n)}(v,w)\leq C…
The Random Walk Metropolis (RWM) algorithm is a Metropolis- Hastings MCMC algorithm designed to sample from a given target distribution \pi with Lebesgue density on R^N. RWM constructs a Markov chain by randomly proposing a new position…
The Metropolis Hastings algorithm and its multi-proposal extensions are aimed at the computation of the expectation $<\pi,f>$ of a function $f$ under a probability measure $\pi$ difficult to simulate. They consist in constructing by an…
In this paper, we consider the problem of online asymptotic variance estimation for particle filtering and smoothing. Current solutions for the particle filter rely on the particle genealogy and are either unstable or hard to tune in…
The Frank-Wolfe algorithm has seen a resurgence in popularity due to its ability to efficiently solve constrained optimization problems in machine learning and high-dimensional statistics. As such, there is much interest in establishing…
Conditional value at risk (CVaR) is a popular measure for quantifying portfolio risk. Sensitivity analysis of CVaR is very useful in risk management and gradient-based optimization algorithms. In this paper, we study the infinitesimal…