Related papers: On Hamiltonian Monte Carlo for Gaussian Random Var…

A method based on multicanonical Monte Carlo is applied to the calculation of large deviations in the largest eigenvalue of random matrices. The method is successfully tested with the Gaussian orthogonal ensemble (GOE), sparse random…

Gaussian multiplicative chaos (GMC) is a canonical random fractal measure obtained by exponentiating log-correlated Gaussian processes, first constructed in the seminal work of Kahane (1985). Since then it has served as an important…

Monte Carlo methods represent a cornerstone of computer science. They allow to sample high dimensional distribution functions in an efficient way. In this paper we consider the extension of Automatic Differentiation (AD) techniques to Monte…

Many Bayesian inference problems require exploring the posterior distribution of high-dimensional parameters that represent the discretization of an underlying function. This work introduces a family of Markov chain Monte Carlo (MCMC)…

We consider (self-adjoint) families of infinite matrices of noncommutative random variables such that the joint distribution of their entries is invariant under conjugation by a free quantum group. For the free orthogonal and…

The random numbers driving Markov chain Monte Carlo (MCMC) simulation are usually modeled as independent U(0,1) random variables. Tribble [Markov chain Monte Carlo algorithms using completely uniformly distributed driving sequences (2007)…

Based on a new coupling approach, we prove that the transition step of the Hamiltonian Monte Carlo algorithm is contractive w.r.t. a carefully designed Kantorovich (L1 Wasserstein) distance. The lower bound for the contraction rate is…

Identifying the active factors that have significant impacts on the output of the complex system is an important but challenging variable selection problem in computer experiments. In this paper, a Bayesian hierarchical Gaussian process…

In Hamiltonian Monte Carlo sampling, the shape of the potential and the choice of the momentum distribution jointly give rise to the Hamiltonian dynamics of the sampler. An efficient sampler propagates quickly in all regions of the…

While the Matrix Generalized Inverse Gaussian ($\mathcal{MGIG}$) distribution arises naturally in some settings as a distribution over symmetric positive semi-definite matrices, certain key properties of the distribution and effective ways…

In machine learning and statistics, probabilistic inference involving multimodal distributions is quite difficult. This is especially true in high dimensional problems, where most existing algorithms cannot easily move from one mode to…

We investigate the nodal count of eigenvectors of random matrices interpreted as operators on signed complete graphs. Our focus is on orthogonally invariant ensembles, with particular attention to the Gaussian Orthogonal Ensemble (GOE). We…

We investigate the inclusion of variable spins in electronic structure quantum Monte Carlo, with a focus on diffusion Monte Carlo with Hamiltonians that include spin-orbit interactions. Following our previous introduction of fixed-phase…

In this article we propose a novel MCMC method based on deterministic transformations T: X x D --> X where X is the state-space and D is some set which may or may not be a subset of X. We refer to our new methodology as Transformation-based…

Along with the recent advances in scalable Markov Chain Monte Carlo methods, sampling techniques that are based on Langevin diffusions have started receiving increasing attention. These so called Langevin Monte Carlo (LMC) methods are based…

Classical hardness-of-sampling results are largely established for random quantum circuits, whereas analog simulators natively realize time evolutions under geometrically local Hamiltonians. Does a typical such Hamiltonian already yield…

We propose a variant of Hamiltonian Monte Carlo (HMC), called the Repelling-Attracting Hamiltonian Monte Carlo (RAHMC), for sampling from multimodal distributions. The key idea that underpins RAHMC is a departure from the conservative…

The paper proposes a Riemannian Manifold Hamiltonian Monte Carlo sampler to resolve the shortcomings of existing Monte Carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations. The…

We provide a framework which admits a number of ``marginal'' sequential Monte Carlo (SMC) algorithms as particular cases -- including the marginal particle filter [Klaas et al., 2005, in: Proceedings of Uncertainty in Artificial…

Markov Chain Monte Carlo inference of target posterior distributions in machine learning is predominately conducted via Hamiltonian Monte Carlo and its variants. This is due to Hamiltonian Monte Carlo based samplers ability to suppress…