Related papers: Fast high-dimensional node generation with variabl…

In this paper, we analyse a method for approximating the distribution function and density of a random variable that depends in a non-trivial way on a possibly high number of independent random variables, each with support on the whole real…

We present a fast method for generating random samples according to a variable density Poisson-disc distribution. A minimum threshold distance is used to create a background grid array for keeping track of those points that might affect any…

One of the most demanding calculations is to generate random samples from a specified probability distribution (usually with an unknown normalizing prefactor) in a high-dimensional configuration space. One often has to resort to using a…

Meshless methods approximate operators in a specific node as a weighted sum of values in its neighbours. Higher order approximations of derivatives provide more accurate solutions with better convergence characteristics, but they come at…

In this paper we propose a new deterministic approximation method, called discretization approximation, for Bayesian computation. Discretization approximation is very simple to understand and to implement, It only requires calculating…

We propose a hierarchical tensor-network approach for approximating high-dimensional probability density via empirical distribution. This leverages randomized singular value decomposition (SVD) techniques and involves solving linear…

In this work, we investigate stochastic quasi-Newton methods for minimizing a finite sum of cost functions over a decentralized network. In Part I, we develop a general algorithmic framework that incorporates stochastic quasi-Newton…

We present a class of diffusion-based algorithms to draw samples from high-dimensional probability distributions given their unnormalized densities. Ideally, our methods can transport samples from a Gaussian distribution to a specified…

We propose a Markov chain Monte Carlo (MCMC) algorithm based on third-order Langevin dynamics for sampling from distributions with log-concave and smooth densities. The higher-order dynamics allow for more flexible discretization schemes,…

Hamiltonian Monte Carlo is a prominent Markov Chain Monte Carlo algorithm, which employs symplectic integrators to sample from high dimensional target distributions in many applications, such as statistical mechanics, Bayesian statistics…

We propose a method for efficiently coupling the finite element method with atomistic simulations, while using molecular dynamics or kinetic Monte Carlo techniques. Our method can dynamically build an optimized unstructured mesh that…

Standard Markov chain Monte Carlo methods struggle to explore distributions that are concentrated in the neighbourhood of low-dimensional structures. These pathologies naturally occur in a number of situations. For example, they are common…

Pseudo-marginal Metropolis-Hastings (pmMH) is a versatile algorithm for sampling from target distributions which are not easy to evaluate point-wise. However, pmMH requires good proposal distributions to sample efficiently from the target,…

Diffusion models have shown remarkable empirical success in sampling from rich multi-modal distributions. Their inference relies on numerically solving a certain differential equation. This differential equation cannot be solved in closed…

Estimating copulas with discrete marginal distributions is challenging, especially in high dimensions, because computing the likelihood contribution of each observation requires evaluating $2^{J}$ terms, with $J$ the number of discrete…

Statistical inference from high-dimensional data with low-dimensional structures has recently attracted lots of attention. In machine learning, deep generative modeling approaches implicitly estimate distributions of complex objects by…

We give a simple, local process for nodes in an undirected graph to form non-adjacent clusters that (1) have at most a polylogarithmic diameter and (2) contain at least half of all vertices. Efficient deterministic distributed clustering…

We propose a simple, projection-based algorithm for clustering mixtures of discrete (Bernoulli) distributions. Unlike previous approaches that rely on coordinate-specific ``combinatorial projections,'' our algorithm is rotationally…

Divide-and-conquer MCMC is a strategy for parallelising Markov Chain Monte Carlo sampling by running independent samplers on disjoint subsets of a dataset and merging their output. An ongoing challenge in the literature is to efficiently…

In this work, we propose a distributed algorithm for stochastic non-convex optimization. We consider a worker-server architecture where a set of $K$ worker nodes (WNs) in collaboration with a server node (SN) jointly aim to minimize a…