Related papers: Path-Guided Particle-based Sampling

Stochastic gradient Markov chain Monte Carlo (SG-MCMC) has been increasingly popular in Bayesian learning due to its ability to deal with large data. A standard SG-MCMC algorithm simulates samples from a discretized-time Markov chain to…

Particle-based variational inference methods (ParVIs) have gained attention in the Bayesian inference literature, for their capacity to yield flexible and accurate approximations. We explore ParVIs from the perspective of Wasserstein…

Task learning in neural networks typically requires finding a globally optimal minimizer to a loss function objective. Conventional designs of swarm based optimization methods apply a fixed update rule, with possibly an adaptive step-size…

We consider the problem of sampling from a distribution governed by a potential function. This work proposes an explicit score based MCMC method that is deterministic, resulting in a deterministic evolution for particles rather than a…

Non-invasive flow measurement techniques, such as particle tracking velocimetry, resolve 3D velocity fields by pairing tracer particle positions in successive time steps. These trajectories are crucial for evaluating physical quantities…

Bayesian estimation strategies represent the most fundamental formulation of the state estimation problem available, and apply readily to nonlinear systems with non-Gaussian uncertainties. The present paper introduces a novel method for…

Stochastic gradient methods are dominant in nonconvex optimization especially for deep models but have low asymptotical convergence due to the fixed smoothness. To address this problem, we propose a simple yet effective method for improving…

Stein Variational Gradient Descent (SVGD) is a popular variational inference algorithm which simulates an interacting particle system to approximately sample from a target distribution, with impressive empirical performance across various…

This paper introduces Wasserstein variational inference, a new form of approximate Bayesian inference based on optimal transport theory. Wasserstein variational inference uses a new family of divergences that includes both f-divergences and…

Anomaly detection (AD) has been an active research area in various domains. Yet, the increasing data scale, complexity, and dimension turn the traditional methods into challenging. Recently, the deep generative model, such as the…

Laplacian-P-splines (LPS) associate the P-splines smoother and the Laplace approximation in a unifying framework for fast and flexible inference under the Bayesian paradigm. Gaussian Markov field priors imposed on penalized latent variables…

Score-based diffusion models currently constitute the state of the art in continuous generative modeling. These methods are typically formulated via overdamped or underdamped Ornstein--Uhlenbeck-type stochastic differential equations, in…

A new Wasserstein multi-element polynomial chaos expansion (WPCE) is proposed, which is inspired by recent advances in computational optimal transport for estimating Wasserstein distances. The developed method combines unsupervised learning…

There introduce Particle Optimized Gradient Descent (POGD), an algorithm based on the gradient descent but integrates the particle swarm optimization (PSO) principle to achieve the iteration. From the experiments, this algorithm has…

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…

In Bayesian inference, the posterior distributions are difficult to obtain analytically for complex models such as neural networks. Variational inference usually uses a parametric distribution for approximation, from which we can easily…

We propose a new unsupervised anomaly detection method based on the sliced-Wasserstein distance for training data selection in machine learning approaches. Our filtering technique is interesting for decision-making pipelines deploying…

We present a performant, general-purpose gradient-guided nested sampling algorithm, ${\tt GGNS}$, combining the state of the art in differentiable programming, Hamiltonian slice sampling, clustering, mode separation, dynamic nested…

High-dimensional state trajectories of state-space models pose challenges for Bayesian inference. Particle Gibbs (PG) methods have been widely used to sample from the posterior of a state space model. Basically, particle Gibbs is a Particle…

We propose a novel projection-based particle method for solving the McKean-Vlasov stochastic differential equations. Our approach is based on a projection-type estimation of the marginal density of the solution in each time step. The…