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Gaussian Processes (GP) have become popular machine-learning methods for kernel-based learning on datasets with complicated covariance structures. In this paper, we present a novel extension to the GP framework using a contaminated normal…

We develop a fast and scalable numerical approach to solve Wasserstein gradient flows (WGFs), particularly suitable for high-dimensional cases. Our approach is to use general reduced-order models, like deep neural networks, to parameterize…

Spatial statistics often rely on Gaussian processes (GPs) to capture dependencies across locations. However, their computational cost increases rapidly with the number of locations, potentially needing multiple hours even for moderate…

Gradient flow in the 2-Wasserstein space is widely used to optimize functionals over probability distributions and is typically implemented using an interacting particle system with $n$ particles. Analyzing these algorithms requires showing…

Recent years have witnessed growing interest in semi-implicit variational inference (SIVI) methods due to their ability to rapidly generate samples from complex distributions. However, since the likelihood of these samples is non-trivial to…

Inferring dynamical models from data continues to be a significant challenge in computational biology, especially given the stochastic nature of many biological processes. We explore a common scenario in omics, where statistically…

A new gradient-based particle sampling method, MPM-ParVI, based on material point method (MPM), is proposed for variational inference. MPM-ParVI simulates the deformation of a deformable body (e.g. a solid or fluid) under external effects…

Deep Gaussian processes (DGPs) provide a robust paradigm for Bayesian deep learning. In DGPs, a set of sparse integration locations called inducing points are selected to approximate the posterior distribution of the model. This is done to…

Recently developed particle flow algorithms provide an alternative to importance sampling for drawing particles from a posterior distribution, and a number of particle filters based on this principle have been proposed. Samples are drawn…

Score Distillation Sampling (SDS) and its variants have been widely used for text-to-3D generation by distilling 2D image diffusion priors. However, the standard SDS objective is prone to severe mode collapse, frequently yielding…

Probabilistic state estimation is essential for robots navigating uncertain environments. Accurately and efficiently managing uncertainty in estimated states is key to robust robotic operation. However, nonlinearities in robotic platforms…

Gaussian processes are powerful models for probabilistic machine learning, but are limited in application by their $O(N^3)$ inference complexity. We propose a method for deriving parametric families of kernel functions with compact spatial…

Stein Variational Gradient Descent (SVGD) is a nonparametric particle-based deterministic sampling algorithm. Despite its wide usage, understanding the theoretical properties of SVGD has remained a challenging problem. For sampling from a…

We introduce a scalable approach to Gaussian process inference that combines spatio-temporal filtering with natural gradient variational inference, resulting in a non-conjugate GP method for multivariate data that scales linearly with…

This paper is concerned with the approximation of probability distributions known up to normalization constants, with a focus on Bayesian inference for large-scale inverse problems in scientific computing. In this context, key challenges…

This paper provides a formulation of the log-homotopy particle flow from the perspective of variational inference. We show that the transient density used to derive the particle flow follows a time-scaled trajectory of the Fisher-Rao…

We reconstruct the velocity field of incompressible flows given a finite set of measurements. For the spatial approximation, we introduce the Sparse Fourier divergence-free (SFdf) approximation based on a discrete $L^2$ projection. Within…

There has been recent interest in developing scalable Bayesian sampling methods such as stochastic gradient MCMC (SG-MCMC) and Stein variational gradient descent (SVGD) for big-data analysis. A standard SG-MCMC algorithm simulates samples…

Full waveform inversion (FWI) enables us to obtain high-resolution velocity models of the subsurface. However, estimating the associated uncertainties in the process is not trivial. Commonly, uncertainty estimation is performed within the…

By building upon the recent theory that established the connection between implicit generative modeling (IGM) and optimal transport, in this study, we propose a novel parameter-free algorithm for learning the underlying distributions of…