Related papers: Stein transport for Bayesian inference

Existing methods to summarize posterior inference for mixture models focus on identifying a point estimate of the implied random partition for clustering, with density estimation as a secondary goal (Wade and Ghahramani, 2018; Dahl et al.,…

An important task in computational statistics and machine learning is to approximate a posterior distribution $p(x)$ with an empirical measure supported on a set of representative points $\{x_i\}_{i=1}^n$. This paper focuses on methods…

Particle-optimization-based sampling (POS) is a recently developed effective sampling technique that interactively updates a set of particles. A representative algorithm is the Stein variational gradient descent (SVGD). We prove, under…

We study the contraction in Wasserstein distance of the coordinate ascent variational inference algorithm. This is shown to hold under a transport-information inequality at the fixed points and a functional smoothness condition. The results…

Gaussian Process Motion Planning (GPMP) is a widely used framework for generating smooth trajectories within a limited compute time--an essential requirement in many robotic applications. However, traditional GPMP approaches often struggle…

We study the estimation problem of distribution-on-distribution regression, where both predictors and responses are probability measures. Existing approaches typically rely on a global optimal transport map or tangent-space linearization,…

In this paper we bring together some of the key ideas and methods of two disparate fields of mathematical research, frame theory and optimal transport, using the methods of the second to answer questions posed in the first. In particular,…

This article deals with the conjugate gradient method on a Riemannian manifold with interest in global convergence analysis. The existing conjugate gradient algorithms on a manifold endowed with a vector transport need the assumption that…

Sliced optimal transport reduces optimal transport on multi-dimensional domains to transport on the line. More precisely, sliced optimal transport is the concatenation of the well-known Radon transform and the cumulative density transform,…

Optimal transport distances are powerful tools to compare probability distributions and have found many applications in machine learning. Yet their algorithmic complexity prevents their direct use on large scale datasets. To overcome this…

This paper introduces a method for Model Predictive Path Integral (MPPI) control that optimizes sample generation towards an optimal trajectory through Stein Variational Gradient Descent (SVGD). MPPI relies upon predictive rollout of…

We develop a general approach to Stein's method for approximating a random process in the path space $D([0,T]\to R^d)$ by a real continuous Gaussian process. We then use the approach in the context of processes that have a representation as…

Distributed Stein Variational Gradient Descent (DSVGD) is a non-parametric distributed learning framework for federated Bayesian learning, where multiple clients jointly train a machine learning model by communicating a number of non-random…

In variational inference (VI), the practitioner approximates a high-dimensional distribution $\pi$ with a simple surrogate one, often a (product) Gaussian distribution. However, in many cases of practical interest, Gaussian distributions…

There has been recently a lot of interest in the analysis of the Stein gradient descent method, a deterministic sampling algorithm. It is based on a particle system moving along the gradient flow of the Kullback-Leibler divergence towards…

Sediment transport is studied as a function of the grain to fluid density ratio using two phase numerical sim- ulations based on a discrete element method (DEM) for particles coupled to a continuum Reynolds averaged description of…

We define a novel class of distances between statistical multivariate distributions by modeling an optimal transport problem on their marginals with respect to a ground distance defined on their conditionals. These new distances are metrics…

This paper presents a new gradient flow dissipation geometry over non-negative and probability measures. This is motivated by a principled construction that combines the unbalanced optimal transport and interaction forces modeled by…

A multivariate distribution can be described by a triangular transport map from the target distribution to a simple reference distribution. We propose Bayesian nonparametric inference on the transport map by modeling its components using…

We study the Stochastic Gradient Descent (SGD) method in nonconvex optimization problems from the point of view of approximating diffusion processes. We prove rigorously that the diffusion process can approximate the SGD algorithm weakly…