相关论文: Wasserstein Gradient Flow over Variational Paramet…

Stochastic models with global parameters and latent variables are common, and for which variational inference (VI) is popular. However, existing methods are often either slow or inaccurate in high dimensions. We suggest a fast and accurate…

Variational inference (VI) seeks to approximate a target distribution $\pi$ by an element of a tractable family of distributions. Of key interest in statistics and machine learning is Gaussian VI, which approximates $\pi$ by minimizing the…

While stochastic variational inference is relatively well known for scaling inference in Bayesian probabilistic models, related methods also offer ways to circumnavigate the approximation of analytically intractable expectations. The key…

We refer to recent inference methodology and formulate a framework for solving the distributionally robust optimization problem, where the true probability measure is inside a Wasserstein ball around the empirical measure and the radius of…

Numerous infinite dimensional dynamical systems arising in different fields have been shown to exhibit a gradient flow structure in the Wasserstein space. We construct Two Point Flux Approximation Finite Volume schemes discretizing such…

Despite of its importance for safe machine learning, uncertainty quantification for neural networks is far from being solved. State-of-the-art approaches to estimate neural uncertainties are often hybrid, combining parametric models with…

In this article, we introduce a new approach towards the statistical learning problem $\operatorname{argmin}_{\rho(\theta) \in \mathcal P_{\theta}} W_{Q}^2 (\rho_{\star},\rho(\theta))$ to approximate a target quantum state $\rho_{\star}$ by…

We show that the continuous-time gradient descent in Rn can be viewed as an optimal controlled evolution for a suitable action functional; a similar result holds for stochastic gradient descent. We then provide an analogous characterization…

We present a novel approximate inference method for diffusion processes, based on the Wasserstein gradient flow formulation of the diffusion. In this formulation, the time-dependent density of the diffusion is derived as the limit of…

Wasserstein barycenters provide a geometrically meaningful way to aggregate probability distributions, built on the theory of optimal transport. They are difficult to compute in practice, however, leading previous work to restrict their…

This paper presents a Wasserstein attraction approach for solving dynamic mass transport problems over networks. In the transport problem over networks, we start with a distribution over the set of nodes that needs to be "transported" to a…

Gradient-based optimization is the foundation of deep learning and reinforcement learning. Even when the mechanism being optimized is unknown or not differentiable, optimization using high-variance or biased gradient estimates is still…

This manuscript introduces a regression-type formulation for approximating the Perron-Frobenius Operator by relying on distributional snapshots of data. These snapshots may represent densities of particles. The Wasserstein metric is…

Variational inference (VI) has emerged as a popular method for approximate inference for high-dimensional Bayesian models. In this paper, we propose a novel VI method that extends the naive mean field via entropic regularization, referred…

There is extensive literature on accelerating first-order optimization methods in a Euclidean setting. Under which conditions such acceleration is feasible in Riemannian optimization problems is an active area of research. Motivated by the…

We consider stochastic programs where the distribution of the uncertain parameters is only observable through a finite training dataset. Using the Wasserstein metric, we construct a ball in the space of (multivariate and non-discrete)…

Variational inference (VI) is a specific type of approximate Bayesian inference that approximates an intractable posterior distribution with a tractable one. VI casts the inference problem as an optimization problem, more specifically, the…

This article details a novel numerical scheme to approximate gradient flows for optimal transport (i.e. Wasserstein) metrics. These flows have proved useful to tackle theoretically and numerically non-linear diffusion equations that model…

Natural gradient methods have been used to optimise the parameters of probability distributions in a variety of settings, often resulting in fast-converging procedures. Unfortunately, for many distributions of interest, computing the…

The goal of this paper is to debunk and dispel the magic behind black-box optimizers and stochastic optimizers. It aims to build a solid foundation on how and why the techniques work. This manuscript crystallizes this knowledge by deriving…