6 papers
Regularity-informed data assimilation: A hierarchical Bayesian approach to ensemble Kalman filtering for hyperbolic conservation laws
Jan Glaubitz, Daniel Sharp, Mathieu le Provost +1
We propose a novel regularity-informed filtering framework for data assimilation in the context of hyperbolic conservation laws and other time-dependent partial differential equati…
To discretize continually: Mean shift interacting particle systems for Bayesian inference
Ayoub Belhadji, Daniel Sharp, Youssef M. Marzouk
Integration against a probability distribution given its unnormalized density is a central task in Bayesian inference and other fields. We introduce new methods for approximating s…
One-Shot Generative Flows: Existence and Obstructions
Panos Tsimpos, Daniel Sharp, Youssef Marzouk
We study dynamic measure transport for generative modeling, focusing on transport maps that connect a source measure to a target measure by integrating a velocity field…
Weighted quantization using MMD: From mean field to mean shift via gradient flows
Ayoub Belhadji, Daniel Sharp, Youssef Marzouk
Approximating a probability distribution using a set of particles is a fundamental problem in machine learning and statistics, with applications including clustering and quantizati…
Sampling through iterated approximation: Gradient-free and multi-fidelity Bayesian inference via transport
Daniel Sharp, Bart van Bloemen Waanders, Youssef Marzouk
We develop an iterative framework for Bayesian inference problems where the posterior distribution may involve computationally intensive models, intractable gradients, significant…
A friendly introduction to triangular transport
Maximilian Ramgraber, Daniel Sharp, Mathieu Le Provost +1
Decision making under uncertainty is a cross-cutting challenge in science and engineering. Most approaches to this challenge employ probabilistic representations of uncertainty. In…