Machine-Learned Sampling of Conditioned Path Measures

2025/06/02 by Jiang, Qijia, Cohn-Gordon, Reuben
#Computation (stat.CO) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML)

paper · doi:10.48550/arxiv.2506.01904

Abstract

We propose algorithms for sampling from posterior path measures P(C([0, T], ℝ^d)) under a general prior process. This leverages ideas from (1) controlled equilibrium dynamics, which gradually transport between two path measures, and (2) optimization in ∞-dimensional probability space endowed with a Wasserstein metric, which can be used to evolve a density curve under the specified likelihood. The resulting algorithms are theoretically grounded and can be integrated seamlessly with neural networks for learning the target trajectory ensembles, without access to data.

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