A generative flow for conditional sampling via optimal transport

• URL: http://arxiv.org/abs/2307.04102v1
• Date: Sun, 9 Jul 2023 05:36:26 GMT
• Title: A generative flow for conditional sampling via optimal transport
• Authors: Jason Alfonso, Ricardo Baptista, Anupam Bhakta, Noam Gal, Alfin Hou, Isa Lyubimova, Daniel Pocklington, Josef Sajonz, Giulio Trigila, and Ryan Tsai
• Abstract summary: This work proposes a non-parametric generative model that iteratively maps reference samples to the target. The model uses block-triangular transport maps, whose components are shown to characterize conditionals of the target distribution. These maps arise from solving an optimal transport problem with a weighted $L2$ cost function, thereby extending the data-driven approach in [Trigila and Tabak, 2016] for conditional sampling.
• Score: 1.0486135378491266
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Sampling conditional distributions is a fundamental task for Bayesian inference and density estimation. Generative models, such as normalizing flows and generative adversarial networks, characterize conditional distributions by learning a transport map that pushes forward a simple reference (e.g., a standard Gaussian) to a target distribution. While these approaches successfully describe many non-Gaussian problems, their performance is often limited by parametric bias and the reliability of gradient-based (adversarial) optimizers to learn these transformations. This work proposes a non-parametric generative model that iteratively maps reference samples to the target. The model uses block-triangular transport maps, whose components are shown to characterize conditionals of the target distribution. These maps arise from solving an optimal transport problem with a weighted $L^2$ cost function, thereby extending the data-driven approach in [Trigila and Tabak, 2016] for conditional sampling. The proposed approach is demonstrated on a two dimensional example and on a parameter inference problem involving nonlinear ODEs.

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