Efficient Neural Network Approaches for Conditional Optimal Transport with Applications in Bayesian Inference Article Swipe

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Zheyu Oliver Wang , Ricardo Baptista , Youssef Marzouk , Lars Ruthotto , Deepanshu Verma · YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2310.16975

We present two neural network approaches that approximate the solutions of static and dynamic $\unicode{x1D450}\unicode{x1D45C}\unicode{x1D45B}\unicode{x1D451}\unicode{x1D456}\unicode{x1D461}\unicode{x1D456}\unicode{x1D45C}\unicode{x1D45B}\unicode{x1D44E}\unicode{x1D459}\unicode{x0020}\unicode{x1D45C}\unicode{x1D45D}\unicode{x1D461}\unicode{x1D456}\unicode{x1D45A}\unicode{x1D44E}\unicode{x1D459}\unicode{x0020}\unicode{x1D461}\unicode{x1D45F}\unicode{x1D44E}\unicode{x1D45B}\unicode{x1D460}\unicode{x1D45D}\unicode{x1D45C}\unicode{x1D45F}\unicode{x1D461}$ (COT) problems. Both approaches enable conditional sampling and conditional density estimation, which are core tasks in Bayesian inference$\unicode{x2013}$particularly in the simulation-based ($\unicode{x201C}$likelihood-free$\unicode{x201D}$) setting. Our methods represent the target conditional distribution as a transformation of a tractable reference distribution. Obtaining such a transformation, chosen here to be an approximation of the COT map, is computationally challenging even in moderate dimensions. To improve scalability, our numerical algorithms use neural networks to parameterize candidate maps and further exploit the structure of the COT problem. Our static approach approximates the map as the gradient of a partially input-convex neural network. It uses a novel numerical implementation to increase computational efficiency compared to state-of-the-art alternatives. Our dynamic approach approximates the conditional optimal transport via the flow map of a regularized neural ODE; compared to the static approach, it is slower to train but offers more modeling choices and can lead to faster sampling. We demonstrate both algorithms numerically, comparing them with competing state-of-the-art approaches, using benchmark datasets and simulation-based Bayesian inverse problems.

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preprint

Language

en

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http://arxiv.org/abs/2310.16975

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https://arxiv.org/pdf/2310.16975

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green

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5

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10

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https://openalex.org/W4387994916

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https://openalex.org/W4387994916

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DOI

https://doi.org/10.48550/arxiv.2310.16975

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Title

Efficient Neural Network Approaches for Conditional Optimal Transport with Applications in Bayesian Inference

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Type

preprint

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Language

en

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Publication year

2023

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Publication date

2023-10-25

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Authors

Zheyu Oliver Wang, Ricardo Baptista, Youssef Marzouk, Lars Ruthotto, Deepanshu Verma

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https://arxiv.org/abs/2310.16975

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https://arxiv.org/pdf/2310.16975

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Yes

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green

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Concepts

Computer science, Leverage (statistics), Artificial neural network, Inference, Posterior probability, Bayesian inference, Conditional probability distribution, Mathematical optimization, Bayesian probability, Algorithm, Artificial intelligence, Mathematics, Econometrics

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Cited by

5

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2025: 4, 2024: 1

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10

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