Transport maps

Inference by measure transport, low-dimensional coupling…

April 4, 2018 — February 21, 2023

Figure 1

Maps moving one probability measure into another. Useful in their own right. If we assign costs to various maps and then prefer some to others then we are in the realm of optimal transport metrics.

1 References

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Cui, and Dolgov. 2022. Deep Composition of Tensor-Trains Using Squared Inverse Rosenblatt Transports.” Foundations of Computational Mathematics.
Marzouk, Moselhy, Parno, et al. 2016. Sampling via Measure Transport: An Introduction.” In Handbook of Uncertainty Quantification.
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Parno, and Marzouk. 2018. Transport Map Accelerated Markov Chain Monte Carlo.” SIAM/ASA Journal on Uncertainty Quantification.
Perrot, Courty, Flamary, et al. n.d. “Mapping Estimation for Discrete Optimal Transport.”
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Spantini, Bigoni, and Marzouk. 2017. Inference via Low-Dimensional Couplings.” Journal of Machine Learning Research.
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Zhao, and Cui. 2023. Tensor-Based Methods for Sequential State and Parameter Estimation in State Space Models.”