Transport maps

Inference by measure transport, low-dimensional coupling…

April 3, 2018 — February 21, 2023

approximation
Bayes
density
likelihood free
nonparametric
optimization
probabilistic algorithms
probability
statistics

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Figure 1

Maps moving one probability measure into another. Most commonly seen in normalising flows. 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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Cunningham, Zabounidis, Agrawal, et al. 2020. “Normalizing Flows Across Dimensions.”
Marzouk, Moselhy, Parno, et al. 2016. “Sampling via Measure Transport: An Introduction.” In Handbook of Uncertainty Quantification.
Panaretos, and Zemel. 2019. “Statistical Aspects of Wasserstein Distances.” Annual Review of Statistics and Its Application.
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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.”