The \(\texttt{deep\_tensor}\) package contains a PyTorch implementation of the deep inverse Rosenblatt transport (DIRT) algorithm introduced by Cui and Dolgov (2022).

Installation

\(\texttt{deep\_tensor}\) can be installed using pip:

pip install deep-tensor-py

The package can then be imported using

import deep_tensor as dt

Getting Started

Check out the examples page and API reference for help getting started with \(\texttt{deep\_tensor}\).

Further Reading

The deep inverse Rosenblatt transport (DIRT) algorithm (Cui and Dolgov 2022) uses a composition of mappings, constructed using functional tensor trains, to approximate the Rosenblatt transport between an arbitrary target density function and a simple product-form reference density. Early work on functional tensor train (FTT) approximations to probability density functions was conducted by Dolgov et al. (2020). Cui and Dolgov (2022) introduced the idea of using a composition of FTT-based mappings to provide a more accurate characterisation of highly correlated or concentrated probability densities.

The DIRT methodology has also been used for problems including amortised inference (Cui, Dolgov, and Zahm 2023), rare event estimation (Cui, Dolgov, and Scheichl 2024), sequential inference (Zhao and Cui 2024), and optimal experimental design (Koval, Herzog, and Scheichl 2024).

References

Cui, Tiangang, and Sergey Dolgov. 2022. “Deep Composition of Tensor-Trains Using Squared Inverse Rosenblatt Transports.” Foundations of Computational Mathematics 22 (6): 1863–1922. https://doi.org/10.1007/s10208-021-09537-5.
Cui, Tiangang, Sergey Dolgov, and Robert Scheichl. 2024. “Deep Importance Sampling Using Tensor Trains with Application to a Priori and a Posteriori Rare Events.” SIAM Journal on Scientific Computing 46 (1): C1–29. https://doi.org/10.1137/23M1546981.
Cui, Tiangang, Sergey Dolgov, and Olivier Zahm. 2023. “Scalable Conditional Deep Inverse Rosenblatt Transports Using Tensor Trains and Gradient-Based Dimension Reduction.” Journal of Computational Physics 485: 112103. https://doi.org/10.1016/j.jcp.2023.112103.
Dolgov, Sergey, Karim Anaya-Izquierdo, Colin Fox, and Robert Scheichl. 2020. “Approximation and Sampling of Multivariate Probability Distributions in the Tensor Train Decomposition.” Statistics and Computing 30: 603–25. https://doi.org/10.1007/s11222-019-09910-z.
Koval, Karina, Roland Herzog, and Robert Scheichl. 2024. “Tractable Optimal Experimental Design Using Transport Maps.” Inverse Problems 40 (12): 125002. https://doi.org/10.1088/1361-6420/ad8260.
Zhao, Yiran, and Tiangang Cui. 2024. “Tensor-Train Methods for Sequential State and Parameter Learning in State-Space Models.” Journal of Machine Learning Research 25 (244): 1–51. http://jmlr.org/papers/v25/23-0743.html.