Trumpets: Injective flows for inference and inverse problems

Konik Kothari, AmirEhsan Khorashadizadeh, Maarten de Hoop, Ivan Dokmanić
Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence, PMLR 161:1269-1278, 2021.

Abstract

We propose injective generative models called Trumpets that generalize invertible normalizing flows. The proposed generators progressively increase dimension from a low-dimensional latent space. We demonstrate that Trumpets can be trained orders of magnitudes faster than standard flows while yielding samples of comparable or better quality. They retain many of the advantages of the standard flows such as training based on maximum likelihood and a fast, exact inverse of the generator. Since Trumpets are injective and have fast inverses, they can be effectively used for downstream Bayesian inference. To wit, we use Trumpet priors for maximum a posteriori estimation in the context of image reconstruction from compressive measurements, outperforming competitive baselines in terms of reconstruction quality and speed. We then propose an efficient method for posterior characterization and uncertainty quantification with Trumpets by taking advantage of the low-dimensional latent space

Cite this Paper

BibTeX
@InProceedings{pmlr-v161-kothari21a, title = {Trumpets: Injective flows for inference and inverse problems}, author = {Kothari, Konik and Khorashadizadeh, AmirEhsan and de Hoop, Maarten and Dokmani\'c, Ivan}, booktitle = {Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence}, pages = {1269--1278}, year = {2021}, editor = {de Campos, Cassio and Maathuis, Marloes H.}, volume = {161}, series = {Proceedings of Machine Learning Research}, month = {27--30 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v161/kothari21a/kothari21a.pdf}, url = {https://proceedings.mlr.press/v161/kothari21a.html}, abstract = {We propose injective generative models called Trumpets that generalize invertible normalizing flows. The proposed generators progressively increase dimension from a low-dimensional latent space. We demonstrate that Trumpets can be trained orders of magnitudes faster than standard flows while yielding samples of comparable or better quality. They retain many of the advantages of the standard flows such as training based on maximum likelihood and a fast, exact inverse of the generator. Since Trumpets are injective and have fast inverses, they can be effectively used for downstream Bayesian inference. To wit, we use Trumpet priors for maximum a posteriori estimation in the context of image reconstruction from compressive measurements, outperforming competitive baselines in terms of reconstruction quality and speed. We then propose an efficient method for posterior characterization and uncertainty quantification with Trumpets by taking advantage of the low-dimensional latent space} }
Endnote
%0 Conference Paper %T Trumpets: Injective flows for inference and inverse problems %A Konik Kothari %A AmirEhsan Khorashadizadeh %A Maarten de Hoop %A Ivan Dokmanić %B Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2021 %E Cassio de Campos %E Marloes H. Maathuis %F pmlr-v161-kothari21a %I PMLR %P 1269--1278 %U https://proceedings.mlr.press/v161/kothari21a.html %V 161 %X We propose injective generative models called Trumpets that generalize invertible normalizing flows. The proposed generators progressively increase dimension from a low-dimensional latent space. We demonstrate that Trumpets can be trained orders of magnitudes faster than standard flows while yielding samples of comparable or better quality. They retain many of the advantages of the standard flows such as training based on maximum likelihood and a fast, exact inverse of the generator. Since Trumpets are injective and have fast inverses, they can be effectively used for downstream Bayesian inference. To wit, we use Trumpet priors for maximum a posteriori estimation in the context of image reconstruction from compressive measurements, outperforming competitive baselines in terms of reconstruction quality and speed. We then propose an efficient method for posterior characterization and uncertainty quantification with Trumpets by taking advantage of the low-dimensional latent space
APA
Kothari, K., Khorashadizadeh, A., de Hoop, M. & Dokmanić, I.. (2021). Trumpets: Injective flows for inference and inverse problems. Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 161:1269-1278 Available from https://proceedings.mlr.press/v161/kothari21a.html.

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