Generative modeling of time-dependent densities via optimal transport and projection pursuit
| Autor: | Botvinick-Greenhouse, Jonah, Yang, Yunan, Maulik, Romit |
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| Rok vydání: | 2023 |
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| Zdroj: | Chaos: An Interdisciplinary Journal of Nonlinear Science 33, 103108 (2023) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1063/5.0155783 |
| Popis: | Motivated by the computational difficulties incurred by popular deep learning algorithms for the generative modeling of temporal densities, we propose a cheap alternative which requires minimal hyperparameter tuning and scales favorably to high dimensional problems. In particular, we use a projection-based optimal transport solver [Meng et al., 2019] to join successive samples and subsequently use transport splines [Chewi et al., 2020] to interpolate the evolving density. When the sampling frequency is sufficiently high, the optimal maps are close to the identity and are thus computationally efficient to compute. Moreover, the training process is highly parallelizable as all optimal maps are independent and can thus be learned simultaneously. Finally, the approach is based solely on numerical linear algebra rather than minimizing a nonconvex objective function, allowing us to easily analyze and control the algorithm. We present several numerical experiments on both synthetic and real-world datasets to demonstrate the efficiency of our method. In particular, these experiments show that the proposed approach is highly competitive compared with state-of-the-art normalizing flows conditioned on time across a wide range of dimensionalities. Comment: This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 10, October 2023 and may be found at https://doi.org/10.1063/5.0155783 |
| Databáze: | arXiv |
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