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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2411.00614 |
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| _version_ | 1866912336164421632 |
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| author | Chen, Yanshuo Hu, Zhengmian Chen, Wei Huang, Heng |
| author_facet | Chen, Yanshuo Hu, Zhengmian Chen, Wei Huang, Heng |
| contents | \textbf{Motivation:} Predicting single-cell perturbation responses requires mapping between two unpaired single-cell data distributions. Optimal transport (OT) theory provides a principled framework for constructing such mappings by minimizing transport cost. Recently, Wasserstein-2 ($W_2$) neural optimal transport solvers (\textit{e.g.}, CellOT) have been employed for this prediction task. However, $W_2$ OT relies on the general Kantorovich dual formulation, which involves optimizing over two conjugate functions, leading to a complex min-max optimization problem that converges slowly. \\ \textbf{Results:} To address these challenges, we propose a novel solver based on the Wasserstein-1 ($W_1$) dual formulation. Unlike $W_2$, the $W_1$ dual simplifies the optimization to a maximization problem over a single 1-Lipschitz function, thus eliminating the need for time-consuming min-max optimization. While solving the $W_1$ dual only reveals the transport direction and does not directly provide a unique optimal transport map, we incorporate an additional step using adversarial training to determine an appropriate transport step size, effectively recovering the transport map. Our experiments demonstrate that the proposed $W_1$ neural optimal transport solver can mimic the $W_2$ OT solvers in finding a unique and ``monotonic" map on 2D datasets. Moreover, the $W_1$ OT solver achieves performance on par with or surpasses $W_2$ OT solvers on real single-cell perturbation datasets. Furthermore, we show that $W_1$ OT solver achieves $25 \sim 45\times$ speedup, scales better on high dimensional transportation task, and can be directly applied on single-cell RNA-seq dataset with highly variable genes. \\ \textbf{Availability and Implementation:} Our implementation and experiments are open-sourced at https://github.com/poseidonchan/w1ot. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_00614 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fast and scalable Wasserstein-1 neural optimal transport solver for single-cell perturbation prediction Chen, Yanshuo Hu, Zhengmian Chen, Wei Huang, Heng Machine Learning Genomics \textbf{Motivation:} Predicting single-cell perturbation responses requires mapping between two unpaired single-cell data distributions. Optimal transport (OT) theory provides a principled framework for constructing such mappings by minimizing transport cost. Recently, Wasserstein-2 ($W_2$) neural optimal transport solvers (\textit{e.g.}, CellOT) have been employed for this prediction task. However, $W_2$ OT relies on the general Kantorovich dual formulation, which involves optimizing over two conjugate functions, leading to a complex min-max optimization problem that converges slowly. \\ \textbf{Results:} To address these challenges, we propose a novel solver based on the Wasserstein-1 ($W_1$) dual formulation. Unlike $W_2$, the $W_1$ dual simplifies the optimization to a maximization problem over a single 1-Lipschitz function, thus eliminating the need for time-consuming min-max optimization. While solving the $W_1$ dual only reveals the transport direction and does not directly provide a unique optimal transport map, we incorporate an additional step using adversarial training to determine an appropriate transport step size, effectively recovering the transport map. Our experiments demonstrate that the proposed $W_1$ neural optimal transport solver can mimic the $W_2$ OT solvers in finding a unique and ``monotonic" map on 2D datasets. Moreover, the $W_1$ OT solver achieves performance on par with or surpasses $W_2$ OT solvers on real single-cell perturbation datasets. Furthermore, we show that $W_1$ OT solver achieves $25 \sim 45\times$ speedup, scales better on high dimensional transportation task, and can be directly applied on single-cell RNA-seq dataset with highly variable genes. \\ \textbf{Availability and Implementation:} Our implementation and experiments are open-sourced at https://github.com/poseidonchan/w1ot. |
| title | Fast and scalable Wasserstein-1 neural optimal transport solver for single-cell perturbation prediction |
| topic | Machine Learning Genomics |
| url | https://arxiv.org/abs/2411.00614 |