Fast filtering of non-Gaussian models using Amortized Optimal Transport Maps
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909617786716160 |
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| author | Al-Jarrah, Mohammad Hosseini, Bamdad Taghvaei, Amirhossein |
| author_facet | Al-Jarrah, Mohammad Hosseini, Bamdad Taghvaei, Amirhossein |
| contents | In this paper, we present the amortized optimal transport filter (A-OTF) designed to mitigate the computational burden associated with the real-time training of optimal transport filters (OTFs). OTFs can perform accurate non-Gaussian Bayesian updates in the filtering procedure, but they require training at every time step, which makes them expensive. The proposed A-OTF framework exploits the similarity between OTF maps during an initial/offline training stage in order to reduce the cost of inference during online calculations. More precisely, we use clustering algorithms to select relevant subsets of pre-trained maps whose weighted average is used to compute the A-OTF model akin to a mixture of experts. A series of numerical experiments validate that A-OTF achieves substantial computational savings during online inference while preserving the inherent flexibility and accuracy of OTF. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_12633 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fast filtering of non-Gaussian models using Amortized Optimal Transport Maps Al-Jarrah, Mohammad Hosseini, Bamdad Taghvaei, Amirhossein Optimization and Control Machine Learning In this paper, we present the amortized optimal transport filter (A-OTF) designed to mitigate the computational burden associated with the real-time training of optimal transport filters (OTFs). OTFs can perform accurate non-Gaussian Bayesian updates in the filtering procedure, but they require training at every time step, which makes them expensive. The proposed A-OTF framework exploits the similarity between OTF maps during an initial/offline training stage in order to reduce the cost of inference during online calculations. More precisely, we use clustering algorithms to select relevant subsets of pre-trained maps whose weighted average is used to compute the A-OTF model akin to a mixture of experts. A series of numerical experiments validate that A-OTF achieves substantial computational savings during online inference while preserving the inherent flexibility and accuracy of OTF. |
| title | Fast filtering of non-Gaussian models using Amortized Optimal Transport Maps |
| topic | Optimization and Control Machine Learning |
| url | https://arxiv.org/abs/2503.12633 |