Sliced Distribution Matching based on Cumulative Distribution Functions with Applications to Control
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916983573839872 |
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| author | Tzikas, Alexandros E. Jamgochian, Arec Ure, Nazim Kemal Kochenderfer, Mykel J. Boyd, Stephen P. |
| author_facet | Tzikas, Alexandros E. Jamgochian, Arec Ure, Nazim Kemal Kochenderfer, Mykel J. Boyd, Stephen P. |
| contents | Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy between the cumulative distribution functions of random linear one-dimensional projections of the random variables. Our proposed distance is interpretable, computationally simple, and admits a differentiable approximation. We establish asymptotic theoretical guarantees for sample-based estimators of the distance. We empirically study the use of the distance in a two-sample test and demonstrate its ability to distinguish different distributions. Finally, we show that the distance allows for simple gradient-based solutions in control by studying distribution steering and ergodic control. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_06220 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sliced Distribution Matching based on Cumulative Distribution Functions with Applications to Control Tzikas, Alexandros E. Jamgochian, Arec Ure, Nazim Kemal Kochenderfer, Mykel J. Boyd, Stephen P. Systems and Control Robotics Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy between the cumulative distribution functions of random linear one-dimensional projections of the random variables. Our proposed distance is interpretable, computationally simple, and admits a differentiable approximation. We establish asymptotic theoretical guarantees for sample-based estimators of the distance. We empirically study the use of the distance in a two-sample test and demonstrate its ability to distinguish different distributions. Finally, we show that the distance allows for simple gradient-based solutions in control by studying distribution steering and ergodic control. |
| title | Sliced Distribution Matching based on Cumulative Distribution Functions with Applications to Control |
| topic | Systems and Control Robotics |
| url | https://arxiv.org/abs/2412.06220 |