Diffeomorphic Measure Matching with Kernels for Generative Modeling
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911776160874496 |
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| author | Pandey, Biraj Hosseini, Bamdad Batlle, Pau Owhadi, Houman |
| author_facet | Pandey, Biraj Hosseini, Bamdad Batlle, Pau Owhadi, Houman |
| contents | This article presents a general framework for the transport of probability measures towards minimum divergence generative modeling and sampling using ordinary differential equations (ODEs) and Reproducing Kernel Hilbert Spaces (RKHSs), inspired by ideas from diffeomorphic matching and image registration. A theoretical analysis of the proposed method is presented, giving a priori error bounds in terms of the complexity of the model, the number of samples in the training set, and model misspecification. An extensive suite of numerical experiments further highlights the properties, strengths, and weaknesses of the method and extends its applicability to other tasks, such as conditional simulation and inference. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08077 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Diffeomorphic Measure Matching with Kernels for Generative Modeling Pandey, Biraj Hosseini, Bamdad Batlle, Pau Owhadi, Houman Machine Learning Dynamical Systems Computation 35Q68 49Q22 62F15 68T07 62R07 This article presents a general framework for the transport of probability measures towards minimum divergence generative modeling and sampling using ordinary differential equations (ODEs) and Reproducing Kernel Hilbert Spaces (RKHSs), inspired by ideas from diffeomorphic matching and image registration. A theoretical analysis of the proposed method is presented, giving a priori error bounds in terms of the complexity of the model, the number of samples in the training set, and model misspecification. An extensive suite of numerical experiments further highlights the properties, strengths, and weaknesses of the method and extends its applicability to other tasks, such as conditional simulation and inference. |
| title | Diffeomorphic Measure Matching with Kernels for Generative Modeling |
| topic | Machine Learning Dynamical Systems Computation 35Q68 49Q22 62F15 68T07 62R07 |
| url | https://arxiv.org/abs/2402.08077 |