Learning non-Gaussian spatial distributions via Bayesian transport maps with parametric shrinkage
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912214005317632 |
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| author | Chakraborty, Anirban Katzfuss, Matthias |
| author_facet | Chakraborty, Anirban Katzfuss, Matthias |
| contents | Many applications, including climate-model analysis and stochastic weather generators, require learning or emulating the distribution of a high-dimensional and non-Gaussian spatial field based on relatively few training samples. To address this challenge, a recently proposed Bayesian transport map (BTM) approach consists of a triangular transport map with nonparametric Gaussian-process (GP) components, which is trained to transform the distribution of interest distribution to a Gaussian reference distribution. To improve the performance of this existing BTM, we propose to shrink the map components toward a ``base'' parametric Gaussian family combined with a Vecchia approximation for scalability. The resulting ShrinkTM approach is more accurate than the existing BTM, especially for small numbers of training samples. It can even outperform the ``base'' family when trained on a single sample of the spatial field. We demonstrate the advantage of ShrinkTM though numerical experiments on simulated data and on climate-model output. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_19208 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Learning non-Gaussian spatial distributions via Bayesian transport maps with parametric shrinkage Chakraborty, Anirban Katzfuss, Matthias Computation Applications Machine Learning Many applications, including climate-model analysis and stochastic weather generators, require learning or emulating the distribution of a high-dimensional and non-Gaussian spatial field based on relatively few training samples. To address this challenge, a recently proposed Bayesian transport map (BTM) approach consists of a triangular transport map with nonparametric Gaussian-process (GP) components, which is trained to transform the distribution of interest distribution to a Gaussian reference distribution. To improve the performance of this existing BTM, we propose to shrink the map components toward a ``base'' parametric Gaussian family combined with a Vecchia approximation for scalability. The resulting ShrinkTM approach is more accurate than the existing BTM, especially for small numbers of training samples. It can even outperform the ``base'' family when trained on a single sample of the spatial field. We demonstrate the advantage of ShrinkTM though numerical experiments on simulated data and on climate-model output. |
| title | Learning non-Gaussian spatial distributions via Bayesian transport maps with parametric shrinkage |
| topic | Computation Applications Machine Learning |
| url | https://arxiv.org/abs/2409.19208 |