Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2310.18047 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911394195046400 |
|---|---|
| author | Tang, Rong Bhattacharya, Anirban Pati, Debdeep Yang, Yun |
| author_facet | Tang, Rong Bhattacharya, Anirban Pati, Debdeep Yang, Yun |
| contents | Manifold-valued parameters routinely arise in modern statistical applications such as in medical imaging, robotics, and computer vision, to name a few. While traditional Bayesian approaches are applicable to such settings by considering an ambient Euclidean space as the parameter space, we demonstrate the benefits of integrating manifold structure into the Bayesian framework, both theoretically and computationally. Moreover, existing Bayesian approaches which are designed specifically for manifold-valued parameters are primarily model-based, which are typically subject to inaccurate uncertainty quantification under model misspecification. In this article, we propose a robust model-free Bayesian inference for parameters defined on a Riemannian submanifold, which is shown to provide valid uncertainty quantification from a frequentist perspective. Computationally, we propose a Markov chain Monte Carlo to sample from the posterior on the Riemannian submanifold, where the mixing time, in the large sample regime, is shown to depend only on the intrinsic dimension of the parameter space instead of the potentially muchlarger ambient dimension. Our numerical results demonstrate the effectiveness of our approach on a variety of problems, such as multiple quantile regression, reduced-rank regression, and Fréchet mean estimation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_18047 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Robust Bayesian Inference on Riemannian Submanifold Tang, Rong Bhattacharya, Anirban Pati, Debdeep Yang, Yun Methodology Manifold-valued parameters routinely arise in modern statistical applications such as in medical imaging, robotics, and computer vision, to name a few. While traditional Bayesian approaches are applicable to such settings by considering an ambient Euclidean space as the parameter space, we demonstrate the benefits of integrating manifold structure into the Bayesian framework, both theoretically and computationally. Moreover, existing Bayesian approaches which are designed specifically for manifold-valued parameters are primarily model-based, which are typically subject to inaccurate uncertainty quantification under model misspecification. In this article, we propose a robust model-free Bayesian inference for parameters defined on a Riemannian submanifold, which is shown to provide valid uncertainty quantification from a frequentist perspective. Computationally, we propose a Markov chain Monte Carlo to sample from the posterior on the Riemannian submanifold, where the mixing time, in the large sample regime, is shown to depend only on the intrinsic dimension of the parameter space instead of the potentially muchlarger ambient dimension. Our numerical results demonstrate the effectiveness of our approach on a variety of problems, such as multiple quantile regression, reduced-rank regression, and Fréchet mean estimation. |
| title | Robust Bayesian Inference on Riemannian Submanifold |
| topic | Methodology |
| url | https://arxiv.org/abs/2310.18047 |