Particle-based Energetic Variational Inference
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2020
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911671220436992 |
|---|---|
| author | Wang, Yiwei Chen, Jiuhai Liu, Chun Kang, Lulu |
| author_facet | Wang, Yiwei Chen, Jiuhai Liu, Chun Kang, Lulu |
| contents | We introduce a new variational inference (VI) framework, called energetic variational inference (EVI). It minimizes the VI objective function based on a prescribed energy-dissipation law. Using the EVI framework, we can derive many existing Particle-based Variational Inference (ParVI) methods, including the popular Stein Variational Gradient Descent (SVGD) approach. More importantly, many new ParVI schemes can be created under this framework. For illustration, we propose a new particle-based EVI scheme, which performs the particle-based approximation of the density first and then uses the approximated density in the variational procedure, or "Approximation-then-Variation" for short. Thanks to this order of approximation and variation, the new scheme can maintain the variational structure at the particle level, and can significantly decrease the KL-divergence in each iteration. Numerical experiments show the proposed method outperforms some existing ParVI methods in terms of fidelity to the target distribution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2004_06443 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Particle-based Energetic Variational Inference Wang, Yiwei Chen, Jiuhai Liu, Chun Kang, Lulu Machine Learning We introduce a new variational inference (VI) framework, called energetic variational inference (EVI). It minimizes the VI objective function based on a prescribed energy-dissipation law. Using the EVI framework, we can derive many existing Particle-based Variational Inference (ParVI) methods, including the popular Stein Variational Gradient Descent (SVGD) approach. More importantly, many new ParVI schemes can be created under this framework. For illustration, we propose a new particle-based EVI scheme, which performs the particle-based approximation of the density first and then uses the approximated density in the variational procedure, or "Approximation-then-Variation" for short. Thanks to this order of approximation and variation, the new scheme can maintain the variational structure at the particle level, and can significantly decrease the KL-divergence in each iteration. Numerical experiments show the proposed method outperforms some existing ParVI methods in terms of fidelity to the target distribution. |
| title | Particle-based Energetic Variational Inference |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2004.06443 |