Optimization Guarantees for Square-Root Natural-Gradient Variational Inference
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913936605970432 |
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| author | Kumar, Navish Möllenhoff, Thomas Khan, Mohammad Emtiyaz Lucchi, Aurelien |
| author_facet | Kumar, Navish Möllenhoff, Thomas Khan, Mohammad Emtiyaz Lucchi, Aurelien |
| contents | Variational inference with natural-gradient descent often shows fast convergence in practice, but its theoretical convergence guarantees have been challenging to establish. This is true even for the simplest cases that involve concave log-likelihoods and use a Gaussian approximation. We show that the challenge can be circumvented for such cases using a square-root parameterization for the Gaussian covariance. This approach establishes novel convergence guarantees for natural-gradient variational-Gaussian inference and its continuous-time gradient flow. Our experiments demonstrate the effectiveness of natural gradient methods and highlight their advantages over algorithms that use Euclidean or Wasserstein geometries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_07853 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimization Guarantees for Square-Root Natural-Gradient Variational Inference Kumar, Navish Möllenhoff, Thomas Khan, Mohammad Emtiyaz Lucchi, Aurelien Machine Learning Artificial Intelligence Variational inference with natural-gradient descent often shows fast convergence in practice, but its theoretical convergence guarantees have been challenging to establish. This is true even for the simplest cases that involve concave log-likelihoods and use a Gaussian approximation. We show that the challenge can be circumvented for such cases using a square-root parameterization for the Gaussian covariance. This approach establishes novel convergence guarantees for natural-gradient variational-Gaussian inference and its continuous-time gradient flow. Our experiments demonstrate the effectiveness of natural gradient methods and highlight their advantages over algorithms that use Euclidean or Wasserstein geometries. |
| title | Optimization Guarantees for Square-Root Natural-Gradient Variational Inference |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2507.07853 |