Student-t processes as infinite-width limits of posterior Bayesian neural networks
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912222454743040 |
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| author | Caporali, Francesco Favaro, Stefano Trevisan, Dario |
| author_facet | Caporali, Francesco Favaro, Stefano Trevisan, Dario |
| contents | The asymptotic properties of Bayesian Neural Networks (BNNs) have been extensively studied, particularly regarding their approximations by Gaussian processes in the infinite-width limit. We extend these results by showing that posterior BNNs can be approximated by Student-t processes, which offer greater flexibility in modeling uncertainty. Specifically, we show that, if the parameters of a BNN follow a Gaussian prior distribution, and the variance of both the last hidden layer and the Gaussian likelihood function follows an Inverse-Gamma prior distribution, then the resulting posterior BNN converges to a Student-t process in the infinite-width limit. Our proof leverages the Wasserstein metric to establish control over the convergence rate of the Student-t process approximation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_04247 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Student-t processes as infinite-width limits of posterior Bayesian neural networks Caporali, Francesco Favaro, Stefano Trevisan, Dario Machine Learning Probability The asymptotic properties of Bayesian Neural Networks (BNNs) have been extensively studied, particularly regarding their approximations by Gaussian processes in the infinite-width limit. We extend these results by showing that posterior BNNs can be approximated by Student-t processes, which offer greater flexibility in modeling uncertainty. Specifically, we show that, if the parameters of a BNN follow a Gaussian prior distribution, and the variance of both the last hidden layer and the Gaussian likelihood function follows an Inverse-Gamma prior distribution, then the resulting posterior BNN converges to a Student-t process in the infinite-width limit. Our proof leverages the Wasserstein metric to establish control over the convergence rate of the Student-t process approximation. |
| title | Student-t processes as infinite-width limits of posterior Bayesian neural networks |
| topic | Machine Learning Probability |
| url | https://arxiv.org/abs/2502.04247 |