Priors in Bayesian Deep Learning: A Review

The paper titled "Priors in Bayesian Deep Learning: A Review" by Vincent Fortuin emphasizes the significance of prior choices in Bayesian deep learning models. While the choice of prior is a critical aspect of the Bayesian inference workflow, recent models have often resorted to vague priors like standard Gaussians. This review aims to highlight the importance of thoughtful prior specification and provides an overview of different priors proposed for (deep) Gaussian processes, variational autoencoders, and Bayesian neural networks. The authors discuss various methods for learning priors from data and present them in detail. By exploring different approaches to prior specification, this review intends to inspire practitioners in Bayesian deep learning to think more carefully about their model's prior choices. The paper serves as a valuable resource for researchers and practitioners seeking guidance on selecting appropriate priors for their Bayesian deep learning models. Overall, this comprehensive review sheds light on the crucial role that prior choices play in Bayesian deep learning and encourages practitioners to consider more informed and tailored prior specifications for their models.

Priors in Bayesian Deep Learning: A Review

Bayesian deep learning is a powerful tool for making predictions and decisions based on data. However, the success of any Bayesian model depends heavily on the choice of prior. Recent models have often resorted to vague priors like standard Gaussians, but this review by Vincent Fortuin emphasizes the importance of thoughtful prior specification. This article provides an overview of different priors proposed for (deep) Gaussian processes, variational autoencoders, and Bayesian neural networks as well as methods for learning priors from data.

The Role of Priors in Bayesian Deep Learning

In Bayesian inference, a prior distribution is used to represent our beliefs about the parameters before we observe any data. The choice of prior can have a major impact on the results obtained from a model since it determines how much influence each parameter has on the posterior distribution. As such, careful consideration must be given when selecting appropriate priors for a particular problem or dataset.

Overview of Different Priors

This review provides an overview of different priors proposed for (deep) Gaussian processes, variational autoencoders, and Bayesian neural networks. For example, some common choices include conjugate priors such as Gamma distributions or Dirichlet distributions; non-conjugate priors such as Student’s t-distributions; hierarchical models that use multiple levels; and more complex structures such as mixtures or spike-and-slab distributions that allow for sparsity in parameters. Additionally, there are various methods available to learn these priors from data including maximum likelihood estimation and Markov chain Monte Carlo sampling techniques like Hamiltonian Monte Carlo or Metropolis Hastings algorithms.

Conclusion

Overall, this comprehensive review sheds light on the crucial role that prior choices play in Bayesian deep learning and encourages practitioners to consider more informed and tailored prior specifications for their models. By exploring different approaches to prior specification, this review intends to inspire practitioners in Bayesian deep learning to think more carefully about their model's prior choices while providing them with valuable resources they can use when selecting appropriate priors for their own models.