• Corpus ID: 54557344

Encoding prior knowledge in the structure of the likelihood

@article{Knollmller2018EncodingPK,
  title={Encoding prior knowledge in the structure of the likelihood},
  author={Jakob Knollm{\"u}ller and Torsten A. Ensslin},
  journal={ArXiv},
  year={2018},
  volume={abs/1812.04403}
}

• Jakob Knollmüller, T. Ensslin
• Published 11 December 2018
• Computer Science
• ArXiv

The inference of deep hierarchical models is problematic due to strong dependencies between the hierarchies. We investigate a specific transformation of the model parameters based on the multivariate distributional transform. This transformation is a special form of the reparametrization trick, flattens the hierarchy and leads to a standard Gaussian prior on all resulting parameters. The transformation also transfers all the prior information into the structure of the likelihood, hereby decoupling the transformed parameters a priori from each other. A variational Gaussian approximation in this standardized space will be excellent in situations of relatively uninformative data. Additionally, the curvature of the log-posterior is well-conditioned in directions that are weakly constrained by the data, allowing for fast inference in such a scenario. In an example we perform the transformation explicitly for Gaussian process regression with a priori unknown correlation structure. Deep models are inferred rapidly in highly and slowly in poorly informed situations. The flat model show exactly the opposite performance pattern. A synthesis of both, the deep and the flat perspective, provides their combined advantages and overcomes the individual limitations, leading to a faster inference.