• 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}
}
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… 

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References

SHOWING 1-10 OF 31 REFERENCES
Auto-Encoding Variational Bayes
TLDR
A stochastic variational inference and learning algorithm that scales to large datasets and, under some mild differentiability conditions, even works in the intractable case is introduced.
Variational Inference with Normalizing Flows
TLDR
It is demonstrated that the theoretical advantages of having posteriors that better match the true posterior, combined with the scalability of amortized variational approaches, provides a clear improvement in performance and applicability of variational inference.
Variational Inference: A Review for Statisticians
TLDR
Variational inference (VI), a method from machine learning that approximates probability densities through optimization, is reviewed and a variant that uses stochastic optimization to scale up to massive data is derived.
DENSITY ESTIMATION BY DUAL ASCENT OF THE LOG-LIKELIHOOD ∗
TLDR
A methodology is developed to assign, from an observed sample, a joint-probability distribution to a set of continuous variables, by mapping the original variables onto a jointly-Gaussian set.
Automatic Differentiation Variational Inference
TLDR
Automatic differentiation variational inference (ADVI) is developed, where the scientist only provides a probabilistic model and a dataset, nothing else, and the algorithm automatically derives an efficient Variational inference algorithm, freeing the scientist to refine and explore many models.
Bayesian reconstruction of the cosmological large-scale structure: methodology, inverse algorithms and numerical optimization
We address the inverse problem of cosmic large-scale structure reconstruction from a Bayesian perspective. For a linear data model, a number of known and novel reconstruction schemes, which differ in
The Variational Gaussian Approximation Revisited
TLDR
The relationship between the Laplace and the variational approximation is discussed, and it is shown that for models with gaussian priors and factorizing likelihoods, the number of variational parameters is actually .
Gaussian Processes for Regression
TLDR
This paper investigates the use of Gaussian process priors over functions, which permit the predictive Bayesian analysis for fixed values of hyperparameters to be carried out exactly using matrix operations.
Fixed-Form Variational Posterior Approximation through Stochastic Linear Regression
TLDR
A general algorithm for approximating nonstandard Bayesian posterior distributions that minimizes the Kullback-Leibler divergence of an approximating distribution to the intractable posterior distribu- tion.
Reconstruction of signals with unknown spectra in information field theory with parameter uncertainty
TLDR
The general problem of signal inference in the presence of unknown parameters within the framework of information field theory is formulated and a generic parameter-uncertainty renormalized estimation (PURE) technique is developed.
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