# Inference with minimal Gibbs free energy in information field theory

@article{Ensslin2010InferenceWM, title={Inference with minimal Gibbs free energy in information field theory}, author={Torsten A. Ensslin and Cornelius Weig}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2010}, volume={82 5 Pt 1}, pages={ 051112 } }

Non-linear and non-gaussian signal inference problems are difficult to tackle. Renormalization techniques permit us to construct good estimators for the posterior signal mean within information field theory (IFT), but the approximations and assumptions made are not very obvious. Here we introduce the simple concept of minimal Gibbs free energy to IFT, and show that previous renormalization results emerge naturally. They can be understood as being the gaussian approximation to the full posteriorâ€¦Â

## 39 Citations

### Comment on "Inference with minimal Gibbs free energy in information field theory".

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2012

It is shown explicitly that MGFE indeed incorporates the MAP principle, as well as the MDI (minimum discrimination information) approach, but not the well-known ME principle of Jaynes, which is important for Bayesian inference problems.

### Reconstruction of Gaussian and log-normal fields with spectral smoothness

- Computer Science
- 2013

It is shown that the minimization of the Gibbs free energy, corresponding to a Gaussian approximation to the posterior marginalized over the power spectrum, is equivalent to the empirical Bayes ansatz, in which the power Spectrum is fixed to its maximum a posteriori value.

### Reconstruction of signals with unknown spectra in information field theory with parameter uncertainty

- PhysicsArXiv
- 2010

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.

### Operator calculus for information field theory.

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- 2016

A way of translating expectation values to a language of operators which is similar to that in quantum mechanics is presented, which simplifies many calculations, for instance such as those involving log-normal priors.

### Reconstructing signals from noisy data with unknown signal and noise covariance.

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2011

A method to reconstruct Gaussian signals from linear measurements with Gaussian noise using the principle of minimum Gibbs free energy and extending this algorithm to simultaneously uncertain noise and signal covariances using the same principles in the derivation.

### Denoising, deconvolving, and decomposing photon observations - Derivation of the D3PO algorithm

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The D 3 PO algorithm addresses the inference problem of denoising, deconvolving, and decomposing photon observations and successfully denoised, deconvolved, and decomposed the data into a diuse and a point-like signal estimate for the respective photon flux components.

### Information Theory for Fields

- Computer Science, PhysicsAnnalen der Physik
- 2019

Information field theory is built upon the language of mathematical physics, in particular, on field theory and statistical mechanics and permits the mathematical derivation of optimal imaging algorithms, data analysis methods, and even computer simulation schemes.

### Generic inference of inflation models by non-Gaussianity and primordial power spectrum reconstruction

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We present a generic inference method for inflation models from observational data by the usage of higher-order statistics of the curvature perturbation on uniform density hypersurfaces. This methodâ€¦

### Signal inference in Galactic astrophysics

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In this thesis we present a combination of methodological work with very wide focus and some specific astrophysical applications. We advance the knowledge on the Galactic interstellar medium byâ€¦

### Information Field Theory and Artificial Intelligence

- Computer ScienceEntropy
- 2022

This paper reformulated the process of inference in IFT in terms of GNN training, suggesting that IFT is well suited to address many problems in AI and ML research and application.

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