Information field theory

Information field theory (IFT) is information theory, logic under uncertainty, applied to fields. A field can be any quantity defined over some space, such as the air temperature over Europe, the magnetic field strength in the Milky Way, or the matter density in the Universe. IFT describes how data and knowledge can be used to infer field properties. Mathematically it is a statistical field theory and exploits many of the tools developed for such. Practically, it is a framework for signal processing and image reconstruction.

IFT is fully Bayesian. How else can infinitely many field degrees of freedom be constrained by finite data?
It can be used without the knowledge of Feynman diagrams. There is a full toolbox of methods.
It reproduces many known well working algorithms. This should be reassuring.
And, there were certainly previous works in a similar spirit, like Bayesian Field Theory (BFT).
See below for IFT & BFT publications and previous works.
Anyhow, in many cases IFT provides novel rigorous ways to extract information from data.

Please, have a look! The specific literature is listed below and more general highlight articles on the right hand side.

IFT highlight articles:

2015/03: FAZ: Rätselhafte Blasen der Milchstraße
Galactic anatomy with gamma rays
2014/05: Resolving the radio sky
2013/12: D³PO: Denoising, Deconvolving, and Decomposing Photon Observations
2013/01: NIFTY: Numerical information field theory for everyone
2011/01: Data analysis and steam engines
40 000 Universen
Mathematics of digital senses

IFT introductions:

`Why information field theory *is* a field theory´
Torsten A. Enßlin, May 2015.

`Information field theory' an introduction in a nutshell
Torsten A. Enßlin, in MaxEnt 2012, the 32nd International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, arXiv:1301.2556
(Abstract) (Source) (PDF)

`Astrophysical data analysis with information field theory' advanced recipes, also in a nutshell
Torsten A. Enßlin, accepted chapter to the conference proceedings for MaxEnt 2013, to be published by AIP, arXiv:1404.3701
Abstract) (PDF)

`Bayesian Field Theory: Nonparametric Approaches to Density Estimation, Regression, Classification, and Inverse Quantum Problems'
J. C. Lemm,
(arXiv e-print) and more of his works ...

`Bayesian field theory applied to scattered data interpolation and inverse problems.'
C. Farmer. Algorithms for Approximation, pages 147–166, 2007.

`Information field theory for cosmological perturbation reconstruction and non-linear signal analysis'
Torsten A. Enßlin, Mona Frommert, Francisco S. Kitaura 2009, Phys. Rev. D 80, 105005
(Abstract) (Source) (Postscript) (PDF) (eJournal)

`A path-integral approach to Bayesian inference for inverse problems using the semiclassical approximation'
Joshua C Chang, Van Savage, Tom Chou, submitted, arXiv:1312.2974

(Abstract) (Source) (PDF)

IFT lecture notes and crash course notes.

IFT publications:

`Mathematical foundation of Information Field Dynamics'
Christian Münch, master thesis, Technical University Munich
(Abstract) (Source) (PDF)

`Signal inference with unknown response: calibration uncertainty renormalized estimator'
Sebastian Dorn, Torsten A. Enßlin, Maksim Greiner, Marco Selig, Vanessa Böhm, submitted, arXiv:1410.6289
(Abstract) (PDF)

`Improving self-calibration'
Torsten A. Enßlin, Henrik Junklewitz, Lars Winderling, Maksim Greiner, Marco Selig, Phys. Rev. E in press, arXiv:1312.1349
(Abstract) (PDF)

`Reconstruction of Gaussian and log-normal fields with spectral smoothness'
Niels Oppermann, Marco Selig, Michael R. Bell, Torsten A. Enßlin, 2013, Phys. Rev. E 87, 032136
(Abstract) (Source) (PDF)

`Information field dynamics for simulation scheme construction'
Torsten A. Enßlin, 2013, Phys. Rev. E 87, 013308
(Abstract) (Source) (PDF)

`Reconstructing signals from noisy data with unknown signal and noise covariances'
Niels Oppermann, Georg Robbers, Torsten A. Enßlin, 2011, Physical Review E 84, 041118
(Abstract) (Source) (PDF) (eJournal)

`Reconstruction of signals with unknown spectra in information field theory with parameter uncertainty'
Torsten A. Enßlin, Mona Frommert 2011, Physical Review D 83, 105014
(Abstract) (Source) (PDF) (eJournal)

`Inference with minimal Gibbs free energy in information field theory'
Torsten A. Enßlin, Cornelius Weig 2010, Physical Review E 82, 051112
(Abstract) (Source) (PDF) (eJournal) (Comment on Paper) (Reply to Comment)

and more related papers …

IFT applications:

`Dynamic system classifier'
Daniel Pumpe, Maksim Greiner, Ewald Müller, Torsten A. Enßlin, Physical Review E (Vol.94, No.1)
DOI: 10.1103/PhysRevE.94.012132
(Abstract) (PDF)

`Tomography of the Galactic free electron density with the Square Kilometer Array'
Maksim Greiner, Dominic Schnitzeler, Torsten A. Enßlin, submitted
(Abstract) (PDF)

`Stochastic determination of matrix determinants'
Sebastian Dorn, Torsten A. Enßlin, Phys. Rev. E 92, 013302 (2015)
(Abstract) (PDF)

`A Bayesian method for pulsar template generation'
M. Imgrund, D.J. Champion, M. Kramer, H. Lesch, submitted, arXiv:1501.03497
(Abstract) (PDF)

`All-sky reconstruction of the primordial scalar potential from WMAP temperature data'
Sebastian Dorn, Maksim Greiner, Torsten A. Enßlin, submitted, arXiv:1412.8315
(Abstract) (PDF) (Data)

`The Denoised, Deconvolved, and Decomposed Fermi γ-ray Sky - An Application of the D³PO Algorithm'
Marco Selig, Valentina Vacca, Niels Oppermann, Torsten A. Enßlin, submitted, arXiv:1410.4562
(Abstract) (PDF) (Data)

`Log-transforming the matter power spectrum'
Maksim Greiner, Torsten A. Enßlin, A&A 574, A86 (2015)
(Abstract) (PDF)

`Estimating extragalactic Faraday rotation'
Niels Oppermann, Henrik Junklewitz, Maksim Greiner, Torsten A. Enßlin, Takuya Akahori, Ettore Carretti, Bryan M. Gaensler, Ariel Goobar, Lisa Harvey-Smith, Melanie Johnston-Hollitt, Luke Pratley, Dominic H. F. M. Schnitzeler, Jeroen M. Stil, Valentina Vacca, accepted ba A&A, arXiv:1404.3701
(Abstract) (PDF) (Data)

`A new approach to multi-frequency synthesis in radio interferometry'
Henrik Junklewitz, Michael Bell, Marco Selig, Torsten A. Enßlin, Astronomy & Astrophysics, Volume 581, id.A5 (2015)
(Abstract) (PDF)

`RESOLVE: A new algorithm for aperture synthesis imaging of extended emission in radio astronomy'
Henrik Junklewitz, Michael Bell, Marco Selig, Torsten A. Enßlin, submitted, arXiv:1311.5282
(Abstract) (PDF)

`D³PO - Denoising, Deconvolving, and Decomposing Photon Observations'
Marco Selig, Torsten A. Enßlin, accepted by Physical Review E, arXiv:1311.1888
(Abstract) (Source) (PDF)

`A fast and precise way to calculate the posterior for the local non-Gaussianity parameter f_nl from Cosmic Microwave Background observations'
Sebastian Dorn, Niels Oppermann, Rishi Khatri, Marco Selig, Torsten A. Enßlin, Phys. Rev. D 88, 103516 (2013)
(Abstract) (Source) (PDF) (eJournal)

`Simulation of stochastic network dynamics via entropic matching'
Tiago Ramalho, Marco Selig, Ulrich Gerland, Torsten A. Enßlin, Phys. Rev. E 87, 022719 (2013)
(Abstract) (Source) (PDF)

`The XENON100 exclusion limit without considering Leff as a nuisance parameter'
Jonathan H. Davis, Celine Boehm, Niels Oppermann, Torsten A. Enßlin, Thomas Lacroix, Physical Review D, vol. 86, Issue 1, id. 015027, 2012
(Abstract) (Source) (PDF)

`An improved map of the Galactic Faraday sky'
Niels Oppermann, et al., 2012, Astronomy & Astrophysics, Volume 542, id.A93 (2012)
(Abstract) (Source) (PDF)

`Improving stochastic estimates with inference methods: calculating matrix diagonals'
Marco Selig, Niels Oppermann, Torsten A. Enßlin, Phys. Rev. E 85, 021134 (2012)
(Abstract) (Source) (PDF)(eJournal)

`Probing Magnetic Helicity with Synchrotron Radiation and Faraday Rotation'
Niels Oppermann, Henrik Junklewitz, Georg Robbers, Torsten A. Enßlin 2011, Astronomy and Astrophysics, 530, id.A89
(Abstract) (Source) (PDF)

`Bayesian analysis of spatially distorted cosmic signals from Poissonian data'
Cornelius Weig, Torsten A. Enßlin 2010, MNRAS 409, 1393
(Abstract) (Source) (PDF)

`Bayesian non-linear large scale structure inference of the Sloan Digital Sky Survey data release 7'
Jens Jasche, Francisco S. Kitaura, Cheng Li, Torsten A. Enßlin 2010, MNRAS 409, 355
(Abstract) (Source) (PDF) (eJournal)

`Fast Hamiltonian sampling for large-scale structure inference'
Jens Jasche, Francisco S. Kitaura 2010, MNRAS 407, 29
(Abstract) (Source) (PDF)

`Bayesian power-spectrum inference for Large Scale Structure data'
Jens Jasche, Francisco S. Kitaura, Benjamin D. Wandelt, Torsten A. Enßlin 2010, MNRAS 406, 60
(Abstract) (Source) (PDF)

`Cosmic Cartography of the Large-Scale Structure with Sloan Digital Sky Survey Data Release 6'
Francisco S. Kitaura, Jens Jasche, Cheng Li, Torsten A. Enßlin, R.Benton Metcalf, Benjamin D. Wandelt, Gerard Lemson, Simon D.M. White 2009, MNRAS 400, 183
(Abstract) (Source) (Postscript) (PDF)

other important openly accessible internet publications:

`DIP -- Diagnostics for Insufficiencies of Posterior calculations in Bayesian signal inference'
Sebastian Dorn, Niels Oppermann, Torsten A. Enßlin, Phy. Rev. E 88, 053303 (2013)
(Abstract) (Source) (PDF) (eJournal)

`Lectures on Probability, Entropy, and Statistical Physics'
A. Caticha,
arXiv e-print (arXiv:0808.0012)

`MAGIC: Exact Bayesian Covariance Estimation and Signal Reconstruction for Gaussian Random Fields'
B. Wandelt,
arXiv e-print (arXiv:astro-ph/0401623)

related discussion forums:

Astrostatistics and Astroinformatics Portal, Bayes Forum, a monthly seminar in Garching

useful tools:

`D2O - a distributed data object for parallel high-performance computing in Python'
Theo Steininger, Maksim Greiner, Frederick Beaujean, Torsten A. Enßlin, submitted,  arXiv:1606.05385
(Abstract) (Source) (PDF) (D2O Code)

`SOMBI: Bayesian identification of parameter relations in unstructured  cosmological data'
Philipp Frank, Jens Jasche, and Torsten A. Enßlin, accepted by Astronomy and Astrophysics, arXiv:1602.08497 
(Abstract) (Source) (PDF)

`NIFTY - Numerical Information Field Theory - a versatile Python library for signal inference'
Marco Selig, Michael R. Bell, Henrik Junklewitz, Niels Oppermann, Martin Reinecke, Maksim Greiner, Carlos Pachajoa, Torsten A. Enßlin, Astronomy and Astrophysics 554A, 26 (2013)
(Abstract) (Source) (PDF) (NIFTy Documentation)

`Estimation of probability densities using scale-free field theories'
Justin B. Kinney, submitted, arXiv:1312.6661
(Abstract) (PDF) (Density Estimation using Field Theory (DEFT) code)

SAGE, a free open source software system for mathematics


Torsten Enßlin


IFT & Feynman diagrams

Thermodynamical inference


 Precision Cosmography

Celestial Cartography

Numerical Information Field Theory

D³PO: Denoising, Deconvolving, and Decomposing Photon Observations

Resolving the radio sky

Fermi/D³PO diffuse gamma ray skyThe Denoised, Deconvolved, and Decomposed Fermi gamma-ray sky

Reconstructed primoridial potentialReconstructed primordial gravitational potential