NIFTY - Numerical Information Field Theory - a versatile Python library for signal inference

@article{Selig2013NIFTYN,
  title={NIFTY - Numerical Information Field Theory - a versatile Python library for signal inference},
  author={Marco Selig and Michael R. Bell and H. Junklewitz and Niels Oppermann and Martin Reinecke and Maksim Greiner and Carlos Pachajoa and Torsten A. Ensslin},
  journal={ArXiv},
  year={2013},
  volume={abs/1301.4499}
}
NIFTy, “Numerical Information Field Theory”, is a software package designed to enable the development of signal inference algorithms that operate regardless of the underlying spatial grid and its resolution. Its object-oriented framework is written in Python, although it accesses libraries written in Cython, C++, and C for eciency. NIFTy oers a toolkit that abstracts discretized representations of continuous spaces, fields in these spaces, and operators acting on fields into classes. Thereby… 

Figures and Tables from this paper

NIFTy 3 – Numerical Information Field Theory: A Python Framework for Multicomponent Signal Inference on HPC Clusters

TLDR
NIFTy 3 allows the user to run inference algorithms on massively parallel high performance computing clusters without changing the implementation of the field equations, and supports n‐dimensional Cartesian spaces, spherical spaces, power spaces, and product spaces as well as transforms to their harmonic counterparts.

Information Theory for Fields

  • T. Ensslin
  • Computer Science, Physics
    Annalen der Physik
  • 2019
TLDR
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.

Matrix-free large-scale Bayesian inference in cosmology

TLDR
A new matrix-free implementation of the Wiener sampler which is traditionally applied to high dimensional analysis when signal covariances are unknown is proposed, permitting to cast the complex multivariate inference problem into a sequence of uni-variate random processes.

Information Field Theory and Artificial Intelligence

TLDR
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.

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

TLDR
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.

Encoding prior knowledge in the structure of the likelihood

TLDR
This work investigates a specific transformation of the model parameters based on the multivariate distributional transform, a special form of the reparametrization trick, which flattens the hierarchy and leads to a standard Gaussian prior on all resulting parameters.

Metric Gaussian Variational Inference

TLDR
The proposed Metric Gaussian Variational Inference (MGVI) is an iterative method that performs a series of Gaussian approximations to the posterior that achieves linear scaling by avoiding to store the covariance explicitly at any time.

Denoising, deconvolving, and decomposing multi-domain photon observations

TLDR
D4PO successfully denoised, deconvolved, and decomposed a photon count image into diffuse, point-like and background flux, each being functions of location as well as energy.

Reconstruction of Gaussian and log-normal fields with spectral smoothness

TLDR
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.

Fast and precise way to calculate the posterior for the local non-Gaussianity parameter fnl from cosmic microwave background observations

We present an approximate calculation of the full Bayesian posterior probability distribution for the local non-Gaussianity parameter $f_{\text{nl}}$ from observations of cosmic microwave background
...

References

SHOWING 1-10 OF 42 REFERENCES

Improving stochastic estimates with inference methods: calculating matrix diagonals.

TLDR
Methods of statistical inference are used to improve the accuracy or the computational costs of matrix probing methods to estimate matrix diagonals and the generalized Wiener filter methodology, as developed within information field theory is shown to significantly improve estimates based on only a few sampling probes.

Inference with minimal Gibbs free energy in information field theory

TLDR
The simple concept of minimal Gibbs free energy to IFT is introduced, and it is shown that previous renormalization results emerge naturally and can be understood as being the gaussian approximation to the full posterior probability.

HEALPix: A Framework for High-Resolution Discretization and Fast Analysis of Data Distributed on the Sphere

TLDR
This paper considers the requirements and implementation constraints on a framework that simultaneously enables an efficient discretization with associated hierarchical indexation and fast analysis/synthesis of functions defined on the sphere and demonstrates how these are explicitly satisfied by HEALPix.

Information field theory for cosmological perturbation reconstruction and non-linear signal analysis

TLDR
It is shown that a Gaussian signal, which should resemble the initial density perturbations of the Universe, observed with a strongly nonlinear, incomplete and Poissonian-noise affected response, can be reconstructed thanks to the virtue of a response-renormalization flow equation.

Bayesian power-spectrum inference for large-scale structure data

We describe an exact, flexible, and computationally e cient algorithm for a joint estimation of the large-scale structure and its power-spectrum, building on a Gibbs sampling framework and present

Fast Hamiltonian sampling for large‐scale structure inference

TLDR
A Hamiltonian Monte Carlo (HMC) sampler is employed to obtain samples from a multivariate highly non-Gaussian lognormal Poissonian density posterior given a set of observations to provide an efficient and flexible basis for future high-precision large-scale structure inference.

Libpsht – algorithms for efficient spherical harmonic transforms

TLDR
Libpsht (or “library for performant spherical harmonic transforms”) is a collection of algorithms for efficient conversion between spatial-domain and spectral-domain representations of data defined on the sphere that can be used for a wide range of pixelisations.

Bayesian non-linear large scale structure inference of the Sloan Digital Sky Survey data release 7

TLDR
This work presents the first non-linear, non-Gaussian full Bayesian large-scale structure analysis of the cosmic density field conducted so far, based on the Sloan Digital Sky Survey Data Release 7, which covers the northern galactic cap.

Reconstruction of Gaussian and log-normal fields with spectral smoothness

TLDR
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

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.