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T A Enslin - One of the best experts on this subject based on the ideXlab platform.
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nifty numerical Information Field theory a versatile python library for signal inference
Astronomy and Astrophysics, 2013Co-Authors: Marco Selig, M R Bell, H Junklewitz, Niels Oppermann, M Reinecke, Maksim Greiner, Carlos Pachajoa, T A EnslinAbstract: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, the correct normalization of operations on Fields is taken care of automatically without concerning the user. This allows for an abstract formulation and programming of inference algorithms, including those derived within Information Field theory. Thus, NIFTy permits its user to rapidly prototype algorithms in 1D, and then apply the developed code in higher-dimensional settings of real world problems. The set of spaces on which NIFTy operates comprises point sets, n-dimensional regular grids, spherical spaces, their harmonic counterparts, and product spaces constructed as combinations of those. The functionality and diversity of the package is demonstrated by a Wiener filter code example that successfully runs without modification regardless of the space on which the inference problem is defined.
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Information Field dynamics for simulation scheme construction
Physical Review E, 2013Co-Authors: T A EnslinAbstract:: Information Field dynamics (IFD) is introduced here as a framework to derive numerical schemes for the simulation of physical and other Fields without assuming a particular subgrid structure as many schemes do. IFD constructs an ensemble of nonparametric subgrid Field configurations from the combination of the data in computer memory, representing constraints on possible Field configurations, and prior assumptions on the subgrid Field statistics. Each of these Field configurations can formally be evolved to a later moment since any differential operator of the dynamics can act on Fields living in continuous space. However, these virtually evolved Fields need again a representation by data in computer memory. The maximum entropy principle of Information theory guides the construction of updated data sets via entropic matching, optimally representing these Field configurations at the later time. The Field dynamics thereby become represented by a finite set of evolution equations for the data that can be solved numerically. The subgrid dynamics is thereby treated within auxiliary analytic considerations. The resulting scheme acts solely on the data space. It should provide a more accurate description of the physical Field dynamics than simulation schemes constructed ad hoc, due to the more rigorous accounting of subgrid physics and the space discretization process. Assimilation of measurement data into an IFD simulation is conceptually straightforward since measurement and simulation data can just be merged. The IFD approach is illustrated using the example of a coarsely discretized representation of a thermally excited classical Klein-Gordon Field. This should pave the way towards the construction of schemes for more complex systems like turbulent hydrodynamics.
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inference with minimal gibbs free energy in Information Field theory
Physical Review E, 2010Co-Authors: T A Enslin, Cornelius WeigAbstract: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 posterior probability, which has maximal cross Information with it. We derive optimized estimators for three applications, to illustrate the usage of the framework: (i) reconstruction of a log-normal signal from Poissonian data with background counts and point spread function, as it is needed for gamma ray astronomy and for cosmography using photometric galaxy redshifts, (ii) inference of a Gaussian signal with unknown spectrum, and (iii) inference of a Poissonian log-normal signal with unknown spectrum, the combination of (i) and (ii). Finally we explain how Gaussian knowledge states constructed by the minimal Gibbs free energy principle at different temperatures can be combined into a more accurate surrogate of the non-Gaussian posterior.
Torsten A. Enßlin - One of the best experts on this subject based on the ideXlab platform.
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Consistency and convergence of simulation schemes in Information Field dynamics
Physical Review E, 2018Co-Authors: Martin Dupont, Torsten A. EnßlinAbstract:We explore a new simulation scheme for partial differential equations (PDE's) called Information Field Dynamics (IFD). Information Field dynamics attempts to improve on existing simulation schemes by incorporating Bayesian Field inference, which seeks to preserve the maximum amount of Information about the Field being simulated. The Field inference is truly Bayesian and thus depends on a notion of prior belief. Here, we analytically prove that a restricted subset of simulation schemes in IFD are consistent, and thus deliver valid predictions in the limit of high resolutions. This has not previously been done for any IFD schemes. This restricted subset is roughly analogous to traditional fixed-grid numerical PDE solvers, given the additional restriction of translational symmetry. Furthermore, given an arbitrary IFD scheme modelling a PDE, it is a-priori not obvious to what order the scheme is accurate in space and time. For this subset of models, we also derive an easy rule-of-thumb for determining the order of accuracy of the simulation. As with all analytic consistency analysis, an analysis for nontrivial systems is intractable, thus these results are intended as a general indicator of the validity of the approach, and it is hoped that the results will generalize.
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Radio Imaging With Information Field Theory
arXiv: Instrumentation and Methods for Astrophysics, 2018Co-Authors: Philipp Arras, Henrik Junklewitz, Jakob Knollmüller, Torsten A. EnßlinAbstract:Data from radio interferometers provide a substantial challenge for statisticians. It is incomplete, noise-dominated and originates from a non-trivial measurement process. The signal is not only corrupted by imperfect measurement devices but also from effects like fluctuations in the ionosphere that act as a distortion screen. In this paper we focus on the imaging part of data reduction in radio astronomy and present RESOLVE, a Bayesian imaging algorithm for radio interferometry in its new incarnation. It is formulated in the language of Information Field theory. Solely by algorithmic advances the inference could be sped up significantly and behaves noticeably more stable now. This is one more step towards a fully user-friendly version of RESOLVE which can be applied routinely by astronomers.
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Radio Imaging with Information Field Theory
2018 26th European Signal Processing Conference (EUSIPCO), 2018Co-Authors: Philipp Arras, Jakob Knollrnüller, Henrik Junklewitz, Torsten A. EnßlinAbstract:Data from radio interferometers provide a substantial challenge for statisticians. It is incomplete, noise-dominated and originates from a non-trivial measurement process. The signal is not only corrupted by imperfect measurement devices but also from effects like fluctuations in the ionosphere that act as a distortion screen. In this paper we focus on the imaging part of data reduction in radio astronomy and present RESOLVE, a Bayesian imaging algorithm for radio interferometry in its new incarnation. It is formulated in the language of Information Field theory. Solely by algorithmic advances the inference could be speed up significantly and behaves noticeably more stable now. This is one more step towards a fully user-friendly version of RESOLVE which can be applied routinely by astronomers.
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Cosmic expansion history from SNe Ia data via Information Field theory: the charm code
Astronomy and Astrophysics, 2017Co-Authors: Natalia Porqueres, Torsten A. Enßlin, Maksim Greiner, Vanessa Böhm, Sebastian Dorn, P. Ruiz-lapuente, Alberto ManriqueAbstract:We present charm (cosmic history agnostic reconstruction method), a novel inference algorithm that reconstructs the cosmic expansion history as encoded in the Hubble parameter H ( z ) from SNe Ia data. The novelty of the approach lies in the usage of Information Field theory, a statistical Field theory that is very well suited for the construction of optimal signal recovery algorithms. The charm algorithm infers non-parametrically s ( a ) = ln( ρ ( a ) / ρ crit0 ), the density evolution which determines H ( z ), without assuming an analytical form of ρ ( a ) but only its smoothness with the scale factor a = (1 + z ) -1 . The inference problem of recovering the signal s ( a ) from the data is formulated in a fully Bayesian way. In detail, we have rewritten the signal as the sum of a background cosmology and a perturbation. This allows us to determine the maximum a posteriory estimate of the signal by an iterative Wiener filter method. Applying charm to the Union2.1 supernova compilation, we have recovered a cosmic expansion history that is fully compatible with the standard ΛCDM cosmological expansion history with parameter values consistent with the results of the Planck mission.
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Operator calculus for Information Field theory.
Physical review. E, 2016Co-Authors: Reimar H Leike, Torsten A. EnßlinAbstract:Signal inference problems with non-Gaussian posteriors can be hard to tackle. Through using the concept of Gibbs free energy these posteriors are rephrased as Gaussian posteriors for the price of computing various expectation values with respect to a Gaussian distribution. We present a way of translating these expectation values to a language of operators which is similar to that in quantum mechanics. This simplifies many calculations, for instance such as those involving log-normal priors. The operator calculus is illustrated by deriving a self-calibrating algorithm which is tested with mock data.
Maksim Greiner - One of the best experts on this subject based on the ideXlab platform.
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nifty 3 numerical Information Field theory a python framework for multicomponent signal inference on hpc clusters
arXiv: Instrumentation and Methods for Astrophysics, 2017Co-Authors: Maksim Greiner, Theo Steininger, Jait Dixit, Philipp Frank, Sebastian Hutschenreuter, Jakob KnollmüllerAbstract:NIFTy, "Numerical Information Field Theory", is a software framework designed to ease the development and implementation of Field inference algorithms. Field equations are formulated independently of the underlying spatial geometry allowing the user to focus on the algorithmic design. Under the hood, NIFTy ensures that the discretization of the implemented equations is consistent. This enables the user to prototype an algorithm rapidly in 1D and then apply it to high-dimensional real-world problems. This paper introduces NIFTy 3, a major upgrade to the original NIFTy framework. NIFTy 3 allows the user to run inference algorithms on massively parallel high performance computing clusters without changing the implementation of the Field equations. It supports n-dimensional Cartesian spaces, spherical spaces, power spaces, and product spaces as well as transforms to their harmonic counterparts. Furthermore, NIFTy 3 is able to treat non-scalar Fields. The functionality and performance of the software package is demonstrated with example code, which implements a real inference algorithm from the realm of Information Field theory. NIFTy 3 is open-source software available under the GNU General Public License v3 (GPL-3) at this https URL
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Cosmic expansion history from SNe Ia data via Information Field theory: the charm code
Astronomy and Astrophysics, 2017Co-Authors: Natalia Porqueres, Torsten A. Enßlin, Maksim Greiner, Vanessa Böhm, Sebastian Dorn, P. Ruiz-lapuente, Alberto ManriqueAbstract:We present charm (cosmic history agnostic reconstruction method), a novel inference algorithm that reconstructs the cosmic expansion history as encoded in the Hubble parameter H ( z ) from SNe Ia data. The novelty of the approach lies in the usage of Information Field theory, a statistical Field theory that is very well suited for the construction of optimal signal recovery algorithms. The charm algorithm infers non-parametrically s ( a ) = ln( ρ ( a ) / ρ crit0 ), the density evolution which determines H ( z ), without assuming an analytical form of ρ ( a ) but only its smoothness with the scale factor a = (1 + z ) -1 . The inference problem of recovering the signal s ( a ) from the data is formulated in a fully Bayesian way. In detail, we have rewritten the signal as the sum of a background cosmology and a perturbation. This allows us to determine the maximum a posteriory estimate of the signal by an iterative Wiener filter method. Applying charm to the Union2.1 supernova compilation, we have recovered a cosmic expansion history that is fully compatible with the standard ΛCDM cosmological expansion history with parameter values consistent with the results of the Planck mission.
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Cosmic expansion history from SN Ia data via Information Field theory
arXiv: Cosmology and Nongalactic Astrophysics, 2016Co-Authors: Natalia Porqueres, Torsten A. Enßlin, Maksim Greiner, Vanessa Böhm, Sebastian Dorn, P. Ruiz-lapuente, Alberto ManriqueAbstract:We present a novel inference algorithm that reconstructs the cosmic expansion history as encoded in the Hubble parameter $H(z)$ from SNe Ia data. The novelty of the approach lies in the usage of Information Field theory, a statistical Field theory that is very well suited for the construction of optimal signal recovery algorithms. The algorithm infers non-parametrically $s(a)=\ln(\rho(a)/\rho_{\mathrm{crit}0})$, the density evolution which determines $H(z)$, without assuming an analytical form of $\rho(a)$ but only its smoothness with the scale factor $a=(1+z)^{-1}$. The inference problem of recovering the signal $s(a)$ from the data is formulated in a fully Bayesian way. In detail, we rewrite the signal as the sum of a background cosmology and a perturbation. This allows to determine the maximum a posteriory estimate of the signal by an iterative Wiener filter method. Applying this method to the Union2.1 supernova compilation, we recover a cosmic expansion history that is fully compatible with the standard $\Lambda$CDM cosmological model with parameter values consistent with the results of the Planck mission.
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nifty numerical Information Field theory a versatile python library for signal inference
Astronomy and Astrophysics, 2013Co-Authors: Marco Selig, M R Bell, H Junklewitz, Niels Oppermann, M Reinecke, Maksim Greiner, Carlos Pachajoa, T A EnslinAbstract: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, the correct normalization of operations on Fields is taken care of automatically without concerning the user. This allows for an abstract formulation and programming of inference algorithms, including those derived within Information Field theory. Thus, NIFTy permits its user to rapidly prototype algorithms in 1D, and then apply the developed code in higher-dimensional settings of real world problems. The set of spaces on which NIFTy operates comprises point sets, n-dimensional regular grids, spherical spaces, their harmonic counterparts, and product spaces constructed as combinations of those. The functionality and diversity of the package is demonstrated by a Wiener filter code example that successfully runs without modification regardless of the space on which the inference problem is defined.
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NIFTY – Numerical Information Field Theory - A versatile PYTHON library for signal inference
Astronomy and Astrophysics, 2013Co-Authors: Marco Selig, M R Bell, H Junklewitz, Niels Oppermann, M Reinecke, Maksim Greiner, Carlos Pachajoa, Torsten A. EnßlinAbstract: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, the correct normalization of operations on Fields is taken care of automatically without concerning the user. This allows for an abstract formulation and programming of inference algorithms, including those derived within Information Field theory. Thus, NIFTy permits its user to rapidly prototype algorithms in 1D, and then apply the developed code in higher-dimensional settings of real world problems. The set of spaces on which NIFTy operates comprises point sets, n-dimensional regular grids, spherical spaces, their harmonic counterparts, and product spaces constructed as combinations of those. The functionality and diversity of the package is demonstrated by a Wiener filter code example that successfully runs without modification regardless of the space on which the inference problem is defined.
Carlos Pachajoa - One of the best experts on this subject based on the ideXlab platform.
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nifty numerical Information Field theory a versatile python library for signal inference
Astronomy and Astrophysics, 2013Co-Authors: Marco Selig, M R Bell, H Junklewitz, Niels Oppermann, M Reinecke, Maksim Greiner, Carlos Pachajoa, T A EnslinAbstract: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, the correct normalization of operations on Fields is taken care of automatically without concerning the user. This allows for an abstract formulation and programming of inference algorithms, including those derived within Information Field theory. Thus, NIFTy permits its user to rapidly prototype algorithms in 1D, and then apply the developed code in higher-dimensional settings of real world problems. The set of spaces on which NIFTy operates comprises point sets, n-dimensional regular grids, spherical spaces, their harmonic counterparts, and product spaces constructed as combinations of those. The functionality and diversity of the package is demonstrated by a Wiener filter code example that successfully runs without modification regardless of the space on which the inference problem is defined.
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NIFTY – Numerical Information Field Theory - A versatile PYTHON library for signal inference
Astronomy and Astrophysics, 2013Co-Authors: Marco Selig, M R Bell, H Junklewitz, Niels Oppermann, M Reinecke, Maksim Greiner, Carlos Pachajoa, Torsten A. EnßlinAbstract: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, the correct normalization of operations on Fields is taken care of automatically without concerning the user. This allows for an abstract formulation and programming of inference algorithms, including those derived within Information Field theory. Thus, NIFTy permits its user to rapidly prototype algorithms in 1D, and then apply the developed code in higher-dimensional settings of real world problems. The set of spaces on which NIFTy operates comprises point sets, n-dimensional regular grids, spherical spaces, their harmonic counterparts, and product spaces constructed as combinations of those. The functionality and diversity of the package is demonstrated by a Wiener filter code example that successfully runs without modification regardless of the space on which the inference problem is defined.
Marco Selig - One of the best experts on this subject based on the ideXlab platform.
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nifty numerical Information Field theory a versatile python library for signal inference
Astronomy and Astrophysics, 2013Co-Authors: Marco Selig, M R Bell, H Junklewitz, Niels Oppermann, M Reinecke, Maksim Greiner, Carlos Pachajoa, T A EnslinAbstract: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, the correct normalization of operations on Fields is taken care of automatically without concerning the user. This allows for an abstract formulation and programming of inference algorithms, including those derived within Information Field theory. Thus, NIFTy permits its user to rapidly prototype algorithms in 1D, and then apply the developed code in higher-dimensional settings of real world problems. The set of spaces on which NIFTy operates comprises point sets, n-dimensional regular grids, spherical spaces, their harmonic counterparts, and product spaces constructed as combinations of those. The functionality and diversity of the package is demonstrated by a Wiener filter code example that successfully runs without modification regardless of the space on which the inference problem is defined.
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NIFTY – Numerical Information Field Theory - A versatile PYTHON library for signal inference
Astronomy and Astrophysics, 2013Co-Authors: Marco Selig, M R Bell, H Junklewitz, Niels Oppermann, M Reinecke, Maksim Greiner, Carlos Pachajoa, Torsten A. EnßlinAbstract: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, the correct normalization of operations on Fields is taken care of automatically without concerning the user. This allows for an abstract formulation and programming of inference algorithms, including those derived within Information Field theory. Thus, NIFTy permits its user to rapidly prototype algorithms in 1D, and then apply the developed code in higher-dimensional settings of real world problems. The set of spaces on which NIFTy operates comprises point sets, n-dimensional regular grids, spherical spaces, their harmonic counterparts, and product spaces constructed as combinations of those. The functionality and diversity of the package is demonstrated by a Wiener filter code example that successfully runs without modification regardless of the space on which the inference problem is defined.