Related papers: Information field theory
Quantum field theory (QFT) for interacting many-electron systems is fundamental to condensed matter physics, yet achieving accurate solutions confronts computational challenges in managing the combinatorial complexity of Feynman diagrams,…
This paper describes the Bayesian Technique for Multi-image Analysis (BaTMAn), a novel image-segmentation technique based on Bayesian statistics that characterizes any astronomical dataset containing spatial information and performs a…
Inverse analysis, such as model calibration, often suffers from a lack of informative data in complex real-world scenarios. The standard remedy, designing new experimental setups, is often costly and time-consuming, while readily available…
The nonlinear Fourier transform (NFT) decomposes waveforms propagating through optical fiber into nonlinear degrees of freedom, which are preserved during transmission. By encoding information on the nonlinear spectrum, a transmission…
Item Response Theory (IRT) is a ubiquitous model for understanding human behaviors and attitudes based on their responses to questions. Large modern datasets offer opportunities to capture more nuances in human behavior, potentially…
Iterative Proportional Fitting (IPF), combined with EM, is commonly used as an algorithm for likelihood maximization in undirected graphical models. In this paper, we present two iterative algorithms that generalize upon IPF. The first one…
We give a detailed exposition of the formalism of Kinetic Field Theory (KFT) with emphasis on the perturbative determination of observables. KFT is a statistical non-equilibrium classical field theory based on the path integral formulation…
In inverse problems, one attempts to infer spatially variable functions from indirect measurements of a system. To practitioners of inverse problems, the concept of "information" is familiar when discussing key questions such as which parts…
Dynamical system state estimation and parameter calibration problems are ubiquitous across science and engineering. Bayesian approaches to the problem are the gold standard as they allow for the quantification of uncertainties and enable…
Nonuniform Fourier data are routinely collected in applications such as magnetic resonance imaging, synthetic aperture radar, and synthetic imaging in radio astronomy. To acquire a fast reconstruction that does not require an online inverse…
Integrated information theory (IIT) is a theoretical framework that provides a quantitative measure to estimate when a physical system is conscious, its degree of consciousness, and the complexity of the qualia space that the system is…
Recovery of signals with elements defined on the nodes of a graph, from compressive measurements is an important problem, which can arise in various domains such as sensor networks, image reconstruction and group testing. In some scenarios,…
We introduce neural information field filter, a Bayesian state and parameter estimation method for high-dimensional nonlinear dynamical systems given large measurement datasets. Solving such a problem using traditional methods, such as…
Inverse problems are prevalent in numerous scientific and engineering disciplines, where the objective is to determine unknown parameters within a physical system using indirect measurements or observations. The inherent challenge lies in…
Statistical inference more often than not involves models which are non-linear in the parameters thus leading to non-Gaussian posteriors. Many computational and analytical tools exist that can deal with non-Gaussian distributions, and…
We present an approach to computing spatial information based on Fourier coefficient distributions. The Fourier transform (FT) of an image contains a complete description of the image, and the values of the FT coefficients are uniquely…
Reconstructing astrophysical and cosmological fields from observations is challenging. It requires accounting for non-linear transformations, mixing of spatial structure, and noise. In contrast, forward simulators that map fields to…
Solving inverse problems involving measurement noise and modeling errors requires regularization in order to avoid data overfit. Geophysical inverse problems, in which the Earth's highly heterogeneous structure is unknown, present a…
Choosing an appropriate frequency definition and norm is critical in graph signal sampling and reconstruction. Most previous works define frequencies based on the spectral properties of the graph and use the same frequency definition and…
The main features of the statistical approach to inverse problems are described on the example of a linear model with additive noise. The approach does not use any Bayesian hypothesis regarding an unknown object; instead, the standard…