Related papers: Information field theory
Causal inference quantifies cause-effect relationships by estimating counterfactual parameters from data. This entails using \emph{identification theory} to establish a link between counterfactual parameters of interest and distributions…
Diffusion models have been used as priors for solving inverse problems. However, existing approaches typically overlook side information that could significantly improve reconstruction quality, especially in severely ill-posed settings. In…
A statistical algorithm for categorizing different types of matches and fraud in image databases is presented. The approach is based on a generative model of a graph representing images and connections between pairs of identities, trained…
This work is a follow up on the newly proposed clustering algorithm called The Inverse Square Mean Shift Algorithm. In this paper a special case of algorithm for dealing with non-homogenous data is formulated and the three dimensional Fast…
In cognitive systems, recent emphasis has been placed on studying the cognitive processes of the subject whose behavior was the primary focus of the system's cognitive response. This approach, known as inverse cognition, arises in…
Effective field theories (EFTs) organize the description of complex systems into an infinite sequence of decreasing importance. Predictions are made with a finite number of terms, which induces a truncation error that is often left…
This paper studies the formulation, well-posedness, and numerical solution of Bayesian inverse problems on metric graphs, in which the edges represent one-dimensional wires connecting vertices. We focus on the inverse problem of recovering…
Identifying the relevant coarse-grained degrees of freedom in a complex physical system is a key stage in developing powerful effective theories in and out of equilibrium. The celebrated renormalization group provides a framework for this…
Bayesian optimization is a methodology for global optimization of unknown and expensive objectives. It combines a surrogate Bayesian regression model with an acquisition function to decide where to evaluate the objective. Typical regression…
In information fusion, one is often confronted with the following problem: given a preexisting set of measurements about an unknown quantity, what new measurements should one collect in order to accomplish a given fusion task with optimal…
Inverse statistical physics aims at inferring models compatible with a set of empirical averages estimated from a high-dimensional dataset of independently distributed equilibrium configurations of a given system. However, in several…
The inverse Ising problem consists in inferring the coupling constants of an Ising model given the correlation matrix. The fastest methods for solving this problem are based on mean-field approximations, but which one performs better in the…
One of the main unsolved problems of cosmology is how to maximize the extraction of information from nonlinear data. If the data are nonlinear the usual approach is to employ a sequence of statistics (N-point statistics, counting statistics…
Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…
We present a general theory of fractal transformations and show how it leads to a new type of method for filtering and transforming digital images. This work substantially generalizes earlier work on fractal tops. The approach involves…
Optimization algorithms appear in the core calculations of numerous Artificial Intelligence (AI) and Machine Learning methods, as well as Engineering and Business applications. Following recent works on the theoretical deficiencies of AI, a…
Mathematical methods of step-by-step and combined shifts are proposed for experimental data processing to reconstruct the measuring system impulse response distorted by shift-invariant blur. Proposed methods base on direct non-blind…
We present an Expectation-Maximization algorithm for the fractal inverse problem: the problem of fitting a fractal model to data. In our setting the fractals are Iterated Function Systems (IFS), with similitudes as the family of…
Since the turn of the century, approximate Bayesian inference has steadily evolved as new computational techniques have been incorporated to handle increasingly complex and large-scale predictive problems. The recent success of deep neural…
An inverse nonequispaced fast Fourier transform (iNFFT) is a fast algorithm to compute the Fourier coefficients of a trigonometric polynomial from nonequispaced sampling data. However, various applications such as magnetic resonance imaging…