Related papers: The Bethe approximation for solving the inverse Is…
Bayesian inference on non-Gaussian data is often non-analytic and requires computationally expensive approximations such as sampling or variational inference. We propose an approximate inference framework primarily designed to be…
The asymmetric exclusion process on a ring in one-dimension is considered with a single defect particle. The steady state has previously been solved by a matrix product method. Here we use the Bethe ansatz to solve exactly for the long time…
We present a systematic small-correlation expansion to solve the inverse Ising problem: find a set of couplings and fields corresponding to a given set of correlations and magnetizations. Couplings are calculated up to the third order in…
We give further support to Smirnov's conjecture on the exact kink S-matrix for the massive Quantum Field Theory describing the integrable perturbation of the c=0.7 minimal Conformal Field theory (known to describe the tri-critical Ising…
The present paper proposes a Bayesian framework for inverse problems that seamlessly integrates optimization and inversion to enable rapid surrogate modeling, accurate parameter inference, and rigorous uncertainty quantification. Bayesian…
In a non supervised Bayesian estimation approach for inverse problems in imaging systems, one tries to estimate jointly the unknown image pixels $f$ and the hyperparameters $\theta$ given the observed data $g$ and a model $M$ linking these…
Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…
The transverse-field Ising model is widely studied as one of the simplest quantum spin systems. It is known that this model exhibits a phase transition at the critical inverse temperature $\beta_{\mathrm{c}}$, which is determined by the…
This article addresses the issue of estimating observation parameters (response and error parameters) in inverse problems. The focus is on cases where regularization is introduced in a Bayesian framework and the prior is modeled by a…
Forward and inverse models are used throughout different engineering fields to predict and understand the behaviour of systems and to find parameters from a set of observations. These models use root-finding and minimisation techniques…
While learning the maximum likelihood value of parameters of an undirected graphical model is hard, modelling the posterior distribution over parameters given data is harder. Yet, undirected models are ubiquitous in computer vision and text…
In indirect measurements, the measurand is determined by solving an inverse problem which requires a model of the measurement process. Such models are often approximations and introduce systematic errors leading to a bias of the posterior…
This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a…
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…
Inverse problems, i.e., estimating parameters of physical models from experimental data, are ubiquitous in science and engineering. The Bayesian formulation is the gold standard because it alleviates ill-posedness issues and quantifies…
When an inverse problem is solved by a gradient-based optimization algorithm, the corresponding forward and adjoint problems, which are introduced to compute the gradient, can be also solved iteratively. The idea of iterating at the same…
Neural networks are popular state-of-the-art models for many different tasks.They are often trained via back-propagation to find a value of the weights that correctly predicts the observed data. Although back-propagation has shown good…
The exact perturbation approach is used to derive the (seven) elementary correlation lengths and related mass gaps of the two-dimensional dilute A$_4$ lattice model in regime 2- from the Bethe ansatz solution. This model provides a…
Variational inference in probabilistic graphical models aims to approximate fundamental quantities such as marginal distributions and the partition function. Popular approaches are the Bethe approximation, tree-reweighted, and other types…
The Ising model is important in statistical modeling and inference in many applications, however its normalizing constant, mean number of active vertices and mean spin interaction -- quantities needed in inference -- are computationally…