Related papers: Solving High-dimensional Inverse Problems Using Am…
We consider the inverse Ising problem, i.e. the inference of network couplings from observed spin trajectories for a model with continuous time Glauber dynamics. By introducing two sets of auxiliary latent random variables we render the…
We present an iterative framework to improve the amortized approximations of posterior distributions in the context of Bayesian inverse problems, which is inspired by loop-unrolled gradient descent methods and is theoretically grounded in…
The efficient resolution of Bayesian inverse problems remains challenging due to the high computational cost of traditional sampling methods. In this paper, we propose a novel framework that integrates Conditional Flow Matching (CFM) with a…
Deep learning models are being used for the analysis of parametric statistical models based on simulation-only frameworks. Bayesian models using normalizing flows simulate data from a prior distribution and are composed of two deep neural…
Two major bottlenecks to the solution of large-scale Bayesian inverse problems are the scaling of posterior sampling algorithms to high-dimensional parameter spaces and the computational cost of forward model evaluations. Yet incomplete or…
With the rapid development of diffusion models and flow-based generative models, there has been a surge of interests in solving noisy linear inverse problems, e.g., super-resolution, deblurring, denoising, colorization, etc, with generative…
Likelihood-free inference involves inferring parameter values given observed data and a simulator model. The simulator is computer code which takes parameters, performs stochastic calculations, and outputs simulated data. In this work, we…
Flow matching is a recent state-of-the-art framework for generative modeling based on ordinary differential equations (ODEs). While closely related to diffusion models, it provides a more general perspective on generative modeling. Although…
Likelihood-free inference (LFI) methods, such as approximate Bayesian computation, have become commonplace for conducting inference in complex models. Many approaches are based on summary statistics or discrepancies derived from synthetic…
In the paper, we develop an ensemble-based implicit sampling method for Bayesian inverse problems. For Bayesian inference, the iterative ensemble smoother (IES) and implicit sampling are integrated to obtain importance ensemble samples,…
Likelihood-free methods perform parameter inference in stochastic simulator models where evaluating the likelihood is intractable but sampling synthetic data is possible. One class of methods for this likelihood-free problem uses a…
Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…
We propose Amortized Posterior Sampling (APS), a novel variational inference approach for efficient posterior sampling in inverse problems. Our method trains a conditional flow model to minimize the divergence between the variational…
Bayesian likelihood-free methods implement Bayesian inference using simulation of data from the model to substitute for intractable likelihood evaluations. Most likelihood-free inference methods replace the full data set with a summary…
This study presents a conditional flow matching framework for solving physics-constrained Bayesian inverse problems. In this setting, samples from the joint distribution of inferred variables and measurements are assumed available, while…
Gravity inversion is a commonly applied data analysis technique in the field of geophysics. While machine learning methods have previously been explored for the problem of gravity inversion, these are deterministic approaches returning a…
Bayesian Likelihood-Free Inference methods yield posterior approximations for simulator models with intractable likelihood. Recently, many works trained neural networks to approximate either the intractable likelihood or the posterior…
Likelihood-free (a.k.a. simulation-based) inference problems are inverse problems with expensive, or intractable, forward models. ODE inverse problems are commonly treated as likelihood-free, as their forward map has to be numerically…
Bayesian inference with computationally expensive likelihood evaluations remains a significant challenge in many scientific domains. We propose normalizing flow regression (NFR), a novel offline inference method for approximating posterior…
Generative models based on flow matching have attracted significant attention for their simplicity and superior performance in high-resolution image synthesis. By leveraging the instantaneous change-of-variables formula, one can directly…