Related papers: A Variational Inference Approach to Inverse Proble…

Adapting pretrained diffusion models to downstream objectives such as inverse problems often requires expensive test-time guidance or optimization. We propose a principled framework for generating high-quality reward-aligned samples at…

Bayesian inference for high-dimensional inverse problems is computationally costly and requires selecting a suitable prior distribution. Amortized variational inference addresses these challenges via a neural network that approximates the…

We propose Bayesian Hierarchical Invariant Prediction (BHIP) reframing Invariant Causal Prediction (ICP) through the lens of Hierarchical Bayes. We leverage the hierarchical structure to explicitly test invariance of causal mechanisms under…

Mixture models are widely used in Bayesian statistics and machine learning, in particular in computational biology, natural language processing and many other fields. Variational inference, a technique for approximating intractable…

Solving high-dimensional Bayesian inverse problems (BIPs) with the variational inference (VI) method is promising but still challenging. The main difficulties arise from two aspects. First, VI methods approximate the posterior distribution…

Computer models play a crucial role in numerous scientific and engineering domains. To ensure the accuracy of simulations, it is essential to properly calibrate the input parameters of these models through statistical inference. While…

Quantifying uncertainty and updating reliability are essential for ensuring the safety and performance of engineering systems. This study develops a hierarchical Bayesian modeling (HBM) framework to quantify uncertainty and update…

In recent years, neural networks have revolutionized various domains, yet challenges such as hyperparameter tuning and overfitting remain significant hurdles. Bayesian neural networks offer a framework to address these challenges by…

Many scientific investigations require that the values of a set of model parameters are estimated using recorded data. In Bayesian inference, information from both observed data and prior knowledge is combined to update model parameters…

Variational inference offers scalable and flexible tools to tackle intractable Bayesian inference of modern statistical models like Bayesian neural networks and Gaussian processes. For largely over-parameterized models, however, the…

Bayesian inference for inverse problems hinges critically on the choice of priors. In the absence of specific prior information, population-level distributions can serve as effective priors for parameters of interest. With the advent of…

Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter…

Inverse problems are characterized by their inherent non-uniqueness and sensitivity with respect to data perturbations. Their stable solution requires the application of regularization methods including variational and iterative…

In this paper, we address the fundamental problem of line spectral estimation in a Bayesian framework. We target model order and parameter estimation via variational inference in a probabilistic model in which the frequencies are…

Differential analysis is a routine procedure in the statistical analysis toolbox across many applied fields, including quantitative proteomics, the main illustration of the present paper. The state-of-the-art limma approach uses a…

The main challenge in Bayesian models is to determine the posterior for the model parameters. Already, in models with only one or few parameters, the analytical posterior can only be determined in special settings. In Bayesian neural…

The choice of the parameter value for regularized inverse problems is critical to the results and remains a topic of interest. This article explores a criterion for selecting a good parameter value by maximizing the probability of the data,…

The Bayesian approach to solving inverse problems relies on the choice of a prior. This critical ingredient allows the formulation of expert knowledge or physical constraints in a probabilistic fashion and plays an important role for the…

In statistical applications, it is common to encounter parameters supported on a varying or unknown dimensional space. Examples include the fused lasso regression, the matrix recovery under an unknown low rank, etc. Despite the ease of…

A Bayesian hierarchical model for total variation regularisation is presented in this paper. All the parameters of an inverse problem, including the "regularisation parameter", are estimated simultaneously from the data in the model. The…