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A novel correction algorithm is proposed for multi-class classification problems with corrupted training data. The algorithm is non-intrusive, in the sense that it post-processes a trained classification model by adding a correction…

Inverse problems aim to determine model parameters of a mathematical problem from given observational data. Neural networks can provide an efficient tool to solve these problems. In the context of Bayesian inverse problems, Uncertainty…

This paper deals with the problem of finding suboptimal values of an unknown function on the basis of measured data corrupted by bounded noise. As a prior, we assume that the unknown function is parameterized in terms of a number of basis…

Traditional supervised denoisers are trained using pairs of noisy input and clean target images. They learn to predict a central tendency of the posterior distribution over possible clean images. When, e.g., trained with the popular…

We present a coupled Variational Auto-Encoder (VAE) method that improves the accuracy and robustness of the probabilistic inferences on represented data. The new method models the dependency between input feature vectors (images) and weighs…

In this paper, we introduce a novel unsupervised network to denoise microscopy videos featured by image sequences captured by a fixed location microscopy camera. Specifically, we propose a DeepTemporal Interpolation method, leveraging a…

Subsampled blind deconvolution is the recovery of two unknown signals from samples of their convolution. To overcome the ill-posedness of this problem, solutions based on priors tailored to specific application have been developed in…

Machine learning methods for computational imaging require uncertainty estimation to be reliable in real settings. While Bayesian models offer a computationally tractable way of recovering uncertainty, they need large data volumes to be…

We present a likelihood-free probabilistic inversion method based on normalizing flows for high-dimensional inverse problems. The proposed method is composed of two complementary networks: a summary network for data compression and an…

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…

We consider the problem of Bayesian regression with trustworthy uncertainty quantification. We define that the uncertainty quantification is trustworthy if the ground truth can be captured by intervals dependent on the predictive…

Hyperparameter tuning is a challenging problem especially when the system itself involves uncertainty. Due to noisy function evaluations, optimization under uncertainty can be computationally expensive. In this paper, we present a novel…

In this work, a method for obtaining pixel-wise error bounds in Bayesian regularization of inverse imaging problems is introduced. The proposed method employs estimates of the posterior variance together with techniques from conformal…

Uncertainty quantification in inverse medical imaging tasks with deep learning has received little attention. However, deep models trained on large data sets tend to hallucinate and create artifacts in the reconstructed output that are not…

Discrete diffusion language models learn to reconstruct text from randomly masked inputs, yet under mild assumptions their denoiser already implements the exact Bayesian posterior over the original tokens. We prove that the expected…

The US Census Bureau will deliberately corrupt data sets derived from the 2020 US Census, enhancing the privacy of respondents while potentially reducing the precision of economic analysis. To investigate whether this trade-off is…

Sample-based Bayesian inference provides a route to uncertainty quantification in the geosciences, and inverse problems in general, though is very computationally demanding in the naive form that requires simulating an accurate computer…

Reduced-rank regression recognises the possibility of a rank-deficient matrix of coefficients. We propose a novel Bayesian model for estimating the rank of the coefficient matrix, which obviates the need for post-processing steps and allows…

Plasma diagnostics often employ computerized tomography to estimate emissivity profiles from a finite, and often limited, number of line-integrated measurements. Decades of algorithmic refinement have brought considerable improvements, and…

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…