Related papers: Uncertainty quantification for wide-bin unfolding:…
In this work, we investigate the use of Besov priors in the context of Bayesian inverse problems. The solution to Bayesian inverse problems is the posterior distribution which naturally enables us to interpret the uncertainties. Besov…
Deep unrolling, or unfolding, is an emerging learning-to-optimize method that unrolls a truncated iterative algorithm in the layers of a trainable neural network. However, the convergence guarantees and generalizability of the unrolled…
Quantifying a model's predictive uncertainty is essential for safety-critical applications such as autonomous driving. We consider quantifying such uncertainty for multi-object detection. In particular, we leverage conformal prediction to…
Statistical learning algorithms provide a generally-applicable framework to sidestep time-consuming experiments, or accurate physics-based modeling, but they introduce a further source of error on top of the intrinsic limitations of the…
The reconstruction of an unknown quantity from noisy measurements is a mathematical problem relevant in most applied sciences, for example, in medical imaging, radar inverse scattering, or astronomy. This underlying mathematical problem is…
The determination of transverse single-spin asymmetries in experiments involving polarized targets and/or beams may encounter challenges when (1) the magnitude of the polarization varies greatly with time, (2) the polarization magnitude is…
Deep unfolding is a method of growing popularity that fuses iterative optimization algorithms with tools from neural networks to efficiently solve a range of tasks in machine learning, signal and image processing, and communication systems.…
We address functional uncertainty quantification for ill-posed inverse problems where it is possible to evaluate a possibly rank-deficient forward model, the observation noise distribution is known, and there are known parameter…
The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…
Bayesian optimisation (BO) has been a successful approach to optimise functions which are expensive to evaluate and whose observations are noisy. Classical BO algorithms, however, do not account for errors about the location where…
When reading peer-reviewed scientific literature describing any analysis of empirical data, it is natural and correct to proceed with the underlying assumption that experiments have made good faith efforts to ensure that their analyses…
Bayesian inference is applied directly to the problem of unfolding. The outcome is a posterior probability density for the spectrum before smearing, defined in the multi-dimensional space of all possible spectra. Regularization consists in…
Rigorous statistical methods, including parameter estimation with accompanying uncertainties, underpin the validity of scientific discovery, especially in the natural sciences. With increasingly complex data models such as deep learning…
Unfolding problems often arise in the context of statistical data analysis. Such problematics occur when the probability distribution of a physical quantity is to be measured, but it is randomized (smeared) by some well understood process,…
Scientific imaging problems are often severely ill-posed, and hence have significant intrinsic uncertainty. Accurately quantifying the uncertainty in the solutions to such problems is therefore critical for the rigorous interpretation of…
In many safety-critical applications such as autonomous driving and surgical robots, it is desirable to obtain prediction uncertainties from object detection modules to help support safe decision-making. Specifically, such modules need to…
Optimization-based solvers play a central role in a wide range of signal processing and communication tasks. However, their applicability in latency-sensitive systems is limited by the sequential nature of iterative methods and the high…
A selection of unfolding methods commonly used in High Energy Physics is compared. The methods discussed here are: bin-by-bin correction factors, matrix inversion, template fit, Tikhonov regularisation and two examples of iterative methods.…
Uncertainty quantification is essential when dealing with ill-conditioned inverse problems due to the inherent nonuniqueness of the solution. Bayesian approaches allow us to determine how likely an estimation of the unknown parameters is…
Inverse scattering problems, such as those in electromagnetic imaging using phaseless data (PD-ISPs), involve imaging objects using phaseless measurements of wave scattering. Such inverse problems can be highly non-linear and ill-posed…