相关论文: Sparse Bayesian mass-mapping with uncertainties: l…

Weak lensing convergence maps - upon which higher order statistics can be calculated - can be recovered from observations of the shear field by solving the lensing inverse problem. For typical surveys this inverse problem is ill-posed…

A crucial aspect of mass-mapping, via weak lensing, is quantification of the uncertainty introduced during the reconstruction process. Properly accounting for these errors has been largely ignored to date. We present a new method to…

To date weak gravitational lensing surveys have typically been restricted to small fields of view, such that the $\textit{flat-sky approximation}$ has been sufficiently satisfied. However, with Stage IV surveys ($\textit{e.g. LSST}$ and…

We propose a novel framework for joint magnetic resonance image reconstruction and uncertainty quantification using under-sampled k-space measurements. The problem is formulated as a Bayesian linear inverse problem, where prior…

We consider machine learning techniques to develop low-latency approximate solutions to a class of inverse problems. More precisely, we use a probabilistic approach for the problem of recovering sparse stochastic signals that are members of…

Many recently developed Bayesian methods have focused on sparse signal detection. However, much less work has been done addressing the natural follow-up question: how to make valid inferences for the magnitude of those signals after…

One of the most prominent methods for uncertainty quantification in high-dimen-sional statistics is the desparsified LASSO that relies on unconstrained $\ell_1$-minimization. The majority of initial works focused on real (sub-)Gaussian…

Uncertainty quantification is a crucial step of cosmological mass-mapping that is often ignored. Suggested methods are typically only approximate or make strong assumptions of Gaussianity of the shear field. Probabilistic sampling methods,…

Weak lensing mass-mapping is a useful tool to access the full distribution of dark matter on the sky, but because of intrinsic galaxy ellipticies and finite fields/missing data, the recovery of dark matter maps constitutes a challenging…

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…

Recovering complex-valued image recovery from noisy indirect data is important in applications such as ultrasound imaging and synthetic aperture radar. While there are many effective algorithms to recover point estimates of the magnitude,…

There is a lack of simple and scalable algorithms for uncertainty quantification. Bayesian methods quantify uncertainty through posterior and predictive distributions, but it is difficult to rapidly estimate summaries of these…

Bayesian modelling allows for the quantification of predictive uncertainty which is crucial in safety-critical applications. Yet for many machine learning (ML) algorithms, it is difficult to construct or implement their Bayesian…

In this work, we describe a Bayesian framework for reconstructing the boundaries of piecewise smooth regions in the X-ray computed tomography (CT) problem in an infinite-dimensional setting. In addition to the reconstruction, we are also…

Uncertainty quantification is a critical missing component in radio interferometric imaging that will only become increasingly important as the big-data era of radio interferometry emerges. Statistical sampling approaches to perform…

We investigate the credible sets and marginal credible intervals resulting from the horseshoe prior in the sparse multivariate normal means model. We do so in an adaptive setting without assuming knowledge of the sparsity level (number of…

Sparse signal reconstruction algorithms have attracted research attention due to their wide applications in various fields. In this paper, we present a simple Bayesian approach that utilizes the sparsity constraint and a priori statistical…

Uncertainty quantification is a critical missing component in radio interferometric imaging that will only become increasingly important as the big-data era of radio interferometry emerges. Since radio interferometric imaging requires…

As black box explanations are increasingly being employed to establish model credibility in high-stakes settings, it is important to ensure that these explanations are accurate and reliable. However, prior work demonstrates that…

For civil structures, structural damage due to severe loading events such as earthquakes, or due to long-term environmental degradation, usually occurs in localized areas of a structure. A new sparse Bayesian probabilistic framework for…