Related papers: Separating Intrinsic Ambiguity from Estimation Unc…

We consider a class of inverse problems characterized by forward operators that are partially specified, non-smooth, and non-differentiable. Although generative inverse solvers have made significant progress, we find that these forward…

Over the last years, deep learning methods have become an increasingly popular choice to solve tasks from the field of inverse problems. Many of these new data-driven methods have produced impressive results, although most only give point…

Uncertainty quantification for deep learning is a challenging open problem. Bayesian statistics offer a mathematically grounded framework to reason about uncertainties; however, approximate posteriors for modern neural networks still…

Uncertainty plays a crucial role in the machine learning field. Both model trustworthiness and performance require the understanding of uncertainty, especially for models used in high-stake applications where errors can cause cataclysmic…

We present a new approach to the electromagnetic inverse problem that explicitly addresses the ambiguity associated with its ill-posed character. Rather than calculating a single ``best'' solution according to some criterion, our approach…

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…

Obtaining reliable and accurate quantification of uncertainty estimates from deep neural networks is important in safety-critical applications. A well-calibrated model should be accurate when it is certain about its prediction and indicate…

Ambiguity is inherently present in many machine learning tasks, but especially for sequential models seldom accounted for, as most only output a single prediction. In this work we propose an extension of the Multiple Hypothesis Prediction…

Handling missing data is a central challenge in data-driven analysis. Modern imputation methods not only aim for accurate reconstruction but also differ in how they represent and quantify uncertainty. Yet, the reliability and calibration of…

The shape of an object is an important characteristic for many vision problems such as segmentation, detection and tracking. Being independent of appearance, it is possible to generalize to a large range of objects from only small amounts…

Many models in natural language processing define probabilistic distributions over linguistic structures. We argue that (1) the quality of a model' s posterior distribution can and should be directly evaluated, as to whether probabilities…

Blind image deblurring plays a very important role in many vision and multimedia applications. Most existing works tend to introduce complex priors to estimate the sharp image structures for blur kernel estimation. However, it has been…

Deep generative models produce data according to a learned representation, e.g. diffusion models, through a process of approximation computing possible samples. Approximation can be understood as reconstruction and the large datasets used…

Solving ill-posed inverse problems requires careful formulation of prior beliefs over the signals of interest and an accurate description of their manifestation into noisy measurements. Handcrafted signal priors based on e.g. sparsity are…

Generative AI has achieved remarkable empirical success, but from the perspective of statistics it often remains opaque: its predictions may be accurate, yet the underlying mechanism is difficult to interpret, analyze, and trust. This book…

In this paper, we leverage predictive uncertainty of deep neural networks to answer challenging questions material scientists usually encounter in machine learning based materials applications workflows. First, we show that by leveraging…

When building a geometric scene understanding system for autonomous vehicles, it is crucial to know when the system might fail. Most contemporary approaches cast the problem as depth regression, whose output is a depth value for each pixel.…

The CSGM framework (Bora-Jalal-Price-Dimakis'17) has shown that deep generative priors can be powerful tools for solving inverse problems. However, to date this framework has been empirically successful only on certain datasets (for…

Learned image reconstruction techniques using deep neural networks have recently gained popularity, and have delivered promising empirical results. However, most approaches focus on one single recovery for each observation, and thus neglect…

We consider solving ill-posed imaging inverse problems without access to an image prior or ground-truth examples. An overarching challenge in these inverse problems is that an infinite number of images, including many that are implausible,…