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We introduce a new approach for estimating the invariant density of a multidimensional diffusion when dealing with high-frequency observations blurred by independent noises. We consider the intermediate regime, where observations occur at…

Model uncertainty quantification involves measuring and evaluating the uncertainty linked to a model's predictions, helping assess their reliability and confidence. Noise injection is a technique used to enhance the robustness of neural…

Emerging deep-learning (DL)-based techniques have significant potential to revolutionize biomedical imaging. However, one outstanding challenge is the lack of reliability assessment in the DL predictions, whose errors are commonly revealed…

In chemistry, deep neural network models have been increasingly utilized in a variety of applications such as molecular property predictions, novel molecule designs, and planning chemical reactions. Despite the rapid increase in the use of…

Kernel mean embeddings have recently attracted the attention of the machine learning community. They map measures $\mu$ from some set $M$ to functions in a reproducing kernel Hilbert space (RKHS) with kernel $k$. The RKHS distance of two…

A Hilbert space embedding of a distribution---in short, a kernel mean embedding---has recently emerged as a powerful tool for machine learning and inference. The basic idea behind this framework is to map distributions into a reproducing…

Image reconstruction methods based on deep neural networks have shown outstanding performance, equalling or exceeding the state-of-the-art results of conventional approaches, but often do not provide uncertainty information about the…

The eigenvalue distribution of the Hessian matrix plays a crucial role in understanding the optimization landscape of deep neural networks. Prior work has attributed the well-documented ``bulk-and-spike'' spectral structure, where a few…

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…

General Stochastic Hybrid Systems (GSHS) have been formulated to represent various types of uncertainties in hybrid dynamical systems. In this paper, we propose computational techniques for Bayesian estimation of GSHS. In particular, the…

Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…

Reliable models of the thermodynamic properties of materials are critical for industrially relevant applications that require a good understanding of equilibrium phase diagrams, thermal and chemical transport, and microstructure evolution.…

Bayesian Neural Networks (BNNs) offer probability distributions for model parameters, enabling uncertainty quantification in predictions. However, they often underperform compared to deterministic neural networks. Utilizing mutual learning…

Automated medical image segmentation, specifically using deep learning, has shown outstanding performance in semantic segmentation tasks. However, these methods rarely quantify their uncertainty, which may lead to errors in downstream…

This paper explores the extension of the classical two-parameter Weibull distribution to a four-parameter Harris extended Weibull (HEW) distribution. The flexibility of this probability distribution is illustrated by the varying shapes of…

Computational molecular modeling and visualization has seen significant progress in recent years with sev- eral molecular modeling and visualization software systems in use today. Nevertheless the molecular biology community lacks…

Populations of heterogeneous cells play an important role in many biological systems. In this paper we consider systems where each cell can be modelled by an ordinary differential equation. To account for heterogeneity, parameter values are…

Survival models are used in various fields, such as the development of cancer treatment protocols. Although many statistical and machine learning models have been proposed to achieve accurate survival predictions, little attention has been…

Datasets in engineering applications are often limited and contaminated, mainly due to unavoidable measurement noise and signal distortion. Thus, using conventional data-driven approaches to build a reliable discriminative model, and…

Uncertainty estimation aims to evaluate the confidence of a trained deep neural network. However, existing uncertainty estimation approaches rely on low-dimensional distributional assumptions and thus suffer from the high dimensionality of…