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Uncertainty quantification (UQ) in scientific machine learning is increasingly critical as neural networks are widely adopted to tackle complex problems across diverse scientific disciplines. For physics-informed neural networks (PINNs), a…

Bringing deep neural networks (DNNs) into safety critical applications such as automated driving, medical imaging and finance, requires a thorough treatment of the model's uncertainties. Training deep neural networks is already resource…

We show that training a deep network using batch normalization is equivalent to approximate inference in Bayesian models. We further demonstrate that this finding allows us to make meaningful estimates of the model uncertainty using…

Modern machine learning (ML) systems excel in recognising and classifying images with remarkable accuracy. However, like many computer software systems, they can fail by generating confusing or erroneous outputs or by deferring to human…

Ubiquitous applications of Deep neural networks (DNNs) in different artificial intelligence systems have led to their adoption in solving challenging visualization problems in recent years. While sophisticated DNNs offer an impressive…

Spectrum sensing is of critical importance in any cognitive radio system. When the primary user's signal has uncertain parameters, the likelihood ratio test, which is the theoretically optimal detector, generally has no closed-form…

We investigate the problem of weight uncertainty originally proposed by [Blundell et al. (2015). Weight uncertainty in neural networks. In International conference on machine learning, 1613-1622, PMLR.] in the context of neural networks…

Deep neural networks (DNNs) have received tremendous attention and achieved great success in various applications, such as image and video analysis, natural language processing, recommendation systems, and drug discovery. However, inherent…

As a compact representation of joint probability distributions over a dependence graph of random variables, and a tool for modelling and reasoning in the presence of uncertainty, Bayesian networks are of great importance for artificial…

Bayesian Neural Networks (BNNs) often result uncalibrated after training, usually tending towards overconfidence. Devising effective calibration methods with low impact in terms of computational complexity is thus of central interest. In…

Explainable AI (XAI) aims to provide interpretations for predictions made by learning machines, such as deep neural networks, in order to make the machines more transparent for the user and furthermore trustworthy also for applications in…

When the historical data are limited, the conditional probabilities associated with the nodes of Bayesian networks are uncertain and can be empirically estimated. Second order estimation methods provide a framework for both estimating the…

Quantum machine learning promises great speedups over classical algorithms, but it often requires repeated computations to achieve a desired level of accuracy for its point estimates. Bayesian learning focuses more on sampling from…

Machine Learning is a powerful tool to reveal and exploit correlations in a multi-dimensional parameter space. Making predictions from such correlations is a highly non-trivial task, in particular when the details of the underlying dynamics…

Deep learning has been successfully applied to the segmentation of 3D Computed Tomography (CT) scans. Establishing the credibility of these segmentations requires uncertainty quantification (UQ) to identify untrustworthy predictions. Recent…

This chapter explores neural networks, topological data analysis, and topological deep learning techniques, alongside statistical Bayesian methods, for processing images, time series, and graphs to maximize the potential of artificial…

We explore Bayesian reasoning as a means to quantify uncertainty in neural networks for question answering. Starting with a multilayer perceptron on the Iris dataset, we show how posterior inference conveys confidence in predictions. We…

Deep neural networks have achieved impressive results on a wide variety of tasks. However, quantifying uncertainty in the network's output is a challenging task. Bayesian models offer a mathematical framework to reason about model…

The accessibility of spatially distributed data, enabled by affordable sensors, field, and numerical experiments, has facilitated the development of data-driven solutions for scientific problems, including climate change, weather…

Deep Neural Networks (DNNs) have performed admirably in classification tasks. However, the characterization of their classification uncertainties, required for certain applications, has been lacking. In this work, we investigate the issue…