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Artificial Intelligence algorithms have now become pervasive in multiple high-stakes domains. However, their internal logic can be obscure to humans. Explainable Artificial Intelligence aims to design tools and techniques to illustrate the…

In this paper, we present a significant improvement of Quick Hypervolume algorithm, one of the state-of-the-art algorithms for calculating exact hypervolume of the space dominated by a set of d-dimensional points. This value is often used…

The field of explainable artificial intelligence (XAI) attempts to develop methods that provide insight into how complicated machine learning methods make predictions. Many methods of explanation have focused on the concept of feature…

A fundamental problem in statistics and learning theory is to test properties of distributions. We show that quantum computers can solve such problems with significant speed-ups. In particular, we give fast quantum algorithms for testing…

Many problems that cloud operators solve are computationally expensive, and operators often use heuristic algorithms (that are faster and scale better than optimal) to solve them more efficiently. Heuristic analyzers enable operators to…

By any account, the 1998 proof of the Kepler conjecture is complex. The thesis underlying this article is that the proof is complex because it is highly under-automated. Throughout that proof, manual procedures are used where automated ones…

Explainability techniques for data-driven predictive models based on artificial intelligence and machine learning algorithms allow us to better understand the operation of such systems and help to hold them accountable. New transparency…

With the increasing deployment of machine learning systems in practice, transparency and explainability have become serious issues. Contrastive explanations are considered to be useful and intuitive, in particular when it comes to…

In recent years, various machine and deep learning architectures have been successfully introduced to the field of predictive process analytics. Nevertheless, the inherent opacity of these algorithms poses a significant challenge for human…

The Halpern iteration for solving monotone inclusion problems has gained increasing interests in recent years due to its simple form and appealing convergence properties. In this paper, we investigate the inexact variants of the scheme in…

The main promise of quantum computing is to efficiently solve certain problems that are prohibitively expensive for a classical computer. Most problems with a proven quantum advantage involve the repeated use of a black box, or oracle,…

Explainable AI (xAI) interventions aim to improve interpretability for complex black-box models, not only to improve user trust but also as a means to extract scientific insights from high-performing predictive systems. In molecular…

This paper was prompted by numerical experiments we performed, in which algorithms already available in the literature (DVS-BDDM) yielded accelerations (or speedups) many times larger (more than seventy in some examples already treated, but…

Counterfactuals operationalised through algorithmic recourse have become a powerful tool to make artificial intelligence systems explainable. Conceptually, given an individual classified as y -- the factual -- we seek actions such that…

Explainable AI has attracted much research attention in recent years with feature attribution algorithms, which compute "feature importance" in predictions, becoming increasingly popular. However, there is little analysis of the validity of…

Finite element methods typically require a high resolution to satisfactorily approximate micro and even macro patterns of an underlying physical model. This issue can be circumvented by appropriate multiscale strategies that are able to…

The need for transparency of predictive systems based on Machine Learning algorithms arises as a consequence of their ever-increasing proliferation in the industry. Whenever black-box algorithmic predictions influence human affairs, the…

Explaining firm decisions made by algorithms in customer-facing applications is increasingly required by regulators and expected by customers. While the emerging field of Explainable Artificial Intelligence (XAI) has mainly focused on…

Computer Algebra systems are widely spread because of some of their remarkable features such as their ease of use and performance. Nonetheless, this focus on performance sometimes leads to unwanted consequences: algorithms and computations…

Divide-and-conquer methods use large-sample approximations to provide frequentist guarantees when each block of data is both small enough to facilitate efficient computation and large enough to support approximately valid inferences. When…