Pawlak rough set and neighborhood rough set are the two most common rough set theoretical models. Pawlawk can use equivalence classes to represent knowledge, but it cannot process continuous data; neighborhood rough sets can process continuous data, but it loses the ability of using equivalence classes to represent knowledge. To this end, this paper presents a granular-ball rough set based on the granlar-ball computing. The granular-ball rough set can simultaneously represent Pawlak rough sets, and the neighborhood rough set, so as to realize the unified representation of the two. This makes the granular-ball rough set not only can deal with continuous data, but also can use equivalence classes for knowledge representation. In addition, we propose an implementation algorithms of granular-ball rough sets. The experimental resuts on benchmark datasets demonstrate that, due to the combination of the robustness and adaptability of the granular-ball computing, the learning accuracy of the granular-ball rough set has been greatly improved compared with the Pawlak rough set and the traditional neighborhood rough set. The granular-ball rough set also outperforms nine popular or the state-of-the-art feature selection methods.

Increasing complexity comes from some factors including uncertainty, ambiguity, inconsistency, multiple dimensionalities, increasing the number of effective factors and relation between them. Some of these features are common among most real-world problems which are considered complex and dynamic problems. In other words, since the data and relations in real world applications are usually highly complex and inaccurate, modeling real complex systems based on observed data is a challenging task especially for large scale, inaccurate and non stationary datasets. Therefore, to cover and address these difficulties, the existence of a computational system with the capability of extracting knowledge from the complex system with the ability to simulate its behavior is essential. In other words, it is needed to find a robust approach and solution to handle real complex problems in an easy and meaningful way [1]. Hard computing methods depend on quantitative values with expensive solutions and lack of ability to represent the problem in real life due to some uncertainties. In contrast, soft computing approaches act as alternative tools to deal with the reasoning of complex problems [2]. Using soft computing methods such as fuzzy logic, neural network, genetic algorithms or a combination of these allows achieving robustness, tractable and more practical solutions. Generally, two types of methods are used for analyzing and modeling dynamic systems including quantitative and qualitative approaches.

Approximate Bayesian inference methods provide a powerful suite of tools for finding approximations to intractable posterior distributions. However, machine learning applications typically involve selecting actions, which -- in a Bayesian setting -- depend on the posterior distribution only via its contribution to expected utility. A growing body of work on loss-calibrated approximate inference methods has therefore sought to develop posterior approximations sensitive to the influence of the utility function. Here we introduce loss-calibrated expectation propagation (Loss-EP), a loss-calibrated variant of expectation propagation. This method resembles standard EP with an additional factor that "tilts" the posterior towards higher-utility decisions. We show applications to Gaussian process classification under binary utility functions with asymmetric penalties on False Negative and False Positive errors, and show how this asymmetry can have dramatic consequences on what information is "useful" to capture in an approximation.

We develop a structural econometric model to capture the decision dynamics of human evaluators on an online micro-lending platform, and estimate the model parameters using a real-world dataset. We find two types of biases in gender, preference-based bias and belief-based bias, are present in human evaluators' decisions. Both types of biases are in favor of female applicants. Through counterfactual simulations, we quantify the effect of gender bias on loan granting outcomes and the welfare of the company and the borrowers. Our results imply that both the existence of the preference-based bias and that of the belief-based bias reduce the company's profits. When the preference-based bias is removed, the company earns more profits. When the belief-based bias is removed, the company's profits also increase. Both increases result from raising the approval probability for borrowers, especially male borrowers, who eventually pay back loans. For borrowers, the elimination of either bias decreases the gender gap of the true positive rates in the credit risk evaluation. We also train machine learning algorithms on both the real-world data and the data from the counterfactual simulations. We compare the decisions made by those algorithms to see how evaluators' biases are inherited by the algorithms and reflected in machine-based decisions. We find that machine learning algorithms can mitigate both the preference-based bias and the belief-based bias.

Humans ability to transfer knowledge through teaching is one of the essential aspects for human intelligence. A human teacher can track the knowledge of students to customize the teaching on students needs. With the rise of online education platforms, there is a similar need for machines to track the knowledge of students and tailor their learning experience. This is known as the Knowledge Tracing (KT) problem in the literature. Effectively solving the KT problem would unlock the potential of computer-aided education applications such as intelligent tutoring systems, curriculum learning, and learning materials' recommendation. Moreover, from a more general viewpoint, a student may represent any kind of intelligent agents including both human and artificial agents. Thus, the potential of KT can be extended to any machine teaching application scenarios which seek for customizing the learning experience for a student agent (i.e., a machine learning model). In this paper, we provide a comprehensive and systematic review for the KT literature. We cover a broad range of methods starting from the early attempts to the recent state-of-the-art methods using deep learning, while highlighting the theoretical aspects of models and the characteristics of benchmark datasets. Besides these, we shed light on key modelling differences between closely related methods and summarize them in an easy-to-understand format. Finally, we discuss current research gaps in the KT literature and possible future research and application directions.

We seek to appoint an assistant or associate professor in the general area of Uncertainty in AI, who is passionate about research as well as teaching. We particularly welcome excellent candidates that can contribute to foundational aspects of AI and machine learning.The successful candidate will help with developing and/or delivering courses in DAI cluster, such as Foundations of AI, Explainable AI, Text Mining, Reinforcement Learning, Uncertainty Representation and Reasoning, and Generative Models, and will supervise students at all levels. The working language in the department and across the university is English. An important aspect of TU/e's vision on education is that research and education go hand in hand, both at Bachelor and Master level.Next to your research, education is an important part of your job.The TU/e helps its scientific staff to further develop their teaching skills by offering a training program that leads to an official teaching certification from Dutch Universities (Basic Teaching Qualification).Furthermore, you should have: Are you inspired to work for the exciting Department of Mathematics and Computer Science at TU Eindhoven? We're looking for you as our new faculty member to expand our academic staff in the Data and AI cluster.

Classification models are a fundamental component of physical-asset management technologies such as structural health monitoring (SHM) systems and digital twins. Previous work introduced \textit{risk-based active learning}, an online approach for the development of statistical classifiers that takes into account the decision-support context in which they are applied. Decision-making is considered by preferentially querying data labels according to \textit{expected value of perfect information} (EVPI). Although several benefits are gained by adopting a risk-based active learning approach, including improved decision-making performance, the algorithms suffer from issues relating to sampling bias as a result of the guided querying process. This sampling bias ultimately manifests as a decline in decision-making performance during the later stages of active learning, which in turn corresponds to lost resource/utility. The current paper proposes two novel approaches to counteract the effects of sampling bias: \textit{semi-supervised learning}, and \textit{discriminative classification models}. These approaches are first visualised using a synthetic dataset, then subsequently applied to an experimental case study, specifically, the Z24 Bridge dataset. The semi-supervised learning approach is shown to have variable performance; with robustness to sampling bias dependent on the suitability of the generative distributions selected for the model with respect to each dataset. In contrast, the discriminative classifiers are shown to have excellent robustness to the effects of sampling bias. Moreover, it was found that the number of inspections made during a monitoring campaign, and therefore resource expenditure, could be reduced with the careful selection of the statistical classifiers used within a decision-supporting monitoring system.

A wide range of modern applications, especially in Bayesian inference framework [1], require the study of probability density functions (pdfs) which can be evaluated stochastically, i.e., only noisy evaluations can be obtained [2, 3, 4, 5]. For instance, this is the case of the pseudo-marginal approaches and doubly intractable posteriors [6, 7], approximate Bayesian computation (ABC) and likelihood-free schemes [8, 9], where the target density cannot be computed in closed-form. The noisy scenario also appears naturally when mini-batches of data are employed instead of considering the complete likelihood of huge amounts of data [10, 11]. More recently, the analysis of noisy functions of densities is required in reinforcement learning (RL), especially in direct policy search which is an important branch of RL, with applications in robotics [12, 13]. The topic of inference in noisy settings (or where a function is known with a certain degree of uncertainty) is also of interest in the inverse problem literature, such as in the calibration of expensive computer codes [14, 15]. This is also the case when the construction of an emulator is considered, as a surrogate model [4, 16, 17].

Understanding capabilities and limitations of different network architectures is of fundamental importance to machine learning. Bayesian inference on Gaussian processes has proven to be a viable approach for studying recurrent and deep networks in the limit of infinite layer width, $n\to\infty$. Here we present a unified and systematic derivation of the mean-field theory for both architectures that starts from first principles by employing established methods from statistical physics of disordered systems. The theory elucidates that while the mean-field equations are different with regard to their temporal structure, they yet yield identical Gaussian kernels when readouts are taken at a single time point or layer, respectively. Bayesian inference applied to classification then predicts identical performance and capabilities for the two architectures. Numerically, we find that convergence towards the mean-field theory is typically slower for recurrent networks than for deep networks and the convergence speed depends non-trivially on the parameters of the weight prior as well as the depth or number of time steps, respectively. Our method exposes that Gaussian processes are but the lowest order of a systematic expansion in $1/n$. The formalism thus paves the way to investigate the fundamental differences between recurrent and deep architectures at finite widths $n$.

Rule-based classifier, that extract a subset of induced rules to efficiently learn/mine while preserving the discernibility information, plays a crucial role in human-explainable artificial intelligence. However, in this era of big data, rule induction on the whole datasets is computationally intensive. So far, to the best of our knowledge, no known method focusing on accelerating rule induction has been reported. This is first study to consider the acceleration technique to reduce the scale of computation in rule induction. We propose an accelerator for rule induction based on fuzzy rough theory; the accelerator can avoid redundant computation and accelerate the building of a rule classifier. First, a rule induction method based on consistence degree, called Consistence-based Value Reduction (CVR), is proposed and used as basis to accelerate. Second, we introduce a compacted search space termed Key Set, which only contains the key instances required to update the induced rule, to conduct value reduction. The monotonicity of Key Set ensures the feasibility of our accelerator. Third, a rule-induction accelerator is designed based on Key Set, and it is theoretically guaranteed to display the same results as the unaccelerated version. Specifically, the rank preservation property of Key Set ensures consistency between the rule induction achieved by the accelerator and the unaccelerated method. Finally, extensive experiments demonstrate that the proposed accelerator can perform remarkably faster than the unaccelerated rule-based classifier methods, especially on datasets with numerous instances.