Search Results (7)

Imprecise probability models generated from data represent epistemic uncertainty by replacing the precise empirical distribution with a set of compatible probability distributions. When this set is described by reachable probability intervals, the induced bounds are tight, so the represented imprecision is not inflated by unattainable interval limits. This paper studies the informational effect of this replacement through the epistemic entropy gap, defined as the difference between the maximum entropy over the induced credal set and the Shannon entropy of the empirical distribution. The gap is a differential quantity: it measures the additional uncertainty introduced by the imprecise model beyond the observed frequencies. We analyze it for three reachable interval models generated from multinomial data: the Imprecise Dirichlet Model, the $ϵ$-contamination model and the approximated Non-Parametric Predictive Inference model. The analysis covers its main properties, its asymptotic behavior and its role in entropy equivalent calibration of model parameters. The results show that the entropy gap offers a common informational scale for comparing how different imprecise models represent the same empirical evidence, and helps interpret the degree of caution associated with limited data reliability and with empirical distributions that may otherwise lead to overconfident uncertainty assessments. Full article

Class imbalance remains a significant challenge in classification, often leading to poor generalization on underrepresented classes. While Oversampling methods mitigate this issue by replicating minority class instances to balance class distributions, they typically overlook the informativeness of individual samples. In this paper, we propose an entropy-guided data selection strategy that dynamically prioritizes samples exhibiting frequent prediction changes during training, that is, those with high predictive entropy. Such uncertain samples are expected to contribute more effectively to the learning process. Moreover, we incorporate a credal set-based weighting scheme that adjusts class-wise selection probabilities according to global imbalance severity, quantified using the Gini coefficient. This adjustment penalizes overrepresented classes while increasing the sampling probability of rare but uncertain examples. Experiments on benchmark datasets show that the proposed method improves overall classification performance across imbalanced data settings, while also showing a more balanced trade-off across head, body, and tail classes. Full article

As the penetration rate of distributed power sources increases and distribution network structures grow increasingly complex, the uncertainty in switch action control during load transfer has become a critical issue affecting grid safety and reliability. Traditional control methods based on precise probability-based predictive control are susceptible to bias introduced by prior settings under small-sample conditions, making it difficult to meet the stringent requirements of time-synchronized control. To address this, this study proposes an imprecise probability-based synchronous load transfer control method for distribution networks. By integrating the Imprecise Dirichlet model (IDM) with a Naive Credal Classifier (NCC), it constructs an interval predictive control model for switching action timing. This approach effectively mitigates the prior dependency issue and enhances estimation robustness under small-sample conditions. Combined with a dynamic delay strategy, this approach strictly controls the interval between disconnection and reconnection actions within 20 ms, preventing circulating current risks and ensuring transfer reliability. The simulation and experimental results demonstrate that the proposed method outperforms traditional Bayesian classifiers in both time prediction control accuracy and model robustness, providing a theoretical foundation and a reference for engineering applications for secure action control in distribution networks. Full article

In the literature on imprecise probability, little attention is paid to the fact that imprecise probabilities are precise on a set of events. We call these sets systems of precision. We show that, under mild assumptions, the system of precision of a lower and upper probability form a so-called (pre-)Dynkin system. Interestingly, there are several settings, ranging from machine learning on partial data over frequential probability theory to quantum probability theory and decision making under uncertainty, in which, a priori, the probabilities are only desired to be precise on a specific underlying set system. Here, (pre-)Dynkin systems have been adopted as systems of precision, too. We show that, under extendability conditions, those pre-Dynkin systems equipped with probabilities can be embedded into algebras of sets. Surprisingly, the extendability conditions elaborated in a strand of work in quantum probability are equivalent to coherence from the imprecise probability literature. On this basis, we spell out a lattice duality which relates systems of precision to credal sets of probabilities. We conclude the presentation with a generalization of the framework to expectation-type counterparts of imprecise probabilities. The analogue of pre-Dynkin systems turns out to be (sets of) linear subspaces in the space of bounded, real-valued functions. We introduce partial expectations, natural generalizations of probabilities defined on pre-Dynkin systems. Again, coherence and extendability are equivalent. A related but more general lattice duality preserves the relation between systems of precision and credal sets of probabilities. Full article

Imprecise classification is a relatively new task within Machine Learning. The difference with standard classification is that not only is one state of the variable under study determined, a set of states that do not have enough information against them and cannot be ruled out is determined as well. For imprecise classification, a mode called an Imprecise Credal Decision Tree (ICDT) that uses imprecise probabilities and maximum of entropy as the information measure has been presented. A difficult and interesting task is to show how to combine this type of imprecise classifiers. A procedure based on the minimum level of dominance has been presented; though it represents a very strong method of combining, it has the drawback of an important risk of possible erroneous prediction. In this research, we use the second-best theory to argue that the aforementioned type of combination can be improved through a new procedure built by relaxing the constraints. The new procedure is compared with the original one in an experimental study on a large set of datasets, and shows improvement. Full article

This paper deals with uncertainty, asymmetric information, and risk modelling in a complex power system. The uncertainty is managed by using probability and decision theory methods. More specifically, influence diagrams—as extended Bayesian network functions with interval probabilities represented through credal sets—were chosen for the predictive modelling scenario of replacing the most critical circuit breakers in optimal time. Namely, based on the available data on circuit breakers and other variables that affect the considered model of a complex power system, a group of experts was able to assess the situation using interval probabilities instead of crisp probabilities. Furthermore, the paper examines how the confidence interval width affects decision-making in this context and eliminates the information asymmetry of different experts. Based on the obtained results for each considered interval width separately on the action to be taken over the considered model in order to minimize the risk of the power system failure, it can be concluded that the proposed approach clearly indicates the advantages of using interval probability when making decisions in systems such as the one considered in this paper. Full article

The belief rule-based classification system (BRBCS) is a promising technique for addressing different types of uncertainty in complex classification problems, by introducing the belief function theory into the classical fuzzy rule-based classification system. However, in the BRBCS, high numbers of instances and features generally induce a belief rule base (BRB) with large size, which degrades the interpretability of the classification model for big data sets. In this paper, a BRB learning method based on the evidential C-means clustering (ECM) algorithm is proposed to efficiently design a compact belief rule-based classification system (CBRBCS). First, a supervised version of the ECM algorithm is designed by means of weighted product-space clustering to partition the training set with the goals of obtaining both good inter-cluster separability and inner-cluster pureness. Then, a systematic method is developed to construct belief rules based on the obtained credal partitions. Finally, an evidential partition entropy-based optimization procedure is designed to get a compact BRB with a better trade-off between accuracy and interpretability. The key benefit of the proposed CBRBCS is that it can provide a more interpretable classification model on the premise of comparative accuracy. Experiments based on synthetic and real data sets have been conducted to evaluate the classification accuracy and interpretability of the proposal. Full article