Abstract
We present parametric probabilistic models for numerical distributional variables. The proposed models are based on the representation of each distribution by a location measure and inter-quantile ranges, for given quantiles, thereby characterizing the underlying empirical distributions in a flexible way. Multivariate Normal distributions are assumed for the whole set of indicators, considering alternative structures of the variance-covariance matrix. For all cases, maximum likelihood estimators of the corresponding parameters are derived. This modelling allows for hypothesis testing and multivariate parametric analysis. The proposed framework is applied to Analysis of Variance and parametric Discriminant Analysis of distributional data. A simulation study examines the performance of the proposed models in classification problems under different data conditions. Applications to Internet traffic data and Portuguese official data illustrate the relevance of the proposed approach.

Abstract
Air pollution is a global challenge with deep implications in public health and environment. We examine air quality data from a monitoring station in Entrecampos, Lisbon, Portugal, using Symbolic Data Analysis. The dataset consists of hourly concentrations of nine pollutants during three years, which are logarithmically transformed and aggregated in intervals, taking the daily minimum and maximum values. The symbolic mean and variance are estimated for each variable through the method of moments, and the pairwise dependencies are captured using a bivariate copula. Symbolic principal component scores are obtained from the estimated covariance matrix and used to fit generalized extreme value distributions. Outlier maps, based on these distributions’ quantiles, are used to identify outlying observations. A comparative analysis with daily average-based outlier detection methods is conducted. The results show the relevance of Symbolic Data Analysis in revealing new insights into air quality. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

Abstract
Recent state-of-the-art forecasting methods are trained on collections of time series. These methods, often referred to as global models, can capture common patterns in different time series to improve their generalization performance. However, they require large amounts of data that might not be available. Moreover, global models may fail to capture relevant patterns unique to a particular time series. In these cases, data augmentation can be useful to increase the sample size of time series datasets. The main contribution of this work is a novel method for generating univariate time series synthetic samples. Our approach stems from the insight that the observations concerning a particular time series of interest represent only a small fraction of all observations. In this context, we frame the problem of training a forecasting model as an imbalanced learning task. Oversampling strategies are popular approaches used to handle the imbalance problem in machine learning. We use these techniques to create synthetic time series observations and improve the accuracy of forecasting models. We carried out experiments using 7 different databases that contain a total of 5502 univariate time series. We found that the proposed solution outperforms both a global and a local model, thus providing a better trade-off between these two approaches.

Abstract
As machine learning technologies are increasingly adopted, the demand for responsible AI practices to ensure transparency and accountability grows. To better understand the decision-making processes of machine learning models, GASTeN was developed to generate realistic yet ambiguous synthetic data near a classifier's decision boundary. However, the results were inconsistent, with few images in the low-confidence region and noise. Therefore, we propose a new GASTeN version with a modified architecture and a novel loss function. This new loss function incorporates a multi-objective measure with a Gaussian loss centered on the classifier probability, targeting the decision boundary. Our study found that while the original GASTeN architecture yields the highest Frechet Inception Distance (FID) scores, the updated version achieves lower Average Confusion Distance (ACD) values and consistent performance across low-confidence regions. Both architectures produce realistic and ambiguous images, but the updated one is more reliable, with no instances of GAN mode collapse. Additionally, the introduction of the Gaussian loss enhanced this architecture by allowing for adjustable tolerance in image generation around the decision boundary.

Abstract
The effectiveness of time series forecasting models can be hampered by conditions in the input space that lead them to underperform. When those are met, negative behaviours, such as higher-than-usual errors or increased uncertainty are shown. Traditionally, stress testing is applied to assess how models respond to adverse, but plausible scenarios, providing insights on how to improve their robustness and reliability. This paper builds upon this technique by contributing with a novel framework called MAST (Meta-learning and data Augmentation for Stress Testing). In particular, MAST is a meta-learning approach that predicts the probability that a given model will perform poorly on a given time series based on a set of statistical features. This way, instead of designing new stress scenarios, this method uses the information provided by instances that led to decreases in forecasting performance. An additional contribution is made, a novel time series data augmentation technique based on oversampling, that improves the information about stress factors in the input space, which elevates the classification capabilities of the method. We conducted experiments using 6 benchmark datasets containing a total of 97.829 time series. The results suggest that MAST is able to identify conditions that lead to large errors effectively.

Abstract
Accurate evaluation of forecasting models is essential for ensuring reliable predictions. Current practices for evaluating and comparing forecasting models focus on summarising performance into a single score, using metrics such as SMAPE. We hypothesize that averaging performance over all samples dilutes relevant information about the relative performance of models. Particularly, conditions in which this relative performance is different than the overall accuracy. We address this limitation by proposing a novel framework for evaluating univariate time series forecasting models from multiple perspectives, such as one-step ahead forecasting versus multi-step ahead forecasting. We show the advantages of this framework by comparing a state-of-the-art deep learning approach with classical forecasting techniques. While classical methods (e.g. ARIMA) are long-standing approaches to forecasting, deep neural networks (e.g. NHITS) have recently shown state-of-the-art forecasting performance in benchmark datasets. We conducted extensive experiments that show NHITS generally performs best, but its superiority varies with forecasting conditions. For instance, concerning the forecasting horizon, NHITS only outperforms classical approaches for multi-step ahead forecasting. Another relevant insight is that, when dealing with anomalies, NHITS is outperformed by methods such as Theta. These findings highlight the importance of evaluating forecasts from multiple dimensions.