Forecasting has always been at the forefront of decision making and planning. The uncertainty that surrounds the future is both exciting and challenging, with individuals and organisations seeking to minimise risks and maximise utilities. The large number of forecasting applications calls for a diverse set of forecasting methods to tackle real-life challenges. This article provides a non-systematic review of the theory and the practice of forecasting. We provide an overview of a wide range of theoretical, state-of-the-art models, methods, principles, and approaches to prepare, produce, organise, and evaluate forecasts. We then demonstrate how such theoretical concepts are applied in a variety of real-life contexts. We do not claim that this review is an exhaustive list of methods and applications. However, we wish that our encyclopedic presentation will offer a point of reference for the rich work that has been undertaken over the last decades, with some key insights for the future of forecasting theory and practice. Given its encyclopedic nature, the intended mode of reading is non-linear. We offer cross-references to allow the readers to navigate through the various topics. We complement the theoretical concepts and applications covered by large lists of free or open-source software implementations and publicly-available databases.

Despite the high accuracy offered by state-of-the-art deep natural-language models (e.g. LSTM, BERT), their application in real-life settings is still widely limited, as they behave like a black-box to the end-user. Hence, explainability is rapidly becoming a fundamental requirement of future-generation data-driven systems based on deep-learning approaches. Several attempts to fulfill the existing gap between accuracy and interpretability have been done. However, robust and specialized xAI (Explainable Artificial Intelligence) solutions tailored to deep natural-language models are still missing. We propose a new framework, named T-EBAnO, which provides innovative prediction-local and class-based model-global explanation strategies tailored to black-box deep natural-language models. Given a deep NLP model and the textual input data, T-EBAnO provides an objective, human-readable, domain-specific assessment of the reasons behind the automatic decision-making process. Specifically, the framework extracts sets of interpretable features mining the inner knowledge of the model. Then, it quantifies the influence of each feature during the prediction process by exploiting the novel normalized Perturbation Influence Relation index at the local level and the novel Global Absolute Influence and Global Relative Influence indexes at the global level. The effectiveness and the quality of the local and global explanations obtained with T-EBAnO are proved on (i) a sentiment analysis task performed by a fine-tuned BERT model, and (ii) a toxic comment classification task performed by an LSTM model.

A key aspect of automating predictive machine learning entails the capability of properly triggering the update of the trained model. To this aim, suitable automatic solutions to self-assess the prediction quality and the data distribution drift between the original training set and the new data have to be devised. In this paper, we propose a novel methodology to automatically detect prediction-quality degradation of machine learning models due to class-based concept drift, i.e., when new data contains samples that do not fit the set of class labels known by the currently-trained predictive model. Experiments on synthetic and real-world public datasets show the effectiveness of the proposed methodology in automatically detecting and describing concept drift caused by changes in the class-label data distributions.