This project aims to develop new explainable ML algorithms based on PGMs addressing a wide range of general machine learning problems (i.e. like anomaly detection, entity profiling, supervised and unsupervised learning, etc.) and domain applications problems in bioinformatics (Sebastiani et al., 2007), environmental modelling (Aguilera et al., 2011) and digital image (aesthetics quality evaluation (Deng et al., 2017) and semantic localization (Tompson et al., 2015)). With the results of this project, we aim to show how PGMs are a promising ML model family to be used in safe-critical and high- stakes decisions real-life explainable AI (XAI) systems (Gunning, 2017). Therefore, the main objective of this project is to generate a set of methodological developments in the field of machine learning using probabilistic models, with a solid and innovative theoretical foundation that makes them explainable. The project also addresses some specific applications as a way to effectively verify the proposed methodological developments.