Predicting the presence of major depressive disorder (MDD) using behavioural and cognitive signals is a highly non-trivial task. The heterogeneous clinical profile of MDD means that any given speech, facial expression and/or observed cognitive pattern may be associated with a unique combination of depressive symptoms. Conventional discriminative machine learning models potentially lack the complexity to robustly model this heterogeneity. Bayesian networks, however, may instead be well-suited to such a scenario. These networks are probabilistic graphical models that efficiently describe the joint probability distribution over a set of random variables by explicitly capturing their conditional dependencies. This framework provides further advantages over standard discriminative modelling by offering the possibility to incorporate expert opinion in the graphical structure of the models, generating explainable model predictions, informing about the uncertainty of predictions, and naturally handling missing data. In this study, we apply a Bayesian framework to capture the relationships between depression, depression symptoms, and features derived from speech, facial expression and cognitive game data collected at thymia.

Recently, two types of simulations (forward and backward simulations) and four types of bisimulations (forward, backward, forward-backward, and backward-forward bisimulations) between fuzzy automata have been introduced. If there is at least one simulation/bisimulation of some of these types between the given fuzzy automata, it has been proved that there is the greatest simulation/bisimulation of this kind. In the present paper, for any of the above-mentioned types of simulations/bisimulations we provide an effective algorithm for deciding whether there is a simulation/bisimulation of this type between the given fuzzy automata, and for computing the greatest one, whenever it exists. The algorithms are based on the method developed in [J. Ignjatovi\'c, M. \'Ciri\'c, S. Bogdanovi\'c, On the greatest solutions to certain systems of fuzzy relation inequalities and equations, Fuzzy Sets and Systems 161 (2010) 3081-3113], which comes down to the computing of the greatest post-fixed point, contained in a given fuzzy relation, of an isotone function on the lattice of fuzzy relations.