The need to comprehend and predict the dynamics of complex systems has spurred developments of time series forecasting methods across several disciplines. Nowadays, time series are collected with event logs for an ever increasing number of systems. Event logs can contain prominent information about the system dynamics. This paper addresses joint modelling of time series and event traces, to enhance time series forecasting. We introduce the Non-Homogeneous Markov Chain AutoRegressive model, to best apprehend the combined influence of past events belonging to several event categories, on a system’s dynamics. The originality of our proposal stems from the synchronization of a Hawkes temporal point process with the classical first-order hidden Markov model, through contextual variables. We also instantiate a basic version whose contextual variables only take into account events’ latest occurrences. Our proof-of-concept experiments address a real-world case related to digitally assisted training in anaesthesiology. We demonstrate that the advanced instantiation outperforms the basic instantiation (maximal prediction error percentage: 5.6% versus 13.5%). Finally, we validate the suitability of the advanced instantiation for the desired simulation, by applying real sequences of medical actions to digital patients. We show that we obtain highly realistic simulations.

The random forest model is a popular framework used in classification and regression. In cases where high correlations exist within the data, it may be beneficial to capture these dependencies through latent variables, for an enhanced use of the random forest framework. In this paper, we present Sylva, the second proposal of a random forest with latent variables after T-Trees, derived from the seminal works of Botta and co-workers (Botta et al., 2008). Sylva is an innovative hybrid approach in which the dynamic generation of latent variables used to learn the random forest is driven by an additional forest model, this time a forest of latent tree models. The latter forest model, a class of Bayesian networks devised in (Mourad et al., 2011), allows a flexible modeling of the dependencies existing within the data. In the comprehensive study reported here, three variants of Sylva, instantiated by different clustering methods (CAST, DBSCAN, Louvain method), are compared to T-Trees using high-dimensional real-world datasets (161 datasets each describing around 5,000 observations and between 5,700 and 39,000 variables) in the context of genetic association studies. We show that T-Trees and Sylva have comparable high predictive powers (aeras under the ROC curves), that lie in range [0.887, 0.961] (T-Trees), and in interval [0.885, 0.979] (over the three Sylva instantiations). Interestingly, T-Trees and Sylva are shown to differ significantly in their importance measure distributions: in Sylva, the importance measure distribution corresponding to top ranked variables is significantly skewed towards higher values than in T-Trees, which meets the feature selection enhancement objective. This property holds true for the three instantiations of Sylva. In addition, the thorough analysis of the number of top-ranked variables jointly identified by T-Trees and Sylva highlights the possibility to cross-validate the findings, in order to constitute a priorized list of features (e.g., to be further analyzed by biologists, in the context of genetic association studies). Finally, we conclude that it is recommended to use CAST or DBSCAN, and not the Louvain method, on the 161 datasets analyzed, to increase the probability of Sylva to detect top variables missedby T-Trees among its top ranked variables.