Machine learning models based on temporal point processes are the state of the art in a wide variety of applications involving discrete events in continuous time. However, these models lack the ability to answer counterfactual questions, which are increasingly relevant as these models are being used to inform targeted interventions. In this work, our goal is to fill this gap. To this end, we first develop a causal model of thinning for temporal point processes that builds upon the Gumbel-Max structural causal model. This model satisfies a desirable counterfactual monotonicity condition, which is sufficient to identify counterfactual dynamics in the process of thinning. Then, given an observed realization of a temporal point process with a given intensity function, we develop a sampling algorithm that uses the above causal model of thinning and the superposition theorem to simulate counterfactual realizations of the temporal point process under a given alternative intensity function. Simulation experiments using synthetic and real epidemiological data show that the counterfactual realizations provided by our algorithm may give valuable insights to enhance targeted interventions.

In the supervised high dimensional settings with a large number of variables and a low number of individuals, one objective is to select the relevant variables and thus to reduce the dimension. That subspace selection is often managed with supervised tools. However, some data can be missing, compromising the validity of the sub-space selection. We propose a Partial Least Square (PLS) based method, called Multi-block Data-Driven sparse PLS mdd-sPLS, allowing jointly variable selection and subspace estimation while training and testing missing data imputation through a new algorithm called Koh-Lanta. This method was challenged through simulations against existing methods such as mean imputation, nipals, softImpute and imputeMFA. In the context of supervised analysis of high dimensional data, the proposed method shows the lowest prediction error of the response variables. So far this is the only method combining data imputation and response variable prediction. The superiority of the supervised multi-block mdd-sPLS method increases with the intra-block and inter-block correlations. The application to a real data-set from a rVSV-ZEBOV Ebola vaccine trial revealed interesting and biologically relevant results. The method is implemented in a R-package available on the CRAN and a Python-package available on pypi.