Nonparametric Modeling and Penalized Learning Methods for Event Processes

In the context of disease progression analysis, estimating the causal effect of a time-continuous treatment assigned to a given population is an important problem. This is particularly relevant for understanding (causal) underlying phenomena in many applications gathering massive high-dimensional and time-dependent data structures, ranging from biomedicine to financial markets for instance. 
We propose, in this work, a nonparametric model for event processes, based on a linear combination of tensor products of kernel functions, composed of stochastic integrals w.r.t. the event processes observed up to a fixed time. Under some assumptions of sparse decomposition and adequate regularity, the optimal parameters involved in the expansion are solution of a LASSO penalized method. Finite-sample concentration bounds for the estimation and prediction errors are derived, yielding data-driven optimal weights for the LASSO penalty term, and allowing for heteroscedastic expansions. 
The results will be applied to propose a conditional local independence test with practical implementations, important to learning causal graphs in that setting. This is a joint work with Prof. Niels R. Hansen (UCPH).