Title: Statistical learning for general point processes
Authors: Ottmar Ottmar Cronie - University of Gothenburg (Sweden) [presenting]
Abstract: A first general (supervised) statistical learning framework is presented for point processes in general spaces, which is based on the combination of two new concepts: i) bivariate prediction errors, which are measures of discrepancy/prediction-accuracy between two-point processes, and ii) point process cross-validation (CV), which we define through point process thinning. The general idea is to carry out the fitting by predicting CV-generated validation sets using the corresponding training sets; the prediction error, which we minimise, is quantified through our bivariate prediction errors. Having presented some theoretical properties of our bivariate innovations, we look closer at the case where the CV procedure is obtained through independent thinning and we apply our statistical learning methodology to non-parametric kernel estimation of spatial intensity functions, showing numerically that it outperforms the state of the art in terms of mean (integrated) squared error. If time permits, we also highlight how our statistical learning approach can be applied to parametric intensity function estimation and Papangelou conditional intensity function estimation.