# Statistical learning and cross-validation for point processes

arXiv: https://arxiv.org/abs/2103.01356 · HTML: https://mlsanity.com/paper/2103.01356/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 102 references that are in the map.
- First posted on arXiv 1 Mar 2021.

## Builds on (most cited first, 11 of 11)

- [A space-time conditional intensity model for invasive meningococcal disease occurrence](https://mlsanity.com/paper/1508.05740/) (2015)
- [Convex and non-convex regularization methods for spatial point processes intensity estimation](https://mlsanity.com/paper/1703.02462/) (2017)
- [Quasi-likelihood for Spatial Point Processes](https://mlsanity.com/paper/1303.0188/) (2013)
- [Functional summary statistics for point processes on the sphere with an application to determinantal point processes](https://mlsanity.com/paper/1601.03448/) (2016)
- [Some recent developments in statistics for spatial point patterns](https://mlsanity.com/paper/1609.00908/) (2016)
- [Detecting multivariate interactions in spatial point patterns with Gibbs models and variable selection](https://mlsanity.com/paper/1705.00689/) (2017)
- [Summary statistics for inhomogeneous marked point processes](https://mlsanity.com/paper/1407.3089/) (2014)
- [Limit theory for geometric statistics of point processes having fast decay of correlations](https://mlsanity.com/paper/1606.03988/) (2016)
- [Bandwidth selection for kernel estimators of the spatial intensity function](https://mlsanity.com/paper/1611.10221/) (2016)
- [Resample-smoothing of Voronoi intensity estimators](https://mlsanity.com/paper/1807.02590/) (2018)
- [Large-scale modelling and forecasting of ambulance calls in northern Sweden using spatio-temporal log-Gaussian Cox processes](https://mlsanity.com/paper/2004.08416/) (2020)

## Abstract (arXiv)

This paper presents the first general (supervised) statistical learning framework for point processes in general spaces. Our approach is based on the combination of two new concepts, which we define in the paper: i) bivariate innovations, which are measures of discrepancy/prediction-accuracy between two point processes, and ii) point process cross-validation (CV), which we here 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 measured by means of bivariate innovations. Having established various theoretical properties of our bivariate innovations, we study in detail the case where the CV procedure is obtained through independent thinning and we apply our statistical learning methodology to three typical spatial statistical settings, namely parametric intensity estimation, non-parametric intensity estimation and Papangelou conditional intensity fitting. Aside from deriving theoretical properties related to these cases, in each of them we numerically show that our statistical learning approach outperforms the state of the art in terms of mean (integrated) squared error.