Statistical learning and cross-validation for point processes

03/01/2021
by   Ottmar Cronie, et al.
0

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.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 41

07/06/2018

Resample-smoothing of Voronoi intensity estimators

Voronoi intensity estimators, which are non-parametric estimators for in...
02/13/2020

Spatial birth-death-move processes : basic properties and estimation of their intensity functions

Spatial birth-death processes are generalisations of simple birth-death ...
12/06/2021

Cross-validation for change-point regression: pitfalls and solutions

Cross-validation is the standard approach for tuning parameter selection...
12/10/2021

Validation design I: construction of validation designs via kernel herding

We construct validation designs Z_m aimed at estimating the integrated s...
10/14/2021

Fitting three-dimensional Laguerre tessellations by hierarchical marked point process models

We present a general statistical methodology for analysing a Laguerre te...
06/24/2020

Automatic Estimation of Self-Reported Pain by Interpretable Representations of Motion Dynamics

We propose an automatic method for pain intensity measurement from video...
06/10/2020

Higher-order interactions in statistical physics and machine learning: A non-parametric solution to the inverse problem

We propose a model-independent definition of n-point interaction within ...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.