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Statistical learnin...
Statistical learning and cross-validation for point processes
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- Cronie, Ottmar, 1979 (författare)
- Gothenburg University,Göteborgs universitet,Institutionen för medicin, avdelningen för samhällsmedicin och folkhälsa,Institute of Medicine, School of Public Health and Community Medicine
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Moradi, Mehdi (författare)
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Biscio, Christophe A.N. (författare)
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(creator_code:org_t)
- arXiv, 2021
- Engelska.
- Relaterad länk:
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https://gup.ub.gu.se...
Abstract
Ämnesord
Stäng
- 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.
Ämnesord
- NATURVETENSKAP -- Data- och informationsvetenskap (hsv//swe)
- NATURAL SCIENCES -- Computer and Information Sciences (hsv//eng)
- NATURVETENSKAP -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Probability Theory and Statistics (hsv//eng)
Nyckelord
- Bivariate innovation
- Cross-Validation
- Generalised random samples
- Kernel intensity estimation
- Loss function
- Monte-Carlo cross-validation
- Multinomial k-fold cross-validation
- Papangelou conditional intensity function
- Prediction
- Subsampling
- Test function
- Thinning
Publikations- och innehållstyp
- vet (ämneskategori)
- rap (ämneskategori)