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Accelerated non‐parametrics for cascades of Poisson processes
Author(s) -
Oates Chris J.
Publication year - 2015
Publication title -
stat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.61
H-Index - 18
ISSN - 2049-1573
DOI - 10.1002/sta4.87
Subject(s) - computer science , estimator , hyperparameter , poisson distribution , parametric statistics , probabilistic logic , parametric model , computational complexity theory , process (computing) , algorithm , machine learning , data mining , artificial intelligence , mathematics , statistics , operating system
Cascades of Poisson processes are probabilistic models for spatio‐temporal phenomena in which (i) previous events may trigger subsequent events and (ii) both the background and triggering processes are conditionally Poisson. Such phenomena are typically “data rich but knowledge poor,” in the sense that large datasets are available, yet a mechanistic understanding of the background and triggering processes that generate the data is unavailable. In these settings, non‐parametric estimation plays a central role. However, existing non‐parametric estimators have computational and storage complexity O ( N 2 ) , precluding their application on large datasets. Here, by assuming the triggering process acts only locally, we derive non‐parametric estimators with computational complexity O ( N log N ) and storage complexity O ( N ) . Our approach automatically learns the domain of the triggering process from data and is essentially free from hyperparameters. The methodology is applied to a large seismic dataset where estimation under existing algorithms would be infeasible. Copyright © 2015 John Wiley & Sons, Ltd.