Nonparametric likelihood based estimation of linear filters for point processes

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Standard

Nonparametric likelihood based estimation of linear filters for point processes. / Hansen, Niels Richard.

I: Statistics and Computing, Bind 25, Nr. 3, 05.2015, s. 609-618.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Hansen, NR 2015, 'Nonparametric likelihood based estimation of linear filters for point processes', Statistics and Computing, bind 25, nr. 3, s. 609-618. https://doi.org/10.1007/s11222-014-9452-6

APA

Hansen, N. R. (2015). Nonparametric likelihood based estimation of linear filters for point processes. Statistics and Computing, 25(3), 609-618. https://doi.org/10.1007/s11222-014-9452-6

Vancouver

Hansen NR. Nonparametric likelihood based estimation of linear filters for point processes. Statistics and Computing. 2015 maj;25(3):609-618. https://doi.org/10.1007/s11222-014-9452-6

Author

Hansen, Niels Richard. / Nonparametric likelihood based estimation of linear filters for point processes. I: Statistics and Computing. 2015 ; Bind 25, Nr. 3. s. 609-618.

Bibtex

@article{b5723f752801488d9a787789c315d3f5,
title = "Nonparametric likelihood based estimation of linear filters for point processes",
abstract = "We consider models for multivariate point processes where the intensity is given nonparametrically in terms of functions in a reproducing kernel Hilbert space. The likelihood function involves a time integral and is consequently not given in terms of a finite number of kernel evaluations. The main result is a representation of the gradient of the log-likelihood, which we use to derive computable approximations of the log-likelihood and the gradient by time discretization. These approximations are then used to minimize the approximate penalized log-likelihood. For time and memory efficiency the implementation relies crucially on the use of sparse matrices. As an illustration we consider neuron network modeling, and we use this example to investigate how the computational costs of the approximations depend on the resolution of the time discretization. The implementation is available in the R package ppsta",
keywords = "Multivariate point processes, Penalization, Reproducing kernel Hilbert spaces, ppstat",
author = "Hansen, {Niels Richard}",
year = "2015",
month = may,
doi = "10.1007/s11222-014-9452-6",
language = "English",
volume = "25",
pages = "609--618",
journal = "Statistics and Computing",
issn = "0960-3174",
publisher = "Springer",
number = "3",

}

RIS

TY - JOUR

T1 - Nonparametric likelihood based estimation of linear filters for point processes

AU - Hansen, Niels Richard

PY - 2015/5

Y1 - 2015/5

N2 - We consider models for multivariate point processes where the intensity is given nonparametrically in terms of functions in a reproducing kernel Hilbert space. The likelihood function involves a time integral and is consequently not given in terms of a finite number of kernel evaluations. The main result is a representation of the gradient of the log-likelihood, which we use to derive computable approximations of the log-likelihood and the gradient by time discretization. These approximations are then used to minimize the approximate penalized log-likelihood. For time and memory efficiency the implementation relies crucially on the use of sparse matrices. As an illustration we consider neuron network modeling, and we use this example to investigate how the computational costs of the approximations depend on the resolution of the time discretization. The implementation is available in the R package ppsta

AB - We consider models for multivariate point processes where the intensity is given nonparametrically in terms of functions in a reproducing kernel Hilbert space. The likelihood function involves a time integral and is consequently not given in terms of a finite number of kernel evaluations. The main result is a representation of the gradient of the log-likelihood, which we use to derive computable approximations of the log-likelihood and the gradient by time discretization. These approximations are then used to minimize the approximate penalized log-likelihood. For time and memory efficiency the implementation relies crucially on the use of sparse matrices. As an illustration we consider neuron network modeling, and we use this example to investigate how the computational costs of the approximations depend on the resolution of the time discretization. The implementation is available in the R package ppsta

KW - Multivariate point processes

KW - Penalization

KW - Reproducing kernel Hilbert spaces

KW - ppstat

U2 - 10.1007/s11222-014-9452-6

DO - 10.1007/s11222-014-9452-6

M3 - Journal article

VL - 25

SP - 609

EP - 618

JO - Statistics and Computing

JF - Statistics and Computing

SN - 0960-3174

IS - 3

ER -

ID: 150697553