PreprintCC BY 4.0arXiv
An RKHS Framework for Fixed Effects in Permanental Process Models
Abstract
This short work describes an extension of the permanental process model which includes fixed effects. By starting with a prior on the fixed effects coefficients we show that, in the diffuse prior limit, the intensity function of the permanental process can be found using the representer theorem and naturally decomposed into a fixed effects term and a function which is an element of a Reproducing Kernel Hilbert Space (RKHS). We show that the limiting equivalent kernel defines an RKHS whose squared norm is exactly the limiting penalty. This allows for straightforward scientific interpretation of permanental process models and the easy incorporation of domain knowledge into the estimation process.
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BibTeX
@misc{leduc2026rkhs,
title = {{An RKHS Framework for Fixed Effects in Permanental Process Models}},
author = {Matthew LeDuc},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.17908},
eprint = {2608.17908},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.17908},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An RKHS Framework for Fixed Effects in Permanental Process Models
AU - Matthew LeDuc
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2608.17908
UR - https://arxiv.org/abs/2608.17908
AB - This short work describes an extension of the permanental process model which includes fixed effects. By starting with a prior on the fixed effects coefficients we show that, in the diffuse prior limit, the intensity function of the permanental process can be found using the representer theorem and naturally decomposed into a fixed effects term and a function which is an element of a Reproducing Kernel Hilbert Space (RKHS). We show that the limiting equivalent kernel defines an RKHS whose squared norm is exactly the limiting penalty. This allows for straightforward scientific interpretation of permanental process models and the easy incorporation of domain knowledge into the estimation process.
ER -