Identication and Estimation of Nonsymmetric Determinantal Point Processes

Abstract

Determinantal point processes (DPPs) provide tractable distributions for nite random sets, but the usual symmetric-kernel specication imposes nonpositive pairwise dependence. Statistical research on nonsymmetric DPPs, which can accommodate positive dependence, remains limited. We study identication and estimation for this class. First, we establish the equivalence of two sucient conditions for a nonsymmetric kernel to dene a valid DPP. Second, we develop the identication theory for nonsymmetric DPPs. Third, we develop cardinality-truncated maximum-likelihood estimation and estimation by averaged stochastic gradient descent. Under suitable identication and regularity conditions, we establish consistency and asymptotic normality for both estimators. Simulations examine identication, the eects of truncation, and the nite-sample performance of the estimators. We illustrate the methods with two cyber applications at markedly dierent sampling frequencies: weekly sector-by-breach data and second-by-second enterprise authentication data with more than ve million set observations.

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BibTeX RIS

BibTeX

@misc{gourieroux2026identication,
  title = {{Identication and Estimation of Nonsymmetric Determinantal Point Processes}},
  author = {Christian Gouriéroux and Yang Lu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.14520},
  eprint = {2610.14520},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.14520},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Identication and Estimation of Nonsymmetric Determinantal Point Processes
AU  - Christian Gouriéroux
AU  - Yang Lu
PY  - 2026
DA  - 2026/10/10
PB  - arXiv
DO  - 10.48550/arxiv.2610.14520
UR  - https://arxiv.org/abs/2610.14520
AB  - Determinantal point processes (DPPs) provide tractable distributions for nite random sets, but the usual symmetric-kernel specication imposes nonpositive pairwise dependence. Statistical research on nonsymmetric DPPs, which can accommodate positive dependence, remains limited. We study identication and estimation for this class. First, we establish the equivalence of two sucient conditions for a nonsymmetric kernel to dene a valid DPP. Second, we develop the identication theory for nonsymmetric DPPs. Third, we develop cardinality-truncated maximum-likelihood estimation and estimation by averaged stochastic gradient descent. Under suitable identication and regularity conditions, we establish consistency and asymptotic normality for both estimators. Simulations examine identication, the eects of truncation, and the nite-sample performance of the estimators. We illustrate the methods with two cyber applications at markedly dierent sampling frequencies: weekly sector-by-breach data and second-by-second enterprise authentication data with more than ve million set observations.
ER  -

Abstract

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