Laplace Variational Inference for Dirichlet Process Mixtures of Marked Poisson Point Processes
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866909030801211392 |
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| author | Choi, Minsung Jeong, Seonghyun |
| author_facet | Choi, Minsung Jeong, Seonghyun |
| contents | Marked point process data arise when events occur in a space with event-level marks. We study clustering of replicated marked Poisson point processes and introduce Dirichlet process mixtures of marked Poisson point processes, a Bayesian nonparametric model that jointly infers latent cluster structure, the number of clusters, and continuous mark-specific intensity surfaces. We use a squared link intensity representation to obtain tractable continuous domain likelihood terms without gridding or thinning. For posterior inference, we develop an efficient variational Bayes algorithm with a constrained Laplace approximation for the nonconjugate basis-coefficient block. The resulting coefficient update is formulated as a constrained optimization problem, which avoids the sign ambiguity and nodal-line issue of squared-link models. We further establish theoretical guarantees for mode finding optimization. We demonstrate the performance of the proposed model and algorithm through synthetic experiments and real-data analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_09562 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Laplace Variational Inference for Dirichlet Process Mixtures of Marked Poisson Point Processes Choi, Minsung Jeong, Seonghyun Methodology Marked point process data arise when events occur in a space with event-level marks. We study clustering of replicated marked Poisson point processes and introduce Dirichlet process mixtures of marked Poisson point processes, a Bayesian nonparametric model that jointly infers latent cluster structure, the number of clusters, and continuous mark-specific intensity surfaces. We use a squared link intensity representation to obtain tractable continuous domain likelihood terms without gridding or thinning. For posterior inference, we develop an efficient variational Bayes algorithm with a constrained Laplace approximation for the nonconjugate basis-coefficient block. The resulting coefficient update is formulated as a constrained optimization problem, which avoids the sign ambiguity and nodal-line issue of squared-link models. We further establish theoretical guarantees for mode finding optimization. We demonstrate the performance of the proposed model and algorithm through synthetic experiments and real-data analysis. |
| title | Laplace Variational Inference for Dirichlet Process Mixtures of Marked Poisson Point Processes |
| topic | Methodology |
| url | https://arxiv.org/abs/2605.09562 |