The Poisson tensor completion parametric estimator
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911494552158208 |
|---|---|
| author | Dunlavy, Daniel M. Lehoucq, Richard B. Mayer, Carolyn D. Prasadan, Arvind |
| author_facet | Dunlavy, Daniel M. Lehoucq, Richard B. Mayer, Carolyn D. Prasadan, Arvind |
| contents | We introduce the Poisson tensor completion (PTC) estimator that exploits inter-sample relationships to compute a low-rank Poisson tensor decomposition of the frequency histogram for samples of a multivariate distribution. Our crucial observation is that the histogram bins are an instance of a space partitioning of counts and thus can be identified with a spatial non-homogeneous Poisson process. The Poisson tensor decomposition leads to a completion of the mean measure over all bins -- including those containing few to no samples -- and leads to our proposed estimator. A Poisson tensor decomposition models the underlying distribution of the count data and guarantees non-negative estimated values obviating the need for additional constraints to ensure non-negativity. Furthermore, we demonstrate that our PTC estimator is a substantial improvement over standard histogram-based estimators for sub-Gaussian probability distributions because of the concentration of norm phenomenon. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04957 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Poisson tensor completion parametric estimator Dunlavy, Daniel M. Lehoucq, Richard B. Mayer, Carolyn D. Prasadan, Arvind Statistics Theory Methodology We introduce the Poisson tensor completion (PTC) estimator that exploits inter-sample relationships to compute a low-rank Poisson tensor decomposition of the frequency histogram for samples of a multivariate distribution. Our crucial observation is that the histogram bins are an instance of a space partitioning of counts and thus can be identified with a spatial non-homogeneous Poisson process. The Poisson tensor decomposition leads to a completion of the mean measure over all bins -- including those containing few to no samples -- and leads to our proposed estimator. A Poisson tensor decomposition models the underlying distribution of the count data and guarantees non-negative estimated values obviating the need for additional constraints to ensure non-negativity. Furthermore, we demonstrate that our PTC estimator is a substantial improvement over standard histogram-based estimators for sub-Gaussian probability distributions because of the concentration of norm phenomenon. |
| title | The Poisson tensor completion parametric estimator |
| topic | Statistics Theory Methodology |
| url | https://arxiv.org/abs/2505.04957 |