Improved estimates for the number of non-negative integer matrices with given row and column sums
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2022
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916104083865600 |
|---|---|
| author | Jerdee, Maximilian Kirkley, Alec Newman, M. E. J. |
| author_facet | Jerdee, Maximilian Kirkley, Alec Newman, M. E. J. |
| contents | The number of non-negative integer matrices with given row and column sums appears in a variety of problems in mathematics and statistics but no closed-form expression for it is known, so we rely on approximations of various kinds. Here we describe a new such approximation, motivated by consideration of the statistics of matrices with non-integer numbers of columns. This estimate can be evaluated in time linear in the size of the matrix and returns results of accuracy as good as or better than existing linear-time approximations across a wide range of settings. We also use this new estimate as the starting point for an improved numerical method for either counting or sampling matrices using sequential importance sampling. Code implementing our methods is provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_14869 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Improved estimates for the number of non-negative integer matrices with given row and column sums Jerdee, Maximilian Kirkley, Alec Newman, M. E. J. Computation The number of non-negative integer matrices with given row and column sums appears in a variety of problems in mathematics and statistics but no closed-form expression for it is known, so we rely on approximations of various kinds. Here we describe a new such approximation, motivated by consideration of the statistics of matrices with non-integer numbers of columns. This estimate can be evaluated in time linear in the size of the matrix and returns results of accuracy as good as or better than existing linear-time approximations across a wide range of settings. We also use this new estimate as the starting point for an improved numerical method for either counting or sampling matrices using sequential importance sampling. Code implementing our methods is provided. |
| title | Improved estimates for the number of non-negative integer matrices with given row and column sums |
| topic | Computation |
| url | https://arxiv.org/abs/2209.14869 |