On Convergence of Discrete Schemes for Computing the Rate-Distortion Function of Continuous Source
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866910430382784512 |
|---|---|
| author | Chen, Lingyi Wu, Shitong Zhang, Wenyi Wu, Huihui Wu, Hao |
| author_facet | Chen, Lingyi Wu, Shitong Zhang, Wenyi Wu, Huihui Wu, Hao |
| contents | Computing the rate-distortion function for continuous sources is commonly regarded as a standard continuous optimization problem. When numerically addressing this problem, a typical approach involves discretizing the source space and subsequently solving the associated discrete problem. However, existing literature has predominantly concentrated on the convergence analysis of solving discrete problems, usually neglecting the convergence relationship between the original continuous optimization and its associated discrete counterpart. This neglect is not rigorous, since the solution of a discrete problem does not necessarily imply convergence to the solution of the original continuous problem, especially for non-linear problems. To address this gap, our study employs rigorous mathematical analysis, which constructs a series of finite-dimensional spaces approximating the infinite-dimensional space of the probability measure, establishing that solutions from discrete schemes converge to those from the continuous problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_00474 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Convergence of Discrete Schemes for Computing the Rate-Distortion Function of Continuous Source Chen, Lingyi Wu, Shitong Zhang, Wenyi Wu, Huihui Wu, Hao Information Theory Computing the rate-distortion function for continuous sources is commonly regarded as a standard continuous optimization problem. When numerically addressing this problem, a typical approach involves discretizing the source space and subsequently solving the associated discrete problem. However, existing literature has predominantly concentrated on the convergence analysis of solving discrete problems, usually neglecting the convergence relationship between the original continuous optimization and its associated discrete counterpart. This neglect is not rigorous, since the solution of a discrete problem does not necessarily imply convergence to the solution of the original continuous problem, especially for non-linear problems. To address this gap, our study employs rigorous mathematical analysis, which constructs a series of finite-dimensional spaces approximating the infinite-dimensional space of the probability measure, establishing that solutions from discrete schemes converge to those from the continuous problems. |
| title | On Convergence of Discrete Schemes for Computing the Rate-Distortion Function of Continuous Source |
| topic | Information Theory |
| url | https://arxiv.org/abs/2405.00474 |