Maximum likelihood estimation of log-affine models using detailed-balanced reaction networks
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_ | 1866914071993909248 |
|---|---|
| author | Henriksson, Oskar Améndola, Carlos Rodriguez, Jose Israel Yu, Polly Y. |
| author_facet | Henriksson, Oskar Améndola, Carlos Rodriguez, Jose Israel Yu, Polly Y. |
| contents | A fundamental question in the field of molecular computation is what computational tasks a biochemical system can carry out. In this work, we focus on the problem of finding the maximum likelihood estimate (MLE) for log-affine models. We revisit a construction due to Gopalkrishnan of a mass-action system with the MLE as its unique positive steady state, which is based on choosing a basis for the kernel of the design matrix of the model. We extend this construction to allow for any finite spanning set of the kernel, and explore how the choice of spanning set influences the dynamics of the resulting network, including the existence of boundary steady states, the deficiency of the network, and the rate of convergence. In particular, we prove that using a Markov basis as the spanning set guarantees global stability of the MLE steady state. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_07986 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Maximum likelihood estimation of log-affine models using detailed-balanced reaction networks Henriksson, Oskar Améndola, Carlos Rodriguez, Jose Israel Yu, Polly Y. Molecular Networks Algebraic Geometry Dynamical Systems 68Q07, 62F10, 62R01, 14M25, 92C42, 92E20 A fundamental question in the field of molecular computation is what computational tasks a biochemical system can carry out. In this work, we focus on the problem of finding the maximum likelihood estimate (MLE) for log-affine models. We revisit a construction due to Gopalkrishnan of a mass-action system with the MLE as its unique positive steady state, which is based on choosing a basis for the kernel of the design matrix of the model. We extend this construction to allow for any finite spanning set of the kernel, and explore how the choice of spanning set influences the dynamics of the resulting network, including the existence of boundary steady states, the deficiency of the network, and the rate of convergence. In particular, we prove that using a Markov basis as the spanning set guarantees global stability of the MLE steady state. |
| title | Maximum likelihood estimation of log-affine models using detailed-balanced reaction networks |
| topic | Molecular Networks Algebraic Geometry Dynamical Systems 68Q07, 62F10, 62R01, 14M25, 92C42, 92E20 |
| url | https://arxiv.org/abs/2411.07986 |