Maximum likelihood estimation of log-affine models using detailed-balanced reaction networks

Autor:	Henriksson, Oskar, Améndola, Carlos, Rodriguez, Jose Israel, Yu, Polly Y.
Rok vydání:	2024
Předmět:	Quantitative Biology - Molecular Networks Mathematics - Algebraic Geometry Mathematics - Dynamical Systems 68Q07 62F10 62R01 14M25 92C42 92E20
Druh dokumentu:	Working Paper
Popis:	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. Comment: 22 pages, 2 figures. Comments welcome!
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2411.07986 Zobrazit plný text záznamu View this record from Arxiv