Analysis of Feedback Mechanisms with Unknown Delay Using Sparse Multivariate Autoregressive Method

摘要: This paper discusses the study of two interacting processes in which a feedback mechanism exists between processes. The was motivated by problems such as circadian oscillation gene expression where protein transcriptions form both negative and positive loops with long delays to equilibrium. Traditionally, data this type could be examined using autoregressive analysis. However, order an model cannot determined priori. We propose sparse multivariate method that incorporates mixed linear effects into regression analysis, uses forward-backward greedy search algorithm select non-zero entries coefficients, number is constrained not exceed pre-specified number. A small simulation provides preliminary evidence validity method. Besides example, additional example blood pressure variations from intervention used illustrate interpretation results obtained matrix These applications demonstrate how representation can for handling high dimensional variables feature dynamic, reciprocal relationships.