Minimal realization of the dynamical structure function and its application to network reconstruction

TL;DR

This paper develops a method to find the simplest state-space model consistent with a given dynamical structure function, aiding network reconstruction by estimating the minimal number of hidden states.

Contribution

It characterizes minimal order realizations of dynamical structure functions and provides an algorithm to explicitly compute such minimal models.

Findings

Algorithm for minimal realization of dynamical structure functions

Enhanced understanding of hidden states in network models

Facilitates simpler and more accurate network reconstructions

Abstract

Network reconstruction, i.e., obtaining network structure from data, is a central theme in systems biology, economics and engineering. In some previous work, we introduced dynamical structure functions as a tool for posing and solving the problem of network reconstruction between measured states. While recovering the network structure between hidden states is not possible since they are not measured, in many situations it is important to estimate the minimal number of hidden states in order to understand the complexity of the network under investigation and help identify potential targets for measurements. Estimating the minimal number of hidden states is also crucial to obtain the simplest state-space model that captures the network structure and is coherent with the measured data. This paper characterizes minimal order state-space realizations that are consistent with a given dynamical structure function by exploring properties of dynamical structure functions and developing an algorithm to explicitly obtain such a minimal realization.