Robust and efficient network reconstruction in complex system via adaptive signal lasso

Network reconstruction is a crucial task in understanding and controlling the collective dynamics of complex systems. Most real-world networks exhibit sparse properties, and the connection parameter is a binary signal (0 or 1). Traditional shrinkage methods, such as lasso or compressed sensing (CS), are not suitable for revealing this property. Recently, the signal lasso method was introduced to solve the network reconstruction problem, which was found to be more effective than lasso and CS methods. However, the signal lasso method has a limitation: it cannot accurately classify estimated coefficients that fall between 0 and 1. To address this issue, this paper proposes a method called adaptive signal lasso, which can accurately estimate the signal parameter and uncover the network topology in complex networks with a small number of observations. Our proposed method has at least three advantages: first, it is highly effective in uncovering the network topology and can completely shrink the signal parameter to either 0 or 1, eliminating the unclassified portion in network reconstruction; second, it performs well in both sparse and nonsparse signal scenarios and is robust to noise contamination; third, it only requires the selection of one tuning parameter, reducing computational cost and making it easy to apply. Theoretical properties of this method have been studied, and numerical simulations from linear regression, evolutionary game, and the Kuramoto model are deeply explored. Finally, two real-world examples from human behavioral experiments and the world trade web are used for illustration. It is expected that our proposed method will establish a reliable and uniform framework for estimating signal parameters in complex systems.