Network reconstruction is important to the understanding and control of
collective dynamics in complex systems. Most real networks exhibit sparsely
connected properties, and the connection parameter is a signal (0 or 1).
Well-known shrinkage methods such as lasso or compressed sensing (CS) to
recover structures of complex networks cannot suitably reveal such a property;
therefore, the signal lasso method was proposed recently to solve the network
reconstruction problem and was found to outperform lasso and CS methods.
However, signal lasso suffers the problem that the estimated coefficients that
fall between 0 and 1 cannot be successfully selected to the correct class. We
propose a new method, adaptive signal lasso, to estimate the signal parameter
and uncover the topology of complex networks with a small number of
observations. The proposed method has three advantages: (1) It can effectively
uncover the network topology with high accuracy and is capable of completely
shrinking the signal parameter to either 0 or 1, which eliminates the
unclassified portion in network reconstruction; (2) The method performs well in
scenarios of both sparse and dense signals and is robust to noise
contamination; (3) The method only needs to select one tuning parameter versus
two in signal lasso, which greatly reduces the computational cost and is easy
to apply. The theoretical properties of this method are studied, and numerical
simulations from linear regression, evolutionary games, and Kuramoto models are
explored. The method is illustrated with real-world examples from a human
behavioral experiment and a world trade web.Comment: 15 pages, 8 figures, 4 table