Signal Lasso with Non-Convex Penalties for Efficient Network Reconstruction and Topology Inference

Abstract

Inferring network structures remains an interesting question for its importance on the understanding and controlling collective dynamics of complex systems. The existing shrinking methods such as Lasso-type estimation can not suitably reveal such property. A new method recently suggested, called by {\it signal lasso} (or its updating version: adaptive signal lasso) was proposed to solve the network reconstruction problem, where the signal parameter can be shrunk to either 0 or 1 in two different directions. The signal lasso or adaptive signal lasso employed the additive penalty of signal and non-signal terms which is a convex function and easily to complementation in computation. However their methods need tuning the one or two parameters to find an optimal solution, which is time cost for large size network. In this paper we propose new signal lasso method based on two penalty functions to estimate the signal parameter and uncovering network topology in complex network with a small amount of observations. The penalty functions we introduced are non-convex function, thus coordinate descent algorithms are suggested. We find in this method the tuning parameter can be set to a large enough values such that the signal parameter can be completely shrunk either 0 or 1. The extensive simulations are conducted in linear regression models with different assumptions, the evolutionary-game-based dynamic model and Kuramoto model of synchronization problem. The advantage and disadvantage of each method are fully discussed in various conditions. Finally a real example comes from behavioral experiment is used for illustration. Our results show that signal lasso with non-convex penalties is effective and fast in estimating signal parameters in linear regression model.