Reconstructing dynamical networks via feature ranking

Abstract

Empirical data on real complex systems are becoming increasingly available. Parallel to this is the need for new methods of reconstructing (inferring) the structure of networks from time-resolved observations of their node-dynamics. The methods based on physical insights often rely on strong assumptions about the properties and dynamics of the scrutinized network. Here, we use the insights from machine learning to design a new method of network reconstruction that essentially makes no such assumptions. Specifically, we interpret the available trajectories (data) as features, and use two independent feature ranking approaches -Random Forest and RReliefF -to rank the importance of each node for predicting the value of each other node, which yields the reconstructed adjacency matrix. We show that our method is fairly robust to coupling strength, system size, trajectory length and noise. We also find that the reconstruction quality strongly depends on the dynamical regime. arXiv:1902.03896v2 [math.DS] 26 Aug 2019This problem is in literature formulated in several ways. Typically, one considers the nodes to be individual dynamical systems, with their local dynamics governed by some difference or differential equation [56]. The interaction among these individual systems (nodes) is then articulated via a mathematical function that captures the nature of interactions between the pairs of connected nodes (either by directed or non-directed links). In this setting, the problem of network reconstruction reduces to estimating the presence/absence of links between the pairs of nodes from time-resolved measurements of their dynamics (time series), which are assumed available. It is within this formulation that we approach the topic in this paper, i.e., we consider the structure of the studied network to be hidden in a "black box", and seek to reconstruct it from time series of node dynamics (i.e., discrete trajectories).Within the realm of physics literature, many methods have been proposed relying on above formulation of the problem, and are usually anchored in empirical physical insights about network collective behavior [46,52,74]. This primarily includes synchronization [3], both theoretically [2,58] and experimentally [6,36], and in the presence of noise [72]. Other methods use techniques such as compressive sensing [80,82] or elaborate statistics of derivative-variable correlations [39,43]. Some methods are designed for specific domain problems, such as networks of neurons [55,59] or even social networks [76]. There are also approaches specifically intended for high-dimensional dynamical system, mostly realized as phase space reconstruction methods [33,41,45,53]. While many methods in general refer to non-directed networks, some aim specifically at discerning the direction of interactions (infer the 'causality network'). One such method is termed Partial Mutual Information from Mixed Embedding (PMIME [35]) and will be of use later in this work.However, a severe drawback of the existing physical reconstruction paradigms i...

Structure and dynamics of financial networks by feature ranking method

“…In this work we adopt feature ranking method introduced by Ref. 15 . We use regression model such as Random Forest 20 and XGBoost 23 .…”

“…In this article, we use a new approach known as feature ranking of machine learning which can take a multivariate view on the correlation [15][16][17] . This approach was completely different than the existing correlation and mutual information technique.…”

“…This approach was completely different than the existing correlation and mutual information technique. In recent past, this method has been used in logistic chaotic time series generated by using logistic map and to construct dynamic network 15 . Hence its real-world applicability was not checked.…”

“…There are different methods such as Random Forest 20 , ReliefF 21 , Decision Tree 22 , Gradient Boosting 23 , which calculate feature ranking implicitly. As features with low ranks usually have a very little or no influence on the target variable, it doesn't contribute to the accuracy of the machine learning model 15 . Rather they complicated the model yet causing a major degrading called over fitting.…”

“…Here we use the monitored discrete time series data to measure how much the target is influenced by each feature and compute the feature ranking accordingly. Some features have such strong impact on the target that we can safely assume that those features have some connection edges with the target node 15 . We use logarithmic return r t of the closing prices of stocks of the current day to predict the state or return r t+1 of the target stock in the next day.…”