Graph Inference via the Energy-efficient Dynamic Precision Matrix Estimation with One-bit Data

Xiao Tan, Yangyang Shen, Meng Wang, Beilun Wang

Abstract: Graph knowledge discovery from graph-structured data is a fascinating data mining topic in various domains, especially in the Internet of Things, where inferring the graph structure from such informative data can benefit many downstream tasks. Deep neural networks are typically used to perform such predictions, but they produce unreliable results without sufficient high-quality data. Therefore, researchers introduce lightweight statistical precision matrix learning to infer the graph structure in many IoT scenarios with limited communication and resolution of sensors. However, these methods still suffer from low-resolution data or the omission of hidden information in time-series data. To address the challenges, we propose a novel approach for Energy-efficient Dynamic Sparse Graph Structure Estimation with one-bit data, EDGE. Our method proposes a novel estimator to estimate the covariance matrix from one-bit data, and then utilize the covariance matrices to capture the dynamic structure. We theoretically demonstrate the effectiveness of the estimators by deriving two non-asymptotic estimation error bounds for the estimated covariance matrix and precision matrix, respectively. The theoretical results show that our method can achieve a consistent result of the precision matrix at the rate O(log p/n). On multiple synthetic and real-world datasets, the experimental results demonstrate that our proposed estimator is able to obtain a relatively high detection rate using one-bit data, which exceeds the baseline by 35%, and identify potentially perturbed nodes in real-time dynamic network inference.