While significant efforts have been attempted in the design, control, and optimization of complex networks, most existing works assume the network structure is known or readily available. However, the network topology can be radically recast after an adversarial attack and may remain unknown for subsequent analysis. In this work, we propose a novel Bayesian sequential learning approach to reconstruct network connectivity adaptively: A sparse Spike and Slab prior is placed on connectivity for all edges, and the connectivity learned from reconstructed nodes will be used to select the next node and update the prior knowledge. Central to our approach is that most realistic networks are sparse, in that the connectivity degree of each node is much smaller compared to the number of nodes in the network. Sequential selection of the most informative nodes is realized via the between-node expected improvement. We corroborate this sequential Bayesian approach in connectivity recovery for a synthetic ultimatum game network and the IEEE-118 power grid system. Results indicate that only a fraction (∼50%) of the nodes need to be interrogated to reveal the network topology.

Comorbidities, dietary supplement use, and prescription drug use may negatively (or positively) affect mental health in cardiovascular patients. Although the significance of mental illnesses, such as depression, anxiety, and schizophrenia, on cardiovascular disease is well documented, mental illnesses resulting from heart disease are not well studied. In this paper, we introduce the risk factors of mental illnesses as an exploratory study and develop a prediction framework for mental illness that uses comorbidities, dietary supplements, and drug usage in heart disease patients. Particularly, the data used in this study consist of the records of 68,647 patients with heart disease, including the patient’s mental illness information and the patient’s intake of dietary supplements, antibiotics, and comorbidities. Patients in age groups $<61$, gender differences, and drug intakes, such as Azithromycin, Clarithromycin, Vitamin B6, and Coenzyme Q10, were associated with mental illness. For predictive modeling, we consider applying various state-of-the-art machine learning techniques with tuned parameters and finally obtain the following: Depression: 78.01% accuracy, 79.13% sensitivity, 72.65% specificity, and 86.26% Area Under the Curve (AUC). Anxiety: 82.93% accuracy, 82.86% sensitivity, 83.35% specificity, and 88.45% AUC. Schizophrenia: 87.59% accuracy, 87.70% sensitivity, 85.14% specificity, and 92.73% AUC. Disease: 86.63% accuracy, 95.50% sensitivity, 77.76% specificity, and 91.59% AUC. From the results, we conclude that using heart disease information, comorbidities, dietary supplement use, and antibiotics enables us to accurately predict the mental health outcome.

While significant efforts have been attempted in the design, control, and optimization of complex networks, most existing works assume the network structure is known or readily available. However, the network topology can be radically recast after an adversarial attack and may remain unknown for subsequent analysis. In this work, we propose a novel Bayesian sequential learning approach to reconstruct network connectivity adaptively: A sparse Spike and Slab prior is placed on connectivity for all edges, and the connectivity learned from reconstructed nodes will be used to select the next node and update the prior knowledge. Central to our approach is that most realistic networks are sparse, in that the connectivity degree of each node is much smaller compared to the number of nodes in the network. Sequential selection of the most informative nodes is realized via the between-node expected improvement. We corroborate this sequential Bayesian approach in connectivity recovery for the IEEE-118 power grid system. Results indicate that only a fraction (~50%) of the nodes need to be interrogated to reveal the network topology.