Predicting epidemic dynamics is of great value in understanding and controlling diffusion processes, such as infectious disease spread and information propagation. This task is intractable, especially when surveillance resources are very limited. To address the challenge, we study the problem of active surveillance, i.e., how to identify a small portion of system components as sentinels to effect monitoring, such that the epidemic dynamics of an entire system can be readily predicted from the partial data collected by such sentinels. We propose a novel measure, the gamma value, to identify the sentinels by modeling a sentinel network with row sparsity structure. We design a flexible group sparse Bayesian learning algorithm to mine the sentinel network suitable for handling both linear and non-linear dynamical systems by using the expectation maximization method and variational approximation. The efficacy of the proposed algorithm is theoretically analyzed and empirically validated using both synthetic and real-world data.
Mathematics has long been an important tool for understanding and controlling the spread of infectious diseases. Here, we begin with an overview of compartmental models, the traditional approach to modeling infectious disease dynamics, and then introduce contact network epidemiology, a relatively new approach that applies bond percolation on random graphs to model the spread of infectious disease through het- erogeneous populations. As we illustrate, these methods can be used to address public health challenges and have recently been coupled with powerful computational meth- ods to optimize epidemic control strategies. A fundamental issue in active learning of Gaussian processes is that of the exploration-exploitation trade-off. This paper presents a novel nonmyopic e-Bayes-optimal active learning (e-BAL) approach that jointly and naturally optimizes the trade-off. In contrast, existing works have primarily developed myopic greedy algorithms or performed exploration and exploitation separately. To perform active learning in real time, we then propose an anytime algorithm based on e-BAL with performance guarantee and empirically demonstrate using synthetic and real-world datasets that, with limited budget, it outperforms the state-of-the-art algorithms. When monitoring spatial phenomena, which can often be modeled as Gaussian processes (GPs), choosing sensor locations is a fundamental task. There are several common strategies to address this task, for example, geometry or disk models, placing sensors at the points of highest entropy (variance) in the GP model, and A-, D-, or E-optimal design. In this paper, we tackle the combinatorial optimization problem of maximizing the mutual information between the chosen locations and the locations which are not selected. We prove that the problem of finding the configuration that maximizes mutual information is NP-complete. To address this issue, we describe a polynomial-time approximation that is within (1-1 e) of the optimum by exploiting the submodularity of mutual information. We also show how submodularity can be used to obtain online bounds, and design branch and bound search procedures. We then extend our algorithm to exploit lazy evaluations and local structure in the GP, yielding significant speedups. We also extend our approach to find placements which are robust against node failures and uncertainties in the model. These extensions are again associated with rigorous theoretical approximation guarantees, exploiting the submodularity of the objective function. We demonstrate the advantages of our approach towards optimizing mutual information in a very extensive empirical study on two real-world data sets.